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Preserve the algorithm and functionality while converting the code from Go to Rust.
package main import ( "fmt" "math/big" ) var ( zero = big.NewInt(0) one = big.NewInt(1) prev = big.NewInt(factorial(20)) ) func factorial(n int64) int64 { res := int64(1) for k := n; k > 1; k-- { res *= k } return res } func wilson(n int64, memo bool) bool { if n <= 1 || (n%2 == 0 && n != 2) { return false } if n <= 21 { return (factorial(n-1)+1)%n == 0 } b := big.NewInt(n) r := big.NewInt(0) z := big.NewInt(0) if !memo { z.MulRange(2, n-1) } else { prev.Mul(prev, r.MulRange(n-2, n-1)) z.Set(prev) } z.Add(z, one) return r.Rem(z, b).Cmp(zero) == 0 } func main() { numbers := []int64{2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659} fmt.Println(" n prime") fmt.Println("--- -----") for _, n := range numbers { fmt.Printf("%3d %t\n", n, wilson(n, false)) } fmt.Println("\nThe first 120 prime numbers are:") for i, count := int64(2), 0; count < 1015; i += 2 { if wilson(i, true) { count++ if count <= 120 { fmt.Printf("%3d ", i) if count%20 == 0 { fmt.Println() } } else if count >= 1000 { if count == 1000 { fmt.Println("\nThe 1,000th to 1,015th prime numbers are:") } fmt.Printf("%4d ", i) } } if i == 2 { i-- } } fmt.Println() }
fn factorial_mod(mut n: u32, p: u32) -> u32 { let mut f = 1; while n != 0 && f != 0 { f = (f * n) % p; n -= 1; } f } fn is_prime(p: u32) -> bool { p > 1 && factorial_mod(p - 1, p) == p - 1 } fn main() { println!(" n | prime?\n------------"); for p in vec![2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659] { println!("{:>3} | {}", p, is_prime(p)); } println!("\nFirst 120 primes by Wilson's theorem:"); let mut n = 0; let mut p = 1; while n < 120 { if is_prime(p) { n += 1; print!("{:>3}{}", p, if n % 20 == 0 { '\n' } else { ' ' }); } p += 1; } println!("\n1000th through 1015th primes:"); let mut i = 0; while n < 1015 { if is_prime(p) { n += 1; if n >= 1000 { i += 1; print!("{:>3}{}", p, if i % 16 == 0 { '\n' } else { ' ' }); } } p += 1; } }
Change the following Rust code into Python without altering its purpose.
fn factorial_mod(mut n: u32, p: u32) -> u32 { let mut f = 1; while n != 0 && f != 0 { f = (f * n) % p; n -= 1; } f } fn is_prime(p: u32) -> bool { p > 1 && factorial_mod(p - 1, p) == p - 1 } fn main() { println!(" n | prime?\n------------"); for p in vec![2, 3, 9, 15, 29, 37, 47, 57, 67, 77, 87, 97, 237, 409, 659] { println!("{:>3} | {}", p, is_prime(p)); } println!("\nFirst 120 primes by Wilson's theorem:"); let mut n = 0; let mut p = 1; while n < 120 { if is_prime(p) { n += 1; print!("{:>3}{}", p, if n % 20 == 0 { '\n' } else { ' ' }); } p += 1; } println!("\n1000th through 1015th primes:"); let mut i = 0; while n < 1015 { if is_prime(p) { n += 1; if n >= 1000 { i += 1; print!("{:>3}{}", p, if i % 16 == 0 { '\n' } else { ' ' }); } } p += 1; } }
from math import factorial def is_wprime(n): return n == 2 or ( n > 1 and n % 2 != 0 and (factorial(n - 1) + 1) % n == 0 ) if __name__ == '__main__': c = int(input('Enter upper limit: ')) print(f'Primes under {c}:') print([n for n in range(c) if is_wprime(n)])
Ensure the translated C# code behaves exactly like the original Ada snippet.
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO; with Ada.Text_IO; use Ada.Text_IO; procedure Fraction_Reduction is type Int_Array is array (Natural range <>) of Integer; function indexOf(haystack : Int_Array; needle : Integer) return Integer is idx : Integer := 0; begin for straw of haystack loop if straw = needle then return idx; else idx := idx + 1; end if; end loop; return -1; end IndexOf; function getDigits(n, le : in Integer; digit_array : in out Int_Array) return Boolean is n_local : Integer := n; le_local : Integer := le; r : Integer; begin while n_local > 0 loop r := n_local mod 10; if r = 0 or indexOf(digit_array, r) >= 0 then return False; end if; le_local := le_local - 1; digit_array(le_local) := r; n_local := n_local / 10; end loop; return True; end getDigits; function removeDigit(digit_array : Int_Array; le, idx : Integer) return Integer is sum : Integer := 0; pow : Integer := 10 ** (le - 2); begin for i in 0 .. le - 1 loop if i /= idx then sum := sum + digit_array(i) * pow; pow := pow / 10; end if; end loop; return sum; end removeDigit; lims : constant array (0 .. 3) of Int_Array (0 .. 1) := ((12, 97), (123, 986), (1234, 9875), (12345, 98764)); count : Int_Array (0 .. 4) := (others => 0); omitted : array (0 .. 4) of Int_Array (0 .. 9) := (others => (others => 0)); begin Ada.Integer_Text_IO.Default_Width := 0; for i in lims'Range loop declare nDigits, dDigits : Int_Array (0 .. i + 1); digit, dix, rn, rd : Integer; begin for n in lims(i)(0) .. lims(i)(1) loop nDigits := (others => 0); if getDigits(n, i + 2, nDigits) then for d in n + 1 .. lims(i)(1) + 1 loop dDigits := (others => 0); if getDigits(d, i + 2, dDigits) then for nix in nDigits'Range loop digit := nDigits(nix); dix := indexOf(dDigits, digit); if dix >= 0 then rn := removeDigit(nDigits, i + 2, nix); rd := removeDigit(dDigits, i + 2, dix); if n*rd = rn*d then count(i) := count(i) + 1; omitted(i)(digit) := omitted(i)(digit) + 1; if count(i) <= 12 then Put (n); Put ("/"); Put (d); Put (" = "); Put (rn); Put ("/"); Put (rd); Put (" by omitting "); Put (digit); Put_Line ("'s"); end if; end if; end if; end loop; end if; end loop; end if; end loop; end; New_Line; end loop; for i in 2 .. 5 loop Put ("There are "); Put (count(i - 2)); Put (" "); Put (i); Put_Line ("-digit fractions of which:"); for j in 1 .. 9 loop if omitted(i - 2)(j) /= 0 then Put (omitted(i - 2)(j), Width => 6); Put (" have "); Put (j); Put_Line ("'s omitted"); end if; end loop; New_Line; end loop; end Fraction_Reduction;
using System; namespace FractionReduction { class Program { static int IndexOf(int n, int[] s) { for (int i = 0; i < s.Length; i++) { if (s[i] == n) { return i; } } return -1; } static bool GetDigits(int n, int le, int[] digits) { while (n > 0) { var r = n % 10; if (r == 0 || IndexOf(r, digits) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } static int RemoveDigit(int[] digits, int le, int idx) { int[] pows = { 1, 10, 100, 1000, 10000 }; var sum = 0; var pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } static void Main() { var lims = new int[,] { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; var count = new int[5]; var omitted = new int[5, 10]; var upperBound = lims.GetLength(0); for (int i = 0; i < upperBound; i++) { var nDigits = new int[i + 2]; var dDigits = new int[i + 2]; var blank = new int[i + 2]; for (int n = lims[i, 0]; n <= lims[i, 1]; n++) { blank.CopyTo(nDigits, 0); var nOk = GetDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i, 1] + 1; d++) { blank.CopyTo(dDigits, 0); var dOk = GetDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.Length; nix++) { var digit = nDigits[nix]; var dix = IndexOf(digit, dDigits); if (dix >= 0) { var rn = RemoveDigit(nDigits, i + 2, nix); var rd = RemoveDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i, digit]++; if (count[i] <= 12) { Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4}'s", n, d, rn, rd, digit); } } } } } } Console.WriteLine(); } for (int i = 2; i <= 5; i++) { Console.WriteLine("There are {0} {1}-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2, j] == 0) { continue; } Console.WriteLine("{0,6} have {1}'s omitted", omitted[i - 2, j], j); } Console.WriteLine(); } } } }
Convert the following code from Ada to C, ensuring the logic remains intact.
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO; with Ada.Text_IO; use Ada.Text_IO; procedure Fraction_Reduction is type Int_Array is array (Natural range <>) of Integer; function indexOf(haystack : Int_Array; needle : Integer) return Integer is idx : Integer := 0; begin for straw of haystack loop if straw = needle then return idx; else idx := idx + 1; end if; end loop; return -1; end IndexOf; function getDigits(n, le : in Integer; digit_array : in out Int_Array) return Boolean is n_local : Integer := n; le_local : Integer := le; r : Integer; begin while n_local > 0 loop r := n_local mod 10; if r = 0 or indexOf(digit_array, r) >= 0 then return False; end if; le_local := le_local - 1; digit_array(le_local) := r; n_local := n_local / 10; end loop; return True; end getDigits; function removeDigit(digit_array : Int_Array; le, idx : Integer) return Integer is sum : Integer := 0; pow : Integer := 10 ** (le - 2); begin for i in 0 .. le - 1 loop if i /= idx then sum := sum + digit_array(i) * pow; pow := pow / 10; end if; end loop; return sum; end removeDigit; lims : constant array (0 .. 3) of Int_Array (0 .. 1) := ((12, 97), (123, 986), (1234, 9875), (12345, 98764)); count : Int_Array (0 .. 4) := (others => 0); omitted : array (0 .. 4) of Int_Array (0 .. 9) := (others => (others => 0)); begin Ada.Integer_Text_IO.Default_Width := 0; for i in lims'Range loop declare nDigits, dDigits : Int_Array (0 .. i + 1); digit, dix, rn, rd : Integer; begin for n in lims(i)(0) .. lims(i)(1) loop nDigits := (others => 0); if getDigits(n, i + 2, nDigits) then for d in n + 1 .. lims(i)(1) + 1 loop dDigits := (others => 0); if getDigits(d, i + 2, dDigits) then for nix in nDigits'Range loop digit := nDigits(nix); dix := indexOf(dDigits, digit); if dix >= 0 then rn := removeDigit(nDigits, i + 2, nix); rd := removeDigit(dDigits, i + 2, dix); if n*rd = rn*d then count(i) := count(i) + 1; omitted(i)(digit) := omitted(i)(digit) + 1; if count(i) <= 12 then Put (n); Put ("/"); Put (d); Put (" = "); Put (rn); Put ("/"); Put (rd); Put (" by omitting "); Put (digit); Put_Line ("'s"); end if; end if; end if; end loop; end if; end loop; end if; end loop; end; New_Line; end loop; for i in 2 .. 5 loop Put ("There are "); Put (count(i - 2)); Put (" "); Put (i); Put_Line ("-digit fractions of which:"); for j in 1 .. 9 loop if omitted(i - 2)(j) /= 0 then Put (omitted(i - 2)(j), Width => 6); Put (" have "); Put (j); Put_Line ("'s omitted"); end if; end loop; New_Line; end loop; end Fraction_Reduction;
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }
Please provide an equivalent version of this Ada code in C++.
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO; with Ada.Text_IO; use Ada.Text_IO; procedure Fraction_Reduction is type Int_Array is array (Natural range <>) of Integer; function indexOf(haystack : Int_Array; needle : Integer) return Integer is idx : Integer := 0; begin for straw of haystack loop if straw = needle then return idx; else idx := idx + 1; end if; end loop; return -1; end IndexOf; function getDigits(n, le : in Integer; digit_array : in out Int_Array) return Boolean is n_local : Integer := n; le_local : Integer := le; r : Integer; begin while n_local > 0 loop r := n_local mod 10; if r = 0 or indexOf(digit_array, r) >= 0 then return False; end if; le_local := le_local - 1; digit_array(le_local) := r; n_local := n_local / 10; end loop; return True; end getDigits; function removeDigit(digit_array : Int_Array; le, idx : Integer) return Integer is sum : Integer := 0; pow : Integer := 10 ** (le - 2); begin for i in 0 .. le - 1 loop if i /= idx then sum := sum + digit_array(i) * pow; pow := pow / 10; end if; end loop; return sum; end removeDigit; lims : constant array (0 .. 3) of Int_Array (0 .. 1) := ((12, 97), (123, 986), (1234, 9875), (12345, 98764)); count : Int_Array (0 .. 4) := (others => 0); omitted : array (0 .. 4) of Int_Array (0 .. 9) := (others => (others => 0)); begin Ada.Integer_Text_IO.Default_Width := 0; for i in lims'Range loop declare nDigits, dDigits : Int_Array (0 .. i + 1); digit, dix, rn, rd : Integer; begin for n in lims(i)(0) .. lims(i)(1) loop nDigits := (others => 0); if getDigits(n, i + 2, nDigits) then for d in n + 1 .. lims(i)(1) + 1 loop dDigits := (others => 0); if getDigits(d, i + 2, dDigits) then for nix in nDigits'Range loop digit := nDigits(nix); dix := indexOf(dDigits, digit); if dix >= 0 then rn := removeDigit(nDigits, i + 2, nix); rd := removeDigit(dDigits, i + 2, dix); if n*rd = rn*d then count(i) := count(i) + 1; omitted(i)(digit) := omitted(i)(digit) + 1; if count(i) <= 12 then Put (n); Put ("/"); Put (d); Put (" = "); Put (rn); Put ("/"); Put (rd); Put (" by omitting "); Put (digit); Put_Line ("'s"); end if; end if; end if; end loop; end if; end loop; end if; end loop; end; New_Line; end loop; for i in 2 .. 5 loop Put ("There are "); Put (count(i - 2)); Put (" "); Put (i); Put_Line ("-digit fractions of which:"); for j in 1 .. 9 loop if omitted(i - 2)(j) /= 0 then Put (omitted(i - 2)(j), Width => 6); Put (" have "); Put (j); Put_Line ("'s omitted"); end if; end loop; New_Line; end loop; end Fraction_Reduction;
#include <array> #include <iomanip> #include <iostream> #include <vector> int indexOf(const std::vector<int> &haystack, int needle) { auto it = haystack.cbegin(); auto end = haystack.cend(); int idx = 0; for (; it != end; it = std::next(it)) { if (*it == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, std::vector<int> &digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(const std::vector<int> &digits, int le, int idx) { static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 }; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } int main() { std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }; std::array<int, 5> count; std::array<std::array<int, 10>, 5> omitted; std::fill(count.begin(), count.end(), 0); std::for_each(omitted.begin(), omitted.end(), [](auto &a) { std::fill(a.begin(), a.end(), 0); } ); for (size_t i = 0; i < lims.size(); i++) { std::vector<int> nDigits(i + 2); std::vector<int> dDigits(i + 2); for (int n = lims[i].first; n <= lims[i].second; n++) { std::fill(nDigits.begin(), nDigits.end(), 0); bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i].second + 1; d++) { std::fill(dDigits.begin(), dDigits.end(), 0); bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (size_t nix = 0; nix < nDigits.size(); nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n"; } } } } } } std::cout << '\n'; } for (int i = 2; i <= 5; i++) { std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n"; for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n"; } std::cout << '\n'; } return 0; }
Write a version of this Ada function in Go with identical behavior.
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO; with Ada.Text_IO; use Ada.Text_IO; procedure Fraction_Reduction is type Int_Array is array (Natural range <>) of Integer; function indexOf(haystack : Int_Array; needle : Integer) return Integer is idx : Integer := 0; begin for straw of haystack loop if straw = needle then return idx; else idx := idx + 1; end if; end loop; return -1; end IndexOf; function getDigits(n, le : in Integer; digit_array : in out Int_Array) return Boolean is n_local : Integer := n; le_local : Integer := le; r : Integer; begin while n_local > 0 loop r := n_local mod 10; if r = 0 or indexOf(digit_array, r) >= 0 then return False; end if; le_local := le_local - 1; digit_array(le_local) := r; n_local := n_local / 10; end loop; return True; end getDigits; function removeDigit(digit_array : Int_Array; le, idx : Integer) return Integer is sum : Integer := 0; pow : Integer := 10 ** (le - 2); begin for i in 0 .. le - 1 loop if i /= idx then sum := sum + digit_array(i) * pow; pow := pow / 10; end if; end loop; return sum; end removeDigit; lims : constant array (0 .. 3) of Int_Array (0 .. 1) := ((12, 97), (123, 986), (1234, 9875), (12345, 98764)); count : Int_Array (0 .. 4) := (others => 0); omitted : array (0 .. 4) of Int_Array (0 .. 9) := (others => (others => 0)); begin Ada.Integer_Text_IO.Default_Width := 0; for i in lims'Range loop declare nDigits, dDigits : Int_Array (0 .. i + 1); digit, dix, rn, rd : Integer; begin for n in lims(i)(0) .. lims(i)(1) loop nDigits := (others => 0); if getDigits(n, i + 2, nDigits) then for d in n + 1 .. lims(i)(1) + 1 loop dDigits := (others => 0); if getDigits(d, i + 2, dDigits) then for nix in nDigits'Range loop digit := nDigits(nix); dix := indexOf(dDigits, digit); if dix >= 0 then rn := removeDigit(nDigits, i + 2, nix); rd := removeDigit(dDigits, i + 2, dix); if n*rd = rn*d then count(i) := count(i) + 1; omitted(i)(digit) := omitted(i)(digit) + 1; if count(i) <= 12 then Put (n); Put ("/"); Put (d); Put (" = "); Put (rn); Put ("/"); Put (rd); Put (" by omitting "); Put (digit); Put_Line ("'s"); end if; end if; end if; end loop; end if; end loop; end if; end loop; end; New_Line; end loop; for i in 2 .. 5 loop Put ("There are "); Put (count(i - 2)); Put (" "); Put (i); Put_Line ("-digit fractions of which:"); for j in 1 .. 9 loop if omitted(i - 2)(j) /= 0 then Put (omitted(i - 2)(j), Width => 6); Put (" have "); Put (j); Put_Line ("'s omitted"); end if; end loop; New_Line; end loop; end Fraction_Reduction;
package main import ( "fmt" "time" ) func indexOf(n int, s []int) int { for i, j := range s { if n == j { return i } } return -1 } func getDigits(n, le int, digits []int) bool { for n > 0 { r := n % 10 if r == 0 || indexOf(r, digits) >= 0 { return false } le-- digits[le] = r n /= 10 } return true } var pows = [5]int{1, 10, 100, 1000, 10000} func removeDigit(digits []int, le, idx int) int { sum := 0 pow := pows[le-2] for i := 0; i < le; i++ { if i == idx { continue } sum += digits[i] * pow pow /= 10 } return sum } func main() { start := time.Now() lims := [5][2]int{ {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}, {123456, 987653}, } var count [5]int var omitted [5][10]int for i, lim := range lims { nDigits := make([]int, i+2) dDigits := make([]int, i+2) blank := make([]int, i+2) for n := lim[0]; n <= lim[1]; n++ { copy(nDigits, blank) nOk := getDigits(n, i+2, nDigits) if !nOk { continue } for d := n + 1; d <= lim[1]+1; d++ { copy(dDigits, blank) dOk := getDigits(d, i+2, dDigits) if !dOk { continue } for nix, digit := range nDigits { if dix := indexOf(digit, dDigits); dix >= 0 { rn := removeDigit(nDigits, i+2, nix) rd := removeDigit(dDigits, i+2, dix) if float64(n)/float64(d) == float64(rn)/float64(rd) { count[i]++ omitted[i][digit]++ if count[i] <= 12 { fmt.Printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit) } } } } } } fmt.Println() } for i := 2; i <= 6; i++ { fmt.Printf("There are %d %d-digit fractions of which:\n", count[i-2], i) for j := 1; j <= 9; j++ { if omitted[i-2][j] == 0 { continue } fmt.Printf("%6d have %d's omitted\n", omitted[i-2][j], j) } fmt.Println() } fmt.Printf("Took %s\n", time.Since(start)) }
Port the provided Ada code into Java while preserving the original functionality.
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO; with Ada.Text_IO; use Ada.Text_IO; procedure Fraction_Reduction is type Int_Array is array (Natural range <>) of Integer; function indexOf(haystack : Int_Array; needle : Integer) return Integer is idx : Integer := 0; begin for straw of haystack loop if straw = needle then return idx; else idx := idx + 1; end if; end loop; return -1; end IndexOf; function getDigits(n, le : in Integer; digit_array : in out Int_Array) return Boolean is n_local : Integer := n; le_local : Integer := le; r : Integer; begin while n_local > 0 loop r := n_local mod 10; if r = 0 or indexOf(digit_array, r) >= 0 then return False; end if; le_local := le_local - 1; digit_array(le_local) := r; n_local := n_local / 10; end loop; return True; end getDigits; function removeDigit(digit_array : Int_Array; le, idx : Integer) return Integer is sum : Integer := 0; pow : Integer := 10 ** (le - 2); begin for i in 0 .. le - 1 loop if i /= idx then sum := sum + digit_array(i) * pow; pow := pow / 10; end if; end loop; return sum; end removeDigit; lims : constant array (0 .. 3) of Int_Array (0 .. 1) := ((12, 97), (123, 986), (1234, 9875), (12345, 98764)); count : Int_Array (0 .. 4) := (others => 0); omitted : array (0 .. 4) of Int_Array (0 .. 9) := (others => (others => 0)); begin Ada.Integer_Text_IO.Default_Width := 0; for i in lims'Range loop declare nDigits, dDigits : Int_Array (0 .. i + 1); digit, dix, rn, rd : Integer; begin for n in lims(i)(0) .. lims(i)(1) loop nDigits := (others => 0); if getDigits(n, i + 2, nDigits) then for d in n + 1 .. lims(i)(1) + 1 loop dDigits := (others => 0); if getDigits(d, i + 2, dDigits) then for nix in nDigits'Range loop digit := nDigits(nix); dix := indexOf(dDigits, digit); if dix >= 0 then rn := removeDigit(nDigits, i + 2, nix); rd := removeDigit(dDigits, i + 2, dix); if n*rd = rn*d then count(i) := count(i) + 1; omitted(i)(digit) := omitted(i)(digit) + 1; if count(i) <= 12 then Put (n); Put ("/"); Put (d); Put (" = "); Put (rn); Put ("/"); Put (rd); Put (" by omitting "); Put (digit); Put_Line ("'s"); end if; end if; end if; end loop; end if; end loop; end if; end loop; end; New_Line; end loop; for i in 2 .. 5 loop Put ("There are "); Put (count(i - 2)); Put (" "); Put (i); Put_Line ("-digit fractions of which:"); for j in 1 .. 9 loop if omitted(i - 2)(j) /= 0 then Put (omitted(i - 2)(j), Width => 6); Put (" have "); Put (j); Put_Line ("'s omitted"); end if; end loop; New_Line; end loop; end Fraction_Reduction;
import java.util.ArrayList; import java.util.Collections; import java.util.HashMap; import java.util.List; import java.util.Map; public class FractionReduction { public static void main(String[] args) { for ( int size = 2 ; size <= 5 ; size++ ) { reduce(size); } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits); int min = (int) Math.pow(10, numDigits-1); int max = (int) Math.pow(10, numDigits) - 1; List<Integer> values = new ArrayList<>(); for ( int number = min ; number <= max ; number++ ) { if ( isValid(number) ) { values.add(number); } } Map<Integer,Integer> cancelCount = new HashMap<>(); int size = values.size(); int solutions = 0; for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) { int numerator = values.get(nIndex); for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) { int denominator = values.get(dIndex); for ( int commonDigit : digitsInCommon(numerator, denominator) ) { int numRemoved = removeDigit(numerator, commonDigit); int denRemoved = removeDigit(denominator, commonDigit); if ( numerator * denRemoved == denominator * numRemoved ) { solutions++; cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2); if ( solutions <= 12 ) { System.out.printf(" When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved); } } } } } System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions); List<Integer> sorted = new ArrayList<>(cancelCount.keySet()); Collections.sort(sorted); for ( int removed : sorted ) { System.out.printf(" The digit %d was removed %d times.%n", removed, cancelCount.get(removed)); } System.out.println(); } private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000}; private static int removeDigit(int n, int removed) { int m = 0; int pow = 0; while ( n > 0 ) { int r = n % 10; if ( r != removed ) { m = m + r*powers[pow]; pow++; } n /= 10; } return m; } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10]; List<Integer> common = new ArrayList<>(); while ( n1 > 0 ) { int r = n1 % 10; count[r] += 1; n1 /= 10; } while ( n2 > 0 ) { int r = n2 % 10; if ( count[r] > 0 ) { common.add(r); } n2 /= 10; } return common; } private static boolean isValid(int num) { int[] count = new int[10]; while ( num > 0 ) { int r = num % 10; if ( r == 0 || count[r] == 1 ) { return false; } count[r] = 1; num /= 10; } return true; } }
Keep all operations the same but rewrite the snippet in Python.
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO; with Ada.Text_IO; use Ada.Text_IO; procedure Fraction_Reduction is type Int_Array is array (Natural range <>) of Integer; function indexOf(haystack : Int_Array; needle : Integer) return Integer is idx : Integer := 0; begin for straw of haystack loop if straw = needle then return idx; else idx := idx + 1; end if; end loop; return -1; end IndexOf; function getDigits(n, le : in Integer; digit_array : in out Int_Array) return Boolean is n_local : Integer := n; le_local : Integer := le; r : Integer; begin while n_local > 0 loop r := n_local mod 10; if r = 0 or indexOf(digit_array, r) >= 0 then return False; end if; le_local := le_local - 1; digit_array(le_local) := r; n_local := n_local / 10; end loop; return True; end getDigits; function removeDigit(digit_array : Int_Array; le, idx : Integer) return Integer is sum : Integer := 0; pow : Integer := 10 ** (le - 2); begin for i in 0 .. le - 1 loop if i /= idx then sum := sum + digit_array(i) * pow; pow := pow / 10; end if; end loop; return sum; end removeDigit; lims : constant array (0 .. 3) of Int_Array (0 .. 1) := ((12, 97), (123, 986), (1234, 9875), (12345, 98764)); count : Int_Array (0 .. 4) := (others => 0); omitted : array (0 .. 4) of Int_Array (0 .. 9) := (others => (others => 0)); begin Ada.Integer_Text_IO.Default_Width := 0; for i in lims'Range loop declare nDigits, dDigits : Int_Array (0 .. i + 1); digit, dix, rn, rd : Integer; begin for n in lims(i)(0) .. lims(i)(1) loop nDigits := (others => 0); if getDigits(n, i + 2, nDigits) then for d in n + 1 .. lims(i)(1) + 1 loop dDigits := (others => 0); if getDigits(d, i + 2, dDigits) then for nix in nDigits'Range loop digit := nDigits(nix); dix := indexOf(dDigits, digit); if dix >= 0 then rn := removeDigit(nDigits, i + 2, nix); rd := removeDigit(dDigits, i + 2, dix); if n*rd = rn*d then count(i) := count(i) + 1; omitted(i)(digit) := omitted(i)(digit) + 1; if count(i) <= 12 then Put (n); Put ("/"); Put (d); Put (" = "); Put (rn); Put ("/"); Put (rd); Put (" by omitting "); Put (digit); Put_Line ("'s"); end if; end if; end if; end loop; end if; end loop; end if; end loop; end; New_Line; end loop; for i in 2 .. 5 loop Put ("There are "); Put (count(i - 2)); Put (" "); Put (i); Put_Line ("-digit fractions of which:"); for j in 1 .. 9 loop if omitted(i - 2)(j) /= 0 then Put (omitted(i - 2)(j), Width => 6); Put (" have "); Put (j); Put_Line ("'s omitted"); end if; end loop; New_Line; end loop; end Fraction_Reduction;
def indexOf(haystack, needle): idx = 0 for straw in haystack: if straw == needle: return idx else: idx += 1 return -1 def getDigits(n, le, digits): while n > 0: r = n % 10 if r == 0 or indexOf(digits, r) >= 0: return False le -= 1 digits[le] = r n = int(n / 10) return True def removeDigit(digits, le, idx): pows = [1, 10, 100, 1000, 10000] sum = 0 pow = pows[le - 2] i = 0 while i < le: if i == idx: i += 1 continue sum = sum + digits[i] * pow pow = int(pow / 10) i += 1 return sum def main(): lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = [0 for i in range(5)] omitted = [[0 for i in range(10)] for j in range(5)] i = 0 while i < len(lims): n = lims[i][0] while n < lims[i][1]: nDigits = [0 for k in range(i + 2)] nOk = getDigits(n, i + 2, nDigits) if not nOk: n += 1 continue d = n + 1 while d <= lims[i][1] + 1: dDigits = [0 for k in range(i + 2)] dOk = getDigits(d, i + 2, dDigits) if not dOk: d += 1 continue nix = 0 while nix < len(nDigits): digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0: rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd): count[i] += 1 omitted[i][digit] += 1 if count[i] <= 12: print "%d/%d = %d/%d by omitting %d's" % (n, d, rn, rd, digit) nix += 1 d += 1 n += 1 print i += 1 i = 2 while i <= 5: print "There are %d %d-digit fractions of which:" % (count[i - 2], i) j = 1 while j <= 9: if omitted[i - 2][j] == 0: j += 1 continue print "%6s have %d's omitted" % (omitted[i - 2][j], j) j += 1 print i += 1 return None main()
Translate this program into VB but keep the logic exactly as in Ada.
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO; with Ada.Text_IO; use Ada.Text_IO; procedure Fraction_Reduction is type Int_Array is array (Natural range <>) of Integer; function indexOf(haystack : Int_Array; needle : Integer) return Integer is idx : Integer := 0; begin for straw of haystack loop if straw = needle then return idx; else idx := idx + 1; end if; end loop; return -1; end IndexOf; function getDigits(n, le : in Integer; digit_array : in out Int_Array) return Boolean is n_local : Integer := n; le_local : Integer := le; r : Integer; begin while n_local > 0 loop r := n_local mod 10; if r = 0 or indexOf(digit_array, r) >= 0 then return False; end if; le_local := le_local - 1; digit_array(le_local) := r; n_local := n_local / 10; end loop; return True; end getDigits; function removeDigit(digit_array : Int_Array; le, idx : Integer) return Integer is sum : Integer := 0; pow : Integer := 10 ** (le - 2); begin for i in 0 .. le - 1 loop if i /= idx then sum := sum + digit_array(i) * pow; pow := pow / 10; end if; end loop; return sum; end removeDigit; lims : constant array (0 .. 3) of Int_Array (0 .. 1) := ((12, 97), (123, 986), (1234, 9875), (12345, 98764)); count : Int_Array (0 .. 4) := (others => 0); omitted : array (0 .. 4) of Int_Array (0 .. 9) := (others => (others => 0)); begin Ada.Integer_Text_IO.Default_Width := 0; for i in lims'Range loop declare nDigits, dDigits : Int_Array (0 .. i + 1); digit, dix, rn, rd : Integer; begin for n in lims(i)(0) .. lims(i)(1) loop nDigits := (others => 0); if getDigits(n, i + 2, nDigits) then for d in n + 1 .. lims(i)(1) + 1 loop dDigits := (others => 0); if getDigits(d, i + 2, dDigits) then for nix in nDigits'Range loop digit := nDigits(nix); dix := indexOf(dDigits, digit); if dix >= 0 then rn := removeDigit(nDigits, i + 2, nix); rd := removeDigit(dDigits, i + 2, dix); if n*rd = rn*d then count(i) := count(i) + 1; omitted(i)(digit) := omitted(i)(digit) + 1; if count(i) <= 12 then Put (n); Put ("/"); Put (d); Put (" = "); Put (rn); Put ("/"); Put (rd); Put (" by omitting "); Put (digit); Put_Line ("'s"); end if; end if; end if; end loop; end if; end loop; end if; end loop; end; New_Line; end loop; for i in 2 .. 5 loop Put ("There are "); Put (count(i - 2)); Put (" "); Put (i); Put_Line ("-digit fractions of which:"); for j in 1 .. 9 loop if omitted(i - 2)(j) /= 0 then Put (omitted(i - 2)(j), Width => 6); Put (" have "); Put (j); Put_Line ("'s omitted"); end if; end loop; New_Line; end loop; end Fraction_Reduction;
Module Module1 Function IndexOf(n As Integer, s As Integer()) As Integer For ii = 1 To s.Length Dim i = ii - 1 If s(i) = n Then Return i End If Next Return -1 End Function Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean While n > 0 Dim r = n Mod 10 If r = 0 OrElse IndexOf(r, digits) >= 0 Then Return False End If le -= 1 digits(le) = r n \= 10 End While Return True End Function Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer Dim pows = {1, 10, 100, 1000, 10000} Dim sum = 0 Dim pow = pows(le - 2) For ii = 1 To le Dim i = ii - 1 If i = idx Then Continue For End If sum += digits(i) * pow pow \= 10 Next Return sum End Function Sub Main() Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}} Dim count(5) As Integer Dim omitted(5, 10) As Integer Dim upperBound = lims.GetLength(0) For ii = 1 To upperBound Dim i = ii - 1 Dim nDigits(i + 2 - 1) As Integer Dim dDigits(i + 2 - 1) As Integer Dim blank(i + 2 - 1) As Integer For n = lims(i, 0) To lims(i, 1) blank.CopyTo(nDigits, 0) Dim nOk = GetDigits(n, i + 2, nDigits) If Not nOk Then Continue For End If For d = n + 1 To lims(i, 1) + 1 blank.CopyTo(dDigits, 0) Dim dOk = GetDigits(d, i + 2, dDigits) If Not dOk Then Continue For End If For nixt = 1 To nDigits.Length Dim nix = nixt - 1 Dim digit = nDigits(nix) Dim dix = IndexOf(digit, dDigits) If dix >= 0 Then Dim rn = RemoveDigit(nDigits, i + 2, nix) Dim rd = RemoveDigit(dDigits, i + 2, dix) If (n / d) = (rn / rd) Then count(i) += 1 omitted(i, digit) += 1 If count(i) <= 12 Then Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4} End If End If End If Next Next Next Console.WriteLine() Next For i = 2 To 5 Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i) For j = 1 To 9 If omitted(i - 2, j) = 0 Then Continue For End If Console.WriteLine("{0,6} have {1} Next Console.WriteLine() Next End Sub End Module
Generate an equivalent C version of this D code.
import std.range; import std.stdio; int indexOf(Range, Element)(Range haystack, scope Element needle) if (isInputRange!Range) { int idx; foreach (straw; haystack) { if (straw == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, int[] digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(int[] digits, int le, int idx) { enum pows = [ 1, 10, 100, 1_000, 10_000 ]; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } void main() { auto lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ]; int[5] count; int[10][5] omitted; for (int i = 0; i < lims.length; i++) { auto nDigits = new int[i + 2]; auto dDigits = new int[i + 2]; for (int n = lims[i][0]; n <= lims[i][1]; n++) { nDigits[] = 0; bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i][1] + 1; d++) { dDigits[] = 0; bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.length; nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if (cast(double)n / d == cast(double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { writefln("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit); } } } } } } writeln; } for (int i = 2; i <= 5; i++) { writefln("There are %d %d-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } writefln("%6s have %d's omitted", omitted[i - 2][j], j); } writeln; } }
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }
Convert this D snippet to C# and keep its semantics consistent.
import std.range; import std.stdio; int indexOf(Range, Element)(Range haystack, scope Element needle) if (isInputRange!Range) { int idx; foreach (straw; haystack) { if (straw == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, int[] digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(int[] digits, int le, int idx) { enum pows = [ 1, 10, 100, 1_000, 10_000 ]; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } void main() { auto lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ]; int[5] count; int[10][5] omitted; for (int i = 0; i < lims.length; i++) { auto nDigits = new int[i + 2]; auto dDigits = new int[i + 2]; for (int n = lims[i][0]; n <= lims[i][1]; n++) { nDigits[] = 0; bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i][1] + 1; d++) { dDigits[] = 0; bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.length; nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if (cast(double)n / d == cast(double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { writefln("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit); } } } } } } writeln; } for (int i = 2; i <= 5; i++) { writefln("There are %d %d-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } writefln("%6s have %d's omitted", omitted[i - 2][j], j); } writeln; } }
using System; namespace FractionReduction { class Program { static int IndexOf(int n, int[] s) { for (int i = 0; i < s.Length; i++) { if (s[i] == n) { return i; } } return -1; } static bool GetDigits(int n, int le, int[] digits) { while (n > 0) { var r = n % 10; if (r == 0 || IndexOf(r, digits) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } static int RemoveDigit(int[] digits, int le, int idx) { int[] pows = { 1, 10, 100, 1000, 10000 }; var sum = 0; var pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } static void Main() { var lims = new int[,] { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; var count = new int[5]; var omitted = new int[5, 10]; var upperBound = lims.GetLength(0); for (int i = 0; i < upperBound; i++) { var nDigits = new int[i + 2]; var dDigits = new int[i + 2]; var blank = new int[i + 2]; for (int n = lims[i, 0]; n <= lims[i, 1]; n++) { blank.CopyTo(nDigits, 0); var nOk = GetDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i, 1] + 1; d++) { blank.CopyTo(dDigits, 0); var dOk = GetDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.Length; nix++) { var digit = nDigits[nix]; var dix = IndexOf(digit, dDigits); if (dix >= 0) { var rn = RemoveDigit(nDigits, i + 2, nix); var rd = RemoveDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i, digit]++; if (count[i] <= 12) { Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4}'s", n, d, rn, rd, digit); } } } } } } Console.WriteLine(); } for (int i = 2; i <= 5; i++) { Console.WriteLine("There are {0} {1}-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2, j] == 0) { continue; } Console.WriteLine("{0,6} have {1}'s omitted", omitted[i - 2, j], j); } Console.WriteLine(); } } } }
Generate an equivalent C++ version of this D code.
import std.range; import std.stdio; int indexOf(Range, Element)(Range haystack, scope Element needle) if (isInputRange!Range) { int idx; foreach (straw; haystack) { if (straw == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, int[] digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(int[] digits, int le, int idx) { enum pows = [ 1, 10, 100, 1_000, 10_000 ]; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } void main() { auto lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ]; int[5] count; int[10][5] omitted; for (int i = 0; i < lims.length; i++) { auto nDigits = new int[i + 2]; auto dDigits = new int[i + 2]; for (int n = lims[i][0]; n <= lims[i][1]; n++) { nDigits[] = 0; bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i][1] + 1; d++) { dDigits[] = 0; bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.length; nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if (cast(double)n / d == cast(double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { writefln("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit); } } } } } } writeln; } for (int i = 2; i <= 5; i++) { writefln("There are %d %d-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } writefln("%6s have %d's omitted", omitted[i - 2][j], j); } writeln; } }
#include <array> #include <iomanip> #include <iostream> #include <vector> int indexOf(const std::vector<int> &haystack, int needle) { auto it = haystack.cbegin(); auto end = haystack.cend(); int idx = 0; for (; it != end; it = std::next(it)) { if (*it == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, std::vector<int> &digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(const std::vector<int> &digits, int le, int idx) { static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 }; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } int main() { std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }; std::array<int, 5> count; std::array<std::array<int, 10>, 5> omitted; std::fill(count.begin(), count.end(), 0); std::for_each(omitted.begin(), omitted.end(), [](auto &a) { std::fill(a.begin(), a.end(), 0); } ); for (size_t i = 0; i < lims.size(); i++) { std::vector<int> nDigits(i + 2); std::vector<int> dDigits(i + 2); for (int n = lims[i].first; n <= lims[i].second; n++) { std::fill(nDigits.begin(), nDigits.end(), 0); bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i].second + 1; d++) { std::fill(dDigits.begin(), dDigits.end(), 0); bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (size_t nix = 0; nix < nDigits.size(); nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n"; } } } } } } std::cout << '\n'; } for (int i = 2; i <= 5; i++) { std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n"; for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n"; } std::cout << '\n'; } return 0; }
Port the provided D code into Java while preserving the original functionality.
import std.range; import std.stdio; int indexOf(Range, Element)(Range haystack, scope Element needle) if (isInputRange!Range) { int idx; foreach (straw; haystack) { if (straw == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, int[] digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(int[] digits, int le, int idx) { enum pows = [ 1, 10, 100, 1_000, 10_000 ]; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } void main() { auto lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ]; int[5] count; int[10][5] omitted; for (int i = 0; i < lims.length; i++) { auto nDigits = new int[i + 2]; auto dDigits = new int[i + 2]; for (int n = lims[i][0]; n <= lims[i][1]; n++) { nDigits[] = 0; bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i][1] + 1; d++) { dDigits[] = 0; bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.length; nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if (cast(double)n / d == cast(double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { writefln("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit); } } } } } } writeln; } for (int i = 2; i <= 5; i++) { writefln("There are %d %d-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } writefln("%6s have %d's omitted", omitted[i - 2][j], j); } writeln; } }
import java.util.ArrayList; import java.util.Collections; import java.util.HashMap; import java.util.List; import java.util.Map; public class FractionReduction { public static void main(String[] args) { for ( int size = 2 ; size <= 5 ; size++ ) { reduce(size); } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits); int min = (int) Math.pow(10, numDigits-1); int max = (int) Math.pow(10, numDigits) - 1; List<Integer> values = new ArrayList<>(); for ( int number = min ; number <= max ; number++ ) { if ( isValid(number) ) { values.add(number); } } Map<Integer,Integer> cancelCount = new HashMap<>(); int size = values.size(); int solutions = 0; for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) { int numerator = values.get(nIndex); for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) { int denominator = values.get(dIndex); for ( int commonDigit : digitsInCommon(numerator, denominator) ) { int numRemoved = removeDigit(numerator, commonDigit); int denRemoved = removeDigit(denominator, commonDigit); if ( numerator * denRemoved == denominator * numRemoved ) { solutions++; cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2); if ( solutions <= 12 ) { System.out.printf(" When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved); } } } } } System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions); List<Integer> sorted = new ArrayList<>(cancelCount.keySet()); Collections.sort(sorted); for ( int removed : sorted ) { System.out.printf(" The digit %d was removed %d times.%n", removed, cancelCount.get(removed)); } System.out.println(); } private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000}; private static int removeDigit(int n, int removed) { int m = 0; int pow = 0; while ( n > 0 ) { int r = n % 10; if ( r != removed ) { m = m + r*powers[pow]; pow++; } n /= 10; } return m; } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10]; List<Integer> common = new ArrayList<>(); while ( n1 > 0 ) { int r = n1 % 10; count[r] += 1; n1 /= 10; } while ( n2 > 0 ) { int r = n2 % 10; if ( count[r] > 0 ) { common.add(r); } n2 /= 10; } return common; } private static boolean isValid(int num) { int[] count = new int[10]; while ( num > 0 ) { int r = num % 10; if ( r == 0 || count[r] == 1 ) { return false; } count[r] = 1; num /= 10; } return true; } }
Change the programming language of this snippet from D to Python without modifying what it does.
import std.range; import std.stdio; int indexOf(Range, Element)(Range haystack, scope Element needle) if (isInputRange!Range) { int idx; foreach (straw; haystack) { if (straw == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, int[] digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(int[] digits, int le, int idx) { enum pows = [ 1, 10, 100, 1_000, 10_000 ]; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } void main() { auto lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ]; int[5] count; int[10][5] omitted; for (int i = 0; i < lims.length; i++) { auto nDigits = new int[i + 2]; auto dDigits = new int[i + 2]; for (int n = lims[i][0]; n <= lims[i][1]; n++) { nDigits[] = 0; bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i][1] + 1; d++) { dDigits[] = 0; bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.length; nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if (cast(double)n / d == cast(double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { writefln("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit); } } } } } } writeln; } for (int i = 2; i <= 5; i++) { writefln("There are %d %d-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } writefln("%6s have %d's omitted", omitted[i - 2][j], j); } writeln; } }
def indexOf(haystack, needle): idx = 0 for straw in haystack: if straw == needle: return idx else: idx += 1 return -1 def getDigits(n, le, digits): while n > 0: r = n % 10 if r == 0 or indexOf(digits, r) >= 0: return False le -= 1 digits[le] = r n = int(n / 10) return True def removeDigit(digits, le, idx): pows = [1, 10, 100, 1000, 10000] sum = 0 pow = pows[le - 2] i = 0 while i < le: if i == idx: i += 1 continue sum = sum + digits[i] * pow pow = int(pow / 10) i += 1 return sum def main(): lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = [0 for i in range(5)] omitted = [[0 for i in range(10)] for j in range(5)] i = 0 while i < len(lims): n = lims[i][0] while n < lims[i][1]: nDigits = [0 for k in range(i + 2)] nOk = getDigits(n, i + 2, nDigits) if not nOk: n += 1 continue d = n + 1 while d <= lims[i][1] + 1: dDigits = [0 for k in range(i + 2)] dOk = getDigits(d, i + 2, dDigits) if not dOk: d += 1 continue nix = 0 while nix < len(nDigits): digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0: rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd): count[i] += 1 omitted[i][digit] += 1 if count[i] <= 12: print "%d/%d = %d/%d by omitting %d's" % (n, d, rn, rd, digit) nix += 1 d += 1 n += 1 print i += 1 i = 2 while i <= 5: print "There are %d %d-digit fractions of which:" % (count[i - 2], i) j = 1 while j <= 9: if omitted[i - 2][j] == 0: j += 1 continue print "%6s have %d's omitted" % (omitted[i - 2][j], j) j += 1 print i += 1 return None main()
Write the same algorithm in VB as shown in this D implementation.
import std.range; import std.stdio; int indexOf(Range, Element)(Range haystack, scope Element needle) if (isInputRange!Range) { int idx; foreach (straw; haystack) { if (straw == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, int[] digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(int[] digits, int le, int idx) { enum pows = [ 1, 10, 100, 1_000, 10_000 ]; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } void main() { auto lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ]; int[5] count; int[10][5] omitted; for (int i = 0; i < lims.length; i++) { auto nDigits = new int[i + 2]; auto dDigits = new int[i + 2]; for (int n = lims[i][0]; n <= lims[i][1]; n++) { nDigits[] = 0; bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i][1] + 1; d++) { dDigits[] = 0; bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.length; nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if (cast(double)n / d == cast(double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { writefln("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit); } } } } } } writeln; } for (int i = 2; i <= 5; i++) { writefln("There are %d %d-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } writefln("%6s have %d's omitted", omitted[i - 2][j], j); } writeln; } }
Module Module1 Function IndexOf(n As Integer, s As Integer()) As Integer For ii = 1 To s.Length Dim i = ii - 1 If s(i) = n Then Return i End If Next Return -1 End Function Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean While n > 0 Dim r = n Mod 10 If r = 0 OrElse IndexOf(r, digits) >= 0 Then Return False End If le -= 1 digits(le) = r n \= 10 End While Return True End Function Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer Dim pows = {1, 10, 100, 1000, 10000} Dim sum = 0 Dim pow = pows(le - 2) For ii = 1 To le Dim i = ii - 1 If i = idx Then Continue For End If sum += digits(i) * pow pow \= 10 Next Return sum End Function Sub Main() Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}} Dim count(5) As Integer Dim omitted(5, 10) As Integer Dim upperBound = lims.GetLength(0) For ii = 1 To upperBound Dim i = ii - 1 Dim nDigits(i + 2 - 1) As Integer Dim dDigits(i + 2 - 1) As Integer Dim blank(i + 2 - 1) As Integer For n = lims(i, 0) To lims(i, 1) blank.CopyTo(nDigits, 0) Dim nOk = GetDigits(n, i + 2, nDigits) If Not nOk Then Continue For End If For d = n + 1 To lims(i, 1) + 1 blank.CopyTo(dDigits, 0) Dim dOk = GetDigits(d, i + 2, dDigits) If Not dOk Then Continue For End If For nixt = 1 To nDigits.Length Dim nix = nixt - 1 Dim digit = nDigits(nix) Dim dix = IndexOf(digit, dDigits) If dix >= 0 Then Dim rn = RemoveDigit(nDigits, i + 2, nix) Dim rd = RemoveDigit(dDigits, i + 2, dix) If (n / d) = (rn / rd) Then count(i) += 1 omitted(i, digit) += 1 If count(i) <= 12 Then Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4} End If End If End If Next Next Next Console.WriteLine() Next For i = 2 To 5 Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i) For j = 1 To 9 If omitted(i - 2, j) = 0 Then Continue For End If Console.WriteLine("{0,6} have {1} Next Console.WriteLine() Next End Sub End Module
Maintain the same structure and functionality when rewriting this code in Go.
import std.range; import std.stdio; int indexOf(Range, Element)(Range haystack, scope Element needle) if (isInputRange!Range) { int idx; foreach (straw; haystack) { if (straw == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, int[] digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(int[] digits, int le, int idx) { enum pows = [ 1, 10, 100, 1_000, 10_000 ]; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } void main() { auto lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ]; int[5] count; int[10][5] omitted; for (int i = 0; i < lims.length; i++) { auto nDigits = new int[i + 2]; auto dDigits = new int[i + 2]; for (int n = lims[i][0]; n <= lims[i][1]; n++) { nDigits[] = 0; bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i][1] + 1; d++) { dDigits[] = 0; bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.length; nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if (cast(double)n / d == cast(double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { writefln("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit); } } } } } } writeln; } for (int i = 2; i <= 5; i++) { writefln("There are %d %d-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } writefln("%6s have %d's omitted", omitted[i - 2][j], j); } writeln; } }
package main import ( "fmt" "time" ) func indexOf(n int, s []int) int { for i, j := range s { if n == j { return i } } return -1 } func getDigits(n, le int, digits []int) bool { for n > 0 { r := n % 10 if r == 0 || indexOf(r, digits) >= 0 { return false } le-- digits[le] = r n /= 10 } return true } var pows = [5]int{1, 10, 100, 1000, 10000} func removeDigit(digits []int, le, idx int) int { sum := 0 pow := pows[le-2] for i := 0; i < le; i++ { if i == idx { continue } sum += digits[i] * pow pow /= 10 } return sum } func main() { start := time.Now() lims := [5][2]int{ {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}, {123456, 987653}, } var count [5]int var omitted [5][10]int for i, lim := range lims { nDigits := make([]int, i+2) dDigits := make([]int, i+2) blank := make([]int, i+2) for n := lim[0]; n <= lim[1]; n++ { copy(nDigits, blank) nOk := getDigits(n, i+2, nDigits) if !nOk { continue } for d := n + 1; d <= lim[1]+1; d++ { copy(dDigits, blank) dOk := getDigits(d, i+2, dDigits) if !dOk { continue } for nix, digit := range nDigits { if dix := indexOf(digit, dDigits); dix >= 0 { rn := removeDigit(nDigits, i+2, nix) rd := removeDigit(dDigits, i+2, dix) if float64(n)/float64(d) == float64(rn)/float64(rd) { count[i]++ omitted[i][digit]++ if count[i] <= 12 { fmt.Printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit) } } } } } } fmt.Println() } for i := 2; i <= 6; i++ { fmt.Printf("There are %d %d-digit fractions of which:\n", count[i-2], i) for j := 1; j <= 9; j++ { if omitted[i-2][j] == 0 { continue } fmt.Printf("%6d have %d's omitted\n", omitted[i-2][j], j) } fmt.Println() } fmt.Printf("Took %s\n", time.Since(start)) }
Produce a language-to-language conversion: from Groovy to C, same semantics.
class FractionReduction { static void main(String[] args) { for (int size = 2; size <= 5; size++) { reduce(size) } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits) int min = (int) Math.pow(10, numDigits - 1) int max = (int) Math.pow(10, numDigits) - 1 List<Integer> values = new ArrayList<>() for (int number = min; number <= max; number++) { if (isValid(number)) { values.add(number) } } Map<Integer, Integer> cancelCount = new HashMap<>() int size = values.size() int solutions = 0 for (int nIndex = 0; nIndex < size - 1; nIndex++) { int numerator = values.get(nIndex) for (int dIndex = nIndex + 1; dIndex < size; dIndex++) { int denominator = values.get(dIndex) for (int commonDigit : digitsInCommon(numerator, denominator)) { int numRemoved = removeDigit(numerator, commonDigit) int denRemoved = removeDigit(denominator, commonDigit) if (numerator * denRemoved == denominator * numRemoved) { solutions++ cancelCount.merge(commonDigit, 1, { v1, v2 -> v1 + v2 }) if (solutions <= 12) { println(" When $commonDigit is removed, $numerator/$denominator = $numRemoved/$denRemoved") } } } } } println("Number of fractions where cancellation is valid = $solutions.") List<Integer> sorted = new ArrayList<>(cancelCount.keySet()) Collections.sort(sorted) for (int removed : sorted) { println(" The digit $removed was removed ${cancelCount.get(removed)} times.") } println() } private static int[] powers = [1, 10, 100, 1000, 10000, 100000] private static int removeDigit(int n, int removed) { int m = 0 int pow = 0 while (n > 0) { int r = n % 10 if (r != removed) { m = m + r * powers[pow] pow++ } n /= 10 } return m } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10] List<Integer> common = new ArrayList<>() while (n1 > 0) { int r = n1 % 10 count[r] += 1 n1 /= 10 } while (n2 > 0) { int r = n2 % 10 if (count[r] > 0) { common.add(r) } n2 /= 10 } return common } private static boolean isValid(int num) { int[] count = new int[10] while (num > 0) { int r = num % 10 if (r == 0 || count[r] == 1) { return false } count[r] = 1 num /= 10 } return true } }
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }
Rewrite this program in C# while keeping its functionality equivalent to the Groovy version.
class FractionReduction { static void main(String[] args) { for (int size = 2; size <= 5; size++) { reduce(size) } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits) int min = (int) Math.pow(10, numDigits - 1) int max = (int) Math.pow(10, numDigits) - 1 List<Integer> values = new ArrayList<>() for (int number = min; number <= max; number++) { if (isValid(number)) { values.add(number) } } Map<Integer, Integer> cancelCount = new HashMap<>() int size = values.size() int solutions = 0 for (int nIndex = 0; nIndex < size - 1; nIndex++) { int numerator = values.get(nIndex) for (int dIndex = nIndex + 1; dIndex < size; dIndex++) { int denominator = values.get(dIndex) for (int commonDigit : digitsInCommon(numerator, denominator)) { int numRemoved = removeDigit(numerator, commonDigit) int denRemoved = removeDigit(denominator, commonDigit) if (numerator * denRemoved == denominator * numRemoved) { solutions++ cancelCount.merge(commonDigit, 1, { v1, v2 -> v1 + v2 }) if (solutions <= 12) { println(" When $commonDigit is removed, $numerator/$denominator = $numRemoved/$denRemoved") } } } } } println("Number of fractions where cancellation is valid = $solutions.") List<Integer> sorted = new ArrayList<>(cancelCount.keySet()) Collections.sort(sorted) for (int removed : sorted) { println(" The digit $removed was removed ${cancelCount.get(removed)} times.") } println() } private static int[] powers = [1, 10, 100, 1000, 10000, 100000] private static int removeDigit(int n, int removed) { int m = 0 int pow = 0 while (n > 0) { int r = n % 10 if (r != removed) { m = m + r * powers[pow] pow++ } n /= 10 } return m } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10] List<Integer> common = new ArrayList<>() while (n1 > 0) { int r = n1 % 10 count[r] += 1 n1 /= 10 } while (n2 > 0) { int r = n2 % 10 if (count[r] > 0) { common.add(r) } n2 /= 10 } return common } private static boolean isValid(int num) { int[] count = new int[10] while (num > 0) { int r = num % 10 if (r == 0 || count[r] == 1) { return false } count[r] = 1 num /= 10 } return true } }
using System; namespace FractionReduction { class Program { static int IndexOf(int n, int[] s) { for (int i = 0; i < s.Length; i++) { if (s[i] == n) { return i; } } return -1; } static bool GetDigits(int n, int le, int[] digits) { while (n > 0) { var r = n % 10; if (r == 0 || IndexOf(r, digits) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } static int RemoveDigit(int[] digits, int le, int idx) { int[] pows = { 1, 10, 100, 1000, 10000 }; var sum = 0; var pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } static void Main() { var lims = new int[,] { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; var count = new int[5]; var omitted = new int[5, 10]; var upperBound = lims.GetLength(0); for (int i = 0; i < upperBound; i++) { var nDigits = new int[i + 2]; var dDigits = new int[i + 2]; var blank = new int[i + 2]; for (int n = lims[i, 0]; n <= lims[i, 1]; n++) { blank.CopyTo(nDigits, 0); var nOk = GetDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i, 1] + 1; d++) { blank.CopyTo(dDigits, 0); var dOk = GetDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.Length; nix++) { var digit = nDigits[nix]; var dix = IndexOf(digit, dDigits); if (dix >= 0) { var rn = RemoveDigit(nDigits, i + 2, nix); var rd = RemoveDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i, digit]++; if (count[i] <= 12) { Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4}'s", n, d, rn, rd, digit); } } } } } } Console.WriteLine(); } for (int i = 2; i <= 5; i++) { Console.WriteLine("There are {0} {1}-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2, j] == 0) { continue; } Console.WriteLine("{0,6} have {1}'s omitted", omitted[i - 2, j], j); } Console.WriteLine(); } } } }
Keep all operations the same but rewrite the snippet in C++.
class FractionReduction { static void main(String[] args) { for (int size = 2; size <= 5; size++) { reduce(size) } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits) int min = (int) Math.pow(10, numDigits - 1) int max = (int) Math.pow(10, numDigits) - 1 List<Integer> values = new ArrayList<>() for (int number = min; number <= max; number++) { if (isValid(number)) { values.add(number) } } Map<Integer, Integer> cancelCount = new HashMap<>() int size = values.size() int solutions = 0 for (int nIndex = 0; nIndex < size - 1; nIndex++) { int numerator = values.get(nIndex) for (int dIndex = nIndex + 1; dIndex < size; dIndex++) { int denominator = values.get(dIndex) for (int commonDigit : digitsInCommon(numerator, denominator)) { int numRemoved = removeDigit(numerator, commonDigit) int denRemoved = removeDigit(denominator, commonDigit) if (numerator * denRemoved == denominator * numRemoved) { solutions++ cancelCount.merge(commonDigit, 1, { v1, v2 -> v1 + v2 }) if (solutions <= 12) { println(" When $commonDigit is removed, $numerator/$denominator = $numRemoved/$denRemoved") } } } } } println("Number of fractions where cancellation is valid = $solutions.") List<Integer> sorted = new ArrayList<>(cancelCount.keySet()) Collections.sort(sorted) for (int removed : sorted) { println(" The digit $removed was removed ${cancelCount.get(removed)} times.") } println() } private static int[] powers = [1, 10, 100, 1000, 10000, 100000] private static int removeDigit(int n, int removed) { int m = 0 int pow = 0 while (n > 0) { int r = n % 10 if (r != removed) { m = m + r * powers[pow] pow++ } n /= 10 } return m } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10] List<Integer> common = new ArrayList<>() while (n1 > 0) { int r = n1 % 10 count[r] += 1 n1 /= 10 } while (n2 > 0) { int r = n2 % 10 if (count[r] > 0) { common.add(r) } n2 /= 10 } return common } private static boolean isValid(int num) { int[] count = new int[10] while (num > 0) { int r = num % 10 if (r == 0 || count[r] == 1) { return false } count[r] = 1 num /= 10 } return true } }
#include <array> #include <iomanip> #include <iostream> #include <vector> int indexOf(const std::vector<int> &haystack, int needle) { auto it = haystack.cbegin(); auto end = haystack.cend(); int idx = 0; for (; it != end; it = std::next(it)) { if (*it == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, std::vector<int> &digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(const std::vector<int> &digits, int le, int idx) { static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 }; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } int main() { std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }; std::array<int, 5> count; std::array<std::array<int, 10>, 5> omitted; std::fill(count.begin(), count.end(), 0); std::for_each(omitted.begin(), omitted.end(), [](auto &a) { std::fill(a.begin(), a.end(), 0); } ); for (size_t i = 0; i < lims.size(); i++) { std::vector<int> nDigits(i + 2); std::vector<int> dDigits(i + 2); for (int n = lims[i].first; n <= lims[i].second; n++) { std::fill(nDigits.begin(), nDigits.end(), 0); bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i].second + 1; d++) { std::fill(dDigits.begin(), dDigits.end(), 0); bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (size_t nix = 0; nix < nDigits.size(); nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n"; } } } } } } std::cout << '\n'; } for (int i = 2; i <= 5; i++) { std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n"; for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n"; } std::cout << '\n'; } return 0; }
Keep all operations the same but rewrite the snippet in Java.
class FractionReduction { static void main(String[] args) { for (int size = 2; size <= 5; size++) { reduce(size) } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits) int min = (int) Math.pow(10, numDigits - 1) int max = (int) Math.pow(10, numDigits) - 1 List<Integer> values = new ArrayList<>() for (int number = min; number <= max; number++) { if (isValid(number)) { values.add(number) } } Map<Integer, Integer> cancelCount = new HashMap<>() int size = values.size() int solutions = 0 for (int nIndex = 0; nIndex < size - 1; nIndex++) { int numerator = values.get(nIndex) for (int dIndex = nIndex + 1; dIndex < size; dIndex++) { int denominator = values.get(dIndex) for (int commonDigit : digitsInCommon(numerator, denominator)) { int numRemoved = removeDigit(numerator, commonDigit) int denRemoved = removeDigit(denominator, commonDigit) if (numerator * denRemoved == denominator * numRemoved) { solutions++ cancelCount.merge(commonDigit, 1, { v1, v2 -> v1 + v2 }) if (solutions <= 12) { println(" When $commonDigit is removed, $numerator/$denominator = $numRemoved/$denRemoved") } } } } } println("Number of fractions where cancellation is valid = $solutions.") List<Integer> sorted = new ArrayList<>(cancelCount.keySet()) Collections.sort(sorted) for (int removed : sorted) { println(" The digit $removed was removed ${cancelCount.get(removed)} times.") } println() } private static int[] powers = [1, 10, 100, 1000, 10000, 100000] private static int removeDigit(int n, int removed) { int m = 0 int pow = 0 while (n > 0) { int r = n % 10 if (r != removed) { m = m + r * powers[pow] pow++ } n /= 10 } return m } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10] List<Integer> common = new ArrayList<>() while (n1 > 0) { int r = n1 % 10 count[r] += 1 n1 /= 10 } while (n2 > 0) { int r = n2 % 10 if (count[r] > 0) { common.add(r) } n2 /= 10 } return common } private static boolean isValid(int num) { int[] count = new int[10] while (num > 0) { int r = num % 10 if (r == 0 || count[r] == 1) { return false } count[r] = 1 num /= 10 } return true } }
import java.util.ArrayList; import java.util.Collections; import java.util.HashMap; import java.util.List; import java.util.Map; public class FractionReduction { public static void main(String[] args) { for ( int size = 2 ; size <= 5 ; size++ ) { reduce(size); } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits); int min = (int) Math.pow(10, numDigits-1); int max = (int) Math.pow(10, numDigits) - 1; List<Integer> values = new ArrayList<>(); for ( int number = min ; number <= max ; number++ ) { if ( isValid(number) ) { values.add(number); } } Map<Integer,Integer> cancelCount = new HashMap<>(); int size = values.size(); int solutions = 0; for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) { int numerator = values.get(nIndex); for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) { int denominator = values.get(dIndex); for ( int commonDigit : digitsInCommon(numerator, denominator) ) { int numRemoved = removeDigit(numerator, commonDigit); int denRemoved = removeDigit(denominator, commonDigit); if ( numerator * denRemoved == denominator * numRemoved ) { solutions++; cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2); if ( solutions <= 12 ) { System.out.printf(" When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved); } } } } } System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions); List<Integer> sorted = new ArrayList<>(cancelCount.keySet()); Collections.sort(sorted); for ( int removed : sorted ) { System.out.printf(" The digit %d was removed %d times.%n", removed, cancelCount.get(removed)); } System.out.println(); } private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000}; private static int removeDigit(int n, int removed) { int m = 0; int pow = 0; while ( n > 0 ) { int r = n % 10; if ( r != removed ) { m = m + r*powers[pow]; pow++; } n /= 10; } return m; } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10]; List<Integer> common = new ArrayList<>(); while ( n1 > 0 ) { int r = n1 % 10; count[r] += 1; n1 /= 10; } while ( n2 > 0 ) { int r = n2 % 10; if ( count[r] > 0 ) { common.add(r); } n2 /= 10; } return common; } private static boolean isValid(int num) { int[] count = new int[10]; while ( num > 0 ) { int r = num % 10; if ( r == 0 || count[r] == 1 ) { return false; } count[r] = 1; num /= 10; } return true; } }
Please provide an equivalent version of this Groovy code in Python.
class FractionReduction { static void main(String[] args) { for (int size = 2; size <= 5; size++) { reduce(size) } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits) int min = (int) Math.pow(10, numDigits - 1) int max = (int) Math.pow(10, numDigits) - 1 List<Integer> values = new ArrayList<>() for (int number = min; number <= max; number++) { if (isValid(number)) { values.add(number) } } Map<Integer, Integer> cancelCount = new HashMap<>() int size = values.size() int solutions = 0 for (int nIndex = 0; nIndex < size - 1; nIndex++) { int numerator = values.get(nIndex) for (int dIndex = nIndex + 1; dIndex < size; dIndex++) { int denominator = values.get(dIndex) for (int commonDigit : digitsInCommon(numerator, denominator)) { int numRemoved = removeDigit(numerator, commonDigit) int denRemoved = removeDigit(denominator, commonDigit) if (numerator * denRemoved == denominator * numRemoved) { solutions++ cancelCount.merge(commonDigit, 1, { v1, v2 -> v1 + v2 }) if (solutions <= 12) { println(" When $commonDigit is removed, $numerator/$denominator = $numRemoved/$denRemoved") } } } } } println("Number of fractions where cancellation is valid = $solutions.") List<Integer> sorted = new ArrayList<>(cancelCount.keySet()) Collections.sort(sorted) for (int removed : sorted) { println(" The digit $removed was removed ${cancelCount.get(removed)} times.") } println() } private static int[] powers = [1, 10, 100, 1000, 10000, 100000] private static int removeDigit(int n, int removed) { int m = 0 int pow = 0 while (n > 0) { int r = n % 10 if (r != removed) { m = m + r * powers[pow] pow++ } n /= 10 } return m } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10] List<Integer> common = new ArrayList<>() while (n1 > 0) { int r = n1 % 10 count[r] += 1 n1 /= 10 } while (n2 > 0) { int r = n2 % 10 if (count[r] > 0) { common.add(r) } n2 /= 10 } return common } private static boolean isValid(int num) { int[] count = new int[10] while (num > 0) { int r = num % 10 if (r == 0 || count[r] == 1) { return false } count[r] = 1 num /= 10 } return true } }
def indexOf(haystack, needle): idx = 0 for straw in haystack: if straw == needle: return idx else: idx += 1 return -1 def getDigits(n, le, digits): while n > 0: r = n % 10 if r == 0 or indexOf(digits, r) >= 0: return False le -= 1 digits[le] = r n = int(n / 10) return True def removeDigit(digits, le, idx): pows = [1, 10, 100, 1000, 10000] sum = 0 pow = pows[le - 2] i = 0 while i < le: if i == idx: i += 1 continue sum = sum + digits[i] * pow pow = int(pow / 10) i += 1 return sum def main(): lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = [0 for i in range(5)] omitted = [[0 for i in range(10)] for j in range(5)] i = 0 while i < len(lims): n = lims[i][0] while n < lims[i][1]: nDigits = [0 for k in range(i + 2)] nOk = getDigits(n, i + 2, nDigits) if not nOk: n += 1 continue d = n + 1 while d <= lims[i][1] + 1: dDigits = [0 for k in range(i + 2)] dOk = getDigits(d, i + 2, dDigits) if not dOk: d += 1 continue nix = 0 while nix < len(nDigits): digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0: rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd): count[i] += 1 omitted[i][digit] += 1 if count[i] <= 12: print "%d/%d = %d/%d by omitting %d's" % (n, d, rn, rd, digit) nix += 1 d += 1 n += 1 print i += 1 i = 2 while i <= 5: print "There are %d %d-digit fractions of which:" % (count[i - 2], i) j = 1 while j <= 9: if omitted[i - 2][j] == 0: j += 1 continue print "%6s have %d's omitted" % (omitted[i - 2][j], j) j += 1 print i += 1 return None main()
Rewrite the snippet below in VB so it works the same as the original Groovy code.
class FractionReduction { static void main(String[] args) { for (int size = 2; size <= 5; size++) { reduce(size) } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits) int min = (int) Math.pow(10, numDigits - 1) int max = (int) Math.pow(10, numDigits) - 1 List<Integer> values = new ArrayList<>() for (int number = min; number <= max; number++) { if (isValid(number)) { values.add(number) } } Map<Integer, Integer> cancelCount = new HashMap<>() int size = values.size() int solutions = 0 for (int nIndex = 0; nIndex < size - 1; nIndex++) { int numerator = values.get(nIndex) for (int dIndex = nIndex + 1; dIndex < size; dIndex++) { int denominator = values.get(dIndex) for (int commonDigit : digitsInCommon(numerator, denominator)) { int numRemoved = removeDigit(numerator, commonDigit) int denRemoved = removeDigit(denominator, commonDigit) if (numerator * denRemoved == denominator * numRemoved) { solutions++ cancelCount.merge(commonDigit, 1, { v1, v2 -> v1 + v2 }) if (solutions <= 12) { println(" When $commonDigit is removed, $numerator/$denominator = $numRemoved/$denRemoved") } } } } } println("Number of fractions where cancellation is valid = $solutions.") List<Integer> sorted = new ArrayList<>(cancelCount.keySet()) Collections.sort(sorted) for (int removed : sorted) { println(" The digit $removed was removed ${cancelCount.get(removed)} times.") } println() } private static int[] powers = [1, 10, 100, 1000, 10000, 100000] private static int removeDigit(int n, int removed) { int m = 0 int pow = 0 while (n > 0) { int r = n % 10 if (r != removed) { m = m + r * powers[pow] pow++ } n /= 10 } return m } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10] List<Integer> common = new ArrayList<>() while (n1 > 0) { int r = n1 % 10 count[r] += 1 n1 /= 10 } while (n2 > 0) { int r = n2 % 10 if (count[r] > 0) { common.add(r) } n2 /= 10 } return common } private static boolean isValid(int num) { int[] count = new int[10] while (num > 0) { int r = num % 10 if (r == 0 || count[r] == 1) { return false } count[r] = 1 num /= 10 } return true } }
Module Module1 Function IndexOf(n As Integer, s As Integer()) As Integer For ii = 1 To s.Length Dim i = ii - 1 If s(i) = n Then Return i End If Next Return -1 End Function Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean While n > 0 Dim r = n Mod 10 If r = 0 OrElse IndexOf(r, digits) >= 0 Then Return False End If le -= 1 digits(le) = r n \= 10 End While Return True End Function Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer Dim pows = {1, 10, 100, 1000, 10000} Dim sum = 0 Dim pow = pows(le - 2) For ii = 1 To le Dim i = ii - 1 If i = idx Then Continue For End If sum += digits(i) * pow pow \= 10 Next Return sum End Function Sub Main() Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}} Dim count(5) As Integer Dim omitted(5, 10) As Integer Dim upperBound = lims.GetLength(0) For ii = 1 To upperBound Dim i = ii - 1 Dim nDigits(i + 2 - 1) As Integer Dim dDigits(i + 2 - 1) As Integer Dim blank(i + 2 - 1) As Integer For n = lims(i, 0) To lims(i, 1) blank.CopyTo(nDigits, 0) Dim nOk = GetDigits(n, i + 2, nDigits) If Not nOk Then Continue For End If For d = n + 1 To lims(i, 1) + 1 blank.CopyTo(dDigits, 0) Dim dOk = GetDigits(d, i + 2, dDigits) If Not dOk Then Continue For End If For nixt = 1 To nDigits.Length Dim nix = nixt - 1 Dim digit = nDigits(nix) Dim dix = IndexOf(digit, dDigits) If dix >= 0 Then Dim rn = RemoveDigit(nDigits, i + 2, nix) Dim rd = RemoveDigit(dDigits, i + 2, dix) If (n / d) = (rn / rd) Then count(i) += 1 omitted(i, digit) += 1 If count(i) <= 12 Then Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4} End If End If End If Next Next Next Console.WriteLine() Next For i = 2 To 5 Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i) For j = 1 To 9 If omitted(i - 2, j) = 0 Then Continue For End If Console.WriteLine("{0,6} have {1} Next Console.WriteLine() Next End Sub End Module
Change the programming language of this snippet from Groovy to Go without modifying what it does.
class FractionReduction { static void main(String[] args) { for (int size = 2; size <= 5; size++) { reduce(size) } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits) int min = (int) Math.pow(10, numDigits - 1) int max = (int) Math.pow(10, numDigits) - 1 List<Integer> values = new ArrayList<>() for (int number = min; number <= max; number++) { if (isValid(number)) { values.add(number) } } Map<Integer, Integer> cancelCount = new HashMap<>() int size = values.size() int solutions = 0 for (int nIndex = 0; nIndex < size - 1; nIndex++) { int numerator = values.get(nIndex) for (int dIndex = nIndex + 1; dIndex < size; dIndex++) { int denominator = values.get(dIndex) for (int commonDigit : digitsInCommon(numerator, denominator)) { int numRemoved = removeDigit(numerator, commonDigit) int denRemoved = removeDigit(denominator, commonDigit) if (numerator * denRemoved == denominator * numRemoved) { solutions++ cancelCount.merge(commonDigit, 1, { v1, v2 -> v1 + v2 }) if (solutions <= 12) { println(" When $commonDigit is removed, $numerator/$denominator = $numRemoved/$denRemoved") } } } } } println("Number of fractions where cancellation is valid = $solutions.") List<Integer> sorted = new ArrayList<>(cancelCount.keySet()) Collections.sort(sorted) for (int removed : sorted) { println(" The digit $removed was removed ${cancelCount.get(removed)} times.") } println() } private static int[] powers = [1, 10, 100, 1000, 10000, 100000] private static int removeDigit(int n, int removed) { int m = 0 int pow = 0 while (n > 0) { int r = n % 10 if (r != removed) { m = m + r * powers[pow] pow++ } n /= 10 } return m } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10] List<Integer> common = new ArrayList<>() while (n1 > 0) { int r = n1 % 10 count[r] += 1 n1 /= 10 } while (n2 > 0) { int r = n2 % 10 if (count[r] > 0) { common.add(r) } n2 /= 10 } return common } private static boolean isValid(int num) { int[] count = new int[10] while (num > 0) { int r = num % 10 if (r == 0 || count[r] == 1) { return false } count[r] = 1 num /= 10 } return true } }
package main import ( "fmt" "time" ) func indexOf(n int, s []int) int { for i, j := range s { if n == j { return i } } return -1 } func getDigits(n, le int, digits []int) bool { for n > 0 { r := n % 10 if r == 0 || indexOf(r, digits) >= 0 { return false } le-- digits[le] = r n /= 10 } return true } var pows = [5]int{1, 10, 100, 1000, 10000} func removeDigit(digits []int, le, idx int) int { sum := 0 pow := pows[le-2] for i := 0; i < le; i++ { if i == idx { continue } sum += digits[i] * pow pow /= 10 } return sum } func main() { start := time.Now() lims := [5][2]int{ {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}, {123456, 987653}, } var count [5]int var omitted [5][10]int for i, lim := range lims { nDigits := make([]int, i+2) dDigits := make([]int, i+2) blank := make([]int, i+2) for n := lim[0]; n <= lim[1]; n++ { copy(nDigits, blank) nOk := getDigits(n, i+2, nDigits) if !nOk { continue } for d := n + 1; d <= lim[1]+1; d++ { copy(dDigits, blank) dOk := getDigits(d, i+2, dDigits) if !dOk { continue } for nix, digit := range nDigits { if dix := indexOf(digit, dDigits); dix >= 0 { rn := removeDigit(nDigits, i+2, nix) rd := removeDigit(dDigits, i+2, dix) if float64(n)/float64(d) == float64(rn)/float64(rd) { count[i]++ omitted[i][digit]++ if count[i] <= 12 { fmt.Printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit) } } } } } } fmt.Println() } for i := 2; i <= 6; i++ { fmt.Printf("There are %d %d-digit fractions of which:\n", count[i-2], i) for j := 1; j <= 9; j++ { if omitted[i-2][j] == 0 { continue } fmt.Printf("%6d have %d's omitted\n", omitted[i-2][j], j) } fmt.Println() } fmt.Printf("Took %s\n", time.Since(start)) }
Port the provided Haskell code into C while preserving the original functionality.
import Control.Monad (guard) import Data.List (intersect, unfoldr, delete, nub, group, sort) import Text.Printf (printf) type Fraction = (Int, Int) type Reduction = (Fraction, Fraction, Int) validIntegers :: [Int] -> [Int] validIntegers xs = [x | x <- xs, not $ hasZeros x, hasUniqueDigits x] where hasZeros = elem 0 . digits 10 hasUniqueDigits n = length ds == length ul where ds = digits 10 n ul = nub ds possibleFractions :: [Int] -> [Fraction] possibleFractions = (\ys -> [(n,d) | n <- ys, d <- ys, n < d, gcd n d /= 1]) . validIntegers digits :: Integral a => a -> a -> [a] digits b = unfoldr (\n -> guard (n /= 0) >> pure (n `mod` b, n `div` b)) digitsToIntegral :: Integral a => [a] -> a digitsToIntegral = sum . zipWith (*) (iterate (*10) 1) findReductions :: Fraction -> [Reduction] findReductions z@(n1, d1) = [ (z, (n2, d2), x) | x <- digits 10 n1 `intersect` digits 10 d1, let n2 = dropDigit x n1 d2 = dropDigit x d1 decimalWithDrop = realToFrac n2 / realToFrac d2, decimalWithDrop == decimal ] where dropDigit d = digitsToIntegral . delete d . digits 10 decimal = realToFrac n1 / realToFrac d1 findGroupReductions :: [Int] -> [Reduction] findGroupReductions = (findReductions =<<) . possibleFractions showReduction :: Reduction -> IO () showReduction ((n1,d1),(n2,d2),d) = printf "%d/%d = %d/%d by dropping %d\n" n1 d1 n2 d2 d showCount :: [Reduction] -> Int -> IO () showCount xs n = do printf "There are %d %d-digit fractions of which:\n" (length xs) n mapM_ (uncurry (printf "%5d have %d's omitted\n")) (countReductions xs) >> printf "\n" where countReductions = fmap ((,) . length <*> head) . group . sort . fmap (\(_, _, x) -> x) main :: IO () main = do mapM_ (\g -> mapM_ showReduction (take 12 g) >> printf "\n") groups mapM_ (uncurry showCount) $ zip groups [2..] where groups = [ findGroupReductions [10^1..99], findGroupReductions [10^2..999] , findGroupReductions [10^3..9999], findGroupReductions [10^4..99999] ]
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }
Generate a C# translation of this Haskell snippet without changing its computational steps.
import Control.Monad (guard) import Data.List (intersect, unfoldr, delete, nub, group, sort) import Text.Printf (printf) type Fraction = (Int, Int) type Reduction = (Fraction, Fraction, Int) validIntegers :: [Int] -> [Int] validIntegers xs = [x | x <- xs, not $ hasZeros x, hasUniqueDigits x] where hasZeros = elem 0 . digits 10 hasUniqueDigits n = length ds == length ul where ds = digits 10 n ul = nub ds possibleFractions :: [Int] -> [Fraction] possibleFractions = (\ys -> [(n,d) | n <- ys, d <- ys, n < d, gcd n d /= 1]) . validIntegers digits :: Integral a => a -> a -> [a] digits b = unfoldr (\n -> guard (n /= 0) >> pure (n `mod` b, n `div` b)) digitsToIntegral :: Integral a => [a] -> a digitsToIntegral = sum . zipWith (*) (iterate (*10) 1) findReductions :: Fraction -> [Reduction] findReductions z@(n1, d1) = [ (z, (n2, d2), x) | x <- digits 10 n1 `intersect` digits 10 d1, let n2 = dropDigit x n1 d2 = dropDigit x d1 decimalWithDrop = realToFrac n2 / realToFrac d2, decimalWithDrop == decimal ] where dropDigit d = digitsToIntegral . delete d . digits 10 decimal = realToFrac n1 / realToFrac d1 findGroupReductions :: [Int] -> [Reduction] findGroupReductions = (findReductions =<<) . possibleFractions showReduction :: Reduction -> IO () showReduction ((n1,d1),(n2,d2),d) = printf "%d/%d = %d/%d by dropping %d\n" n1 d1 n2 d2 d showCount :: [Reduction] -> Int -> IO () showCount xs n = do printf "There are %d %d-digit fractions of which:\n" (length xs) n mapM_ (uncurry (printf "%5d have %d's omitted\n")) (countReductions xs) >> printf "\n" where countReductions = fmap ((,) . length <*> head) . group . sort . fmap (\(_, _, x) -> x) main :: IO () main = do mapM_ (\g -> mapM_ showReduction (take 12 g) >> printf "\n") groups mapM_ (uncurry showCount) $ zip groups [2..] where groups = [ findGroupReductions [10^1..99], findGroupReductions [10^2..999] , findGroupReductions [10^3..9999], findGroupReductions [10^4..99999] ]
using System; namespace FractionReduction { class Program { static int IndexOf(int n, int[] s) { for (int i = 0; i < s.Length; i++) { if (s[i] == n) { return i; } } return -1; } static bool GetDigits(int n, int le, int[] digits) { while (n > 0) { var r = n % 10; if (r == 0 || IndexOf(r, digits) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } static int RemoveDigit(int[] digits, int le, int idx) { int[] pows = { 1, 10, 100, 1000, 10000 }; var sum = 0; var pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } static void Main() { var lims = new int[,] { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; var count = new int[5]; var omitted = new int[5, 10]; var upperBound = lims.GetLength(0); for (int i = 0; i < upperBound; i++) { var nDigits = new int[i + 2]; var dDigits = new int[i + 2]; var blank = new int[i + 2]; for (int n = lims[i, 0]; n <= lims[i, 1]; n++) { blank.CopyTo(nDigits, 0); var nOk = GetDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i, 1] + 1; d++) { blank.CopyTo(dDigits, 0); var dOk = GetDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.Length; nix++) { var digit = nDigits[nix]; var dix = IndexOf(digit, dDigits); if (dix >= 0) { var rn = RemoveDigit(nDigits, i + 2, nix); var rd = RemoveDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i, digit]++; if (count[i] <= 12) { Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4}'s", n, d, rn, rd, digit); } } } } } } Console.WriteLine(); } for (int i = 2; i <= 5; i++) { Console.WriteLine("There are {0} {1}-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2, j] == 0) { continue; } Console.WriteLine("{0,6} have {1}'s omitted", omitted[i - 2, j], j); } Console.WriteLine(); } } } }
Generate a C++ translation of this Haskell snippet without changing its computational steps.
import Control.Monad (guard) import Data.List (intersect, unfoldr, delete, nub, group, sort) import Text.Printf (printf) type Fraction = (Int, Int) type Reduction = (Fraction, Fraction, Int) validIntegers :: [Int] -> [Int] validIntegers xs = [x | x <- xs, not $ hasZeros x, hasUniqueDigits x] where hasZeros = elem 0 . digits 10 hasUniqueDigits n = length ds == length ul where ds = digits 10 n ul = nub ds possibleFractions :: [Int] -> [Fraction] possibleFractions = (\ys -> [(n,d) | n <- ys, d <- ys, n < d, gcd n d /= 1]) . validIntegers digits :: Integral a => a -> a -> [a] digits b = unfoldr (\n -> guard (n /= 0) >> pure (n `mod` b, n `div` b)) digitsToIntegral :: Integral a => [a] -> a digitsToIntegral = sum . zipWith (*) (iterate (*10) 1) findReductions :: Fraction -> [Reduction] findReductions z@(n1, d1) = [ (z, (n2, d2), x) | x <- digits 10 n1 `intersect` digits 10 d1, let n2 = dropDigit x n1 d2 = dropDigit x d1 decimalWithDrop = realToFrac n2 / realToFrac d2, decimalWithDrop == decimal ] where dropDigit d = digitsToIntegral . delete d . digits 10 decimal = realToFrac n1 / realToFrac d1 findGroupReductions :: [Int] -> [Reduction] findGroupReductions = (findReductions =<<) . possibleFractions showReduction :: Reduction -> IO () showReduction ((n1,d1),(n2,d2),d) = printf "%d/%d = %d/%d by dropping %d\n" n1 d1 n2 d2 d showCount :: [Reduction] -> Int -> IO () showCount xs n = do printf "There are %d %d-digit fractions of which:\n" (length xs) n mapM_ (uncurry (printf "%5d have %d's omitted\n")) (countReductions xs) >> printf "\n" where countReductions = fmap ((,) . length <*> head) . group . sort . fmap (\(_, _, x) -> x) main :: IO () main = do mapM_ (\g -> mapM_ showReduction (take 12 g) >> printf "\n") groups mapM_ (uncurry showCount) $ zip groups [2..] where groups = [ findGroupReductions [10^1..99], findGroupReductions [10^2..999] , findGroupReductions [10^3..9999], findGroupReductions [10^4..99999] ]
#include <array> #include <iomanip> #include <iostream> #include <vector> int indexOf(const std::vector<int> &haystack, int needle) { auto it = haystack.cbegin(); auto end = haystack.cend(); int idx = 0; for (; it != end; it = std::next(it)) { if (*it == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, std::vector<int> &digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(const std::vector<int> &digits, int le, int idx) { static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 }; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } int main() { std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }; std::array<int, 5> count; std::array<std::array<int, 10>, 5> omitted; std::fill(count.begin(), count.end(), 0); std::for_each(omitted.begin(), omitted.end(), [](auto &a) { std::fill(a.begin(), a.end(), 0); } ); for (size_t i = 0; i < lims.size(); i++) { std::vector<int> nDigits(i + 2); std::vector<int> dDigits(i + 2); for (int n = lims[i].first; n <= lims[i].second; n++) { std::fill(nDigits.begin(), nDigits.end(), 0); bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i].second + 1; d++) { std::fill(dDigits.begin(), dDigits.end(), 0); bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (size_t nix = 0; nix < nDigits.size(); nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n"; } } } } } } std::cout << '\n'; } for (int i = 2; i <= 5; i++) { std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n"; for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n"; } std::cout << '\n'; } return 0; }
Convert this Haskell block to Java, preserving its control flow and logic.
import Control.Monad (guard) import Data.List (intersect, unfoldr, delete, nub, group, sort) import Text.Printf (printf) type Fraction = (Int, Int) type Reduction = (Fraction, Fraction, Int) validIntegers :: [Int] -> [Int] validIntegers xs = [x | x <- xs, not $ hasZeros x, hasUniqueDigits x] where hasZeros = elem 0 . digits 10 hasUniqueDigits n = length ds == length ul where ds = digits 10 n ul = nub ds possibleFractions :: [Int] -> [Fraction] possibleFractions = (\ys -> [(n,d) | n <- ys, d <- ys, n < d, gcd n d /= 1]) . validIntegers digits :: Integral a => a -> a -> [a] digits b = unfoldr (\n -> guard (n /= 0) >> pure (n `mod` b, n `div` b)) digitsToIntegral :: Integral a => [a] -> a digitsToIntegral = sum . zipWith (*) (iterate (*10) 1) findReductions :: Fraction -> [Reduction] findReductions z@(n1, d1) = [ (z, (n2, d2), x) | x <- digits 10 n1 `intersect` digits 10 d1, let n2 = dropDigit x n1 d2 = dropDigit x d1 decimalWithDrop = realToFrac n2 / realToFrac d2, decimalWithDrop == decimal ] where dropDigit d = digitsToIntegral . delete d . digits 10 decimal = realToFrac n1 / realToFrac d1 findGroupReductions :: [Int] -> [Reduction] findGroupReductions = (findReductions =<<) . possibleFractions showReduction :: Reduction -> IO () showReduction ((n1,d1),(n2,d2),d) = printf "%d/%d = %d/%d by dropping %d\n" n1 d1 n2 d2 d showCount :: [Reduction] -> Int -> IO () showCount xs n = do printf "There are %d %d-digit fractions of which:\n" (length xs) n mapM_ (uncurry (printf "%5d have %d's omitted\n")) (countReductions xs) >> printf "\n" where countReductions = fmap ((,) . length <*> head) . group . sort . fmap (\(_, _, x) -> x) main :: IO () main = do mapM_ (\g -> mapM_ showReduction (take 12 g) >> printf "\n") groups mapM_ (uncurry showCount) $ zip groups [2..] where groups = [ findGroupReductions [10^1..99], findGroupReductions [10^2..999] , findGroupReductions [10^3..9999], findGroupReductions [10^4..99999] ]
import java.util.ArrayList; import java.util.Collections; import java.util.HashMap; import java.util.List; import java.util.Map; public class FractionReduction { public static void main(String[] args) { for ( int size = 2 ; size <= 5 ; size++ ) { reduce(size); } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits); int min = (int) Math.pow(10, numDigits-1); int max = (int) Math.pow(10, numDigits) - 1; List<Integer> values = new ArrayList<>(); for ( int number = min ; number <= max ; number++ ) { if ( isValid(number) ) { values.add(number); } } Map<Integer,Integer> cancelCount = new HashMap<>(); int size = values.size(); int solutions = 0; for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) { int numerator = values.get(nIndex); for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) { int denominator = values.get(dIndex); for ( int commonDigit : digitsInCommon(numerator, denominator) ) { int numRemoved = removeDigit(numerator, commonDigit); int denRemoved = removeDigit(denominator, commonDigit); if ( numerator * denRemoved == denominator * numRemoved ) { solutions++; cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2); if ( solutions <= 12 ) { System.out.printf(" When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved); } } } } } System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions); List<Integer> sorted = new ArrayList<>(cancelCount.keySet()); Collections.sort(sorted); for ( int removed : sorted ) { System.out.printf(" The digit %d was removed %d times.%n", removed, cancelCount.get(removed)); } System.out.println(); } private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000}; private static int removeDigit(int n, int removed) { int m = 0; int pow = 0; while ( n > 0 ) { int r = n % 10; if ( r != removed ) { m = m + r*powers[pow]; pow++; } n /= 10; } return m; } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10]; List<Integer> common = new ArrayList<>(); while ( n1 > 0 ) { int r = n1 % 10; count[r] += 1; n1 /= 10; } while ( n2 > 0 ) { int r = n2 % 10; if ( count[r] > 0 ) { common.add(r); } n2 /= 10; } return common; } private static boolean isValid(int num) { int[] count = new int[10]; while ( num > 0 ) { int r = num % 10; if ( r == 0 || count[r] == 1 ) { return false; } count[r] = 1; num /= 10; } return true; } }
Produce a language-to-language conversion: from Haskell to Python, same semantics.
import Control.Monad (guard) import Data.List (intersect, unfoldr, delete, nub, group, sort) import Text.Printf (printf) type Fraction = (Int, Int) type Reduction = (Fraction, Fraction, Int) validIntegers :: [Int] -> [Int] validIntegers xs = [x | x <- xs, not $ hasZeros x, hasUniqueDigits x] where hasZeros = elem 0 . digits 10 hasUniqueDigits n = length ds == length ul where ds = digits 10 n ul = nub ds possibleFractions :: [Int] -> [Fraction] possibleFractions = (\ys -> [(n,d) | n <- ys, d <- ys, n < d, gcd n d /= 1]) . validIntegers digits :: Integral a => a -> a -> [a] digits b = unfoldr (\n -> guard (n /= 0) >> pure (n `mod` b, n `div` b)) digitsToIntegral :: Integral a => [a] -> a digitsToIntegral = sum . zipWith (*) (iterate (*10) 1) findReductions :: Fraction -> [Reduction] findReductions z@(n1, d1) = [ (z, (n2, d2), x) | x <- digits 10 n1 `intersect` digits 10 d1, let n2 = dropDigit x n1 d2 = dropDigit x d1 decimalWithDrop = realToFrac n2 / realToFrac d2, decimalWithDrop == decimal ] where dropDigit d = digitsToIntegral . delete d . digits 10 decimal = realToFrac n1 / realToFrac d1 findGroupReductions :: [Int] -> [Reduction] findGroupReductions = (findReductions =<<) . possibleFractions showReduction :: Reduction -> IO () showReduction ((n1,d1),(n2,d2),d) = printf "%d/%d = %d/%d by dropping %d\n" n1 d1 n2 d2 d showCount :: [Reduction] -> Int -> IO () showCount xs n = do printf "There are %d %d-digit fractions of which:\n" (length xs) n mapM_ (uncurry (printf "%5d have %d's omitted\n")) (countReductions xs) >> printf "\n" where countReductions = fmap ((,) . length <*> head) . group . sort . fmap (\(_, _, x) -> x) main :: IO () main = do mapM_ (\g -> mapM_ showReduction (take 12 g) >> printf "\n") groups mapM_ (uncurry showCount) $ zip groups [2..] where groups = [ findGroupReductions [10^1..99], findGroupReductions [10^2..999] , findGroupReductions [10^3..9999], findGroupReductions [10^4..99999] ]
def indexOf(haystack, needle): idx = 0 for straw in haystack: if straw == needle: return idx else: idx += 1 return -1 def getDigits(n, le, digits): while n > 0: r = n % 10 if r == 0 or indexOf(digits, r) >= 0: return False le -= 1 digits[le] = r n = int(n / 10) return True def removeDigit(digits, le, idx): pows = [1, 10, 100, 1000, 10000] sum = 0 pow = pows[le - 2] i = 0 while i < le: if i == idx: i += 1 continue sum = sum + digits[i] * pow pow = int(pow / 10) i += 1 return sum def main(): lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = [0 for i in range(5)] omitted = [[0 for i in range(10)] for j in range(5)] i = 0 while i < len(lims): n = lims[i][0] while n < lims[i][1]: nDigits = [0 for k in range(i + 2)] nOk = getDigits(n, i + 2, nDigits) if not nOk: n += 1 continue d = n + 1 while d <= lims[i][1] + 1: dDigits = [0 for k in range(i + 2)] dOk = getDigits(d, i + 2, dDigits) if not dOk: d += 1 continue nix = 0 while nix < len(nDigits): digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0: rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd): count[i] += 1 omitted[i][digit] += 1 if count[i] <= 12: print "%d/%d = %d/%d by omitting %d's" % (n, d, rn, rd, digit) nix += 1 d += 1 n += 1 print i += 1 i = 2 while i <= 5: print "There are %d %d-digit fractions of which:" % (count[i - 2], i) j = 1 while j <= 9: if omitted[i - 2][j] == 0: j += 1 continue print "%6s have %d's omitted" % (omitted[i - 2][j], j) j += 1 print i += 1 return None main()
Write the same code in VB as shown below in Haskell.
import Control.Monad (guard) import Data.List (intersect, unfoldr, delete, nub, group, sort) import Text.Printf (printf) type Fraction = (Int, Int) type Reduction = (Fraction, Fraction, Int) validIntegers :: [Int] -> [Int] validIntegers xs = [x | x <- xs, not $ hasZeros x, hasUniqueDigits x] where hasZeros = elem 0 . digits 10 hasUniqueDigits n = length ds == length ul where ds = digits 10 n ul = nub ds possibleFractions :: [Int] -> [Fraction] possibleFractions = (\ys -> [(n,d) | n <- ys, d <- ys, n < d, gcd n d /= 1]) . validIntegers digits :: Integral a => a -> a -> [a] digits b = unfoldr (\n -> guard (n /= 0) >> pure (n `mod` b, n `div` b)) digitsToIntegral :: Integral a => [a] -> a digitsToIntegral = sum . zipWith (*) (iterate (*10) 1) findReductions :: Fraction -> [Reduction] findReductions z@(n1, d1) = [ (z, (n2, d2), x) | x <- digits 10 n1 `intersect` digits 10 d1, let n2 = dropDigit x n1 d2 = dropDigit x d1 decimalWithDrop = realToFrac n2 / realToFrac d2, decimalWithDrop == decimal ] where dropDigit d = digitsToIntegral . delete d . digits 10 decimal = realToFrac n1 / realToFrac d1 findGroupReductions :: [Int] -> [Reduction] findGroupReductions = (findReductions =<<) . possibleFractions showReduction :: Reduction -> IO () showReduction ((n1,d1),(n2,d2),d) = printf "%d/%d = %d/%d by dropping %d\n" n1 d1 n2 d2 d showCount :: [Reduction] -> Int -> IO () showCount xs n = do printf "There are %d %d-digit fractions of which:\n" (length xs) n mapM_ (uncurry (printf "%5d have %d's omitted\n")) (countReductions xs) >> printf "\n" where countReductions = fmap ((,) . length <*> head) . group . sort . fmap (\(_, _, x) -> x) main :: IO () main = do mapM_ (\g -> mapM_ showReduction (take 12 g) >> printf "\n") groups mapM_ (uncurry showCount) $ zip groups [2..] where groups = [ findGroupReductions [10^1..99], findGroupReductions [10^2..999] , findGroupReductions [10^3..9999], findGroupReductions [10^4..99999] ]
Module Module1 Function IndexOf(n As Integer, s As Integer()) As Integer For ii = 1 To s.Length Dim i = ii - 1 If s(i) = n Then Return i End If Next Return -1 End Function Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean While n > 0 Dim r = n Mod 10 If r = 0 OrElse IndexOf(r, digits) >= 0 Then Return False End If le -= 1 digits(le) = r n \= 10 End While Return True End Function Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer Dim pows = {1, 10, 100, 1000, 10000} Dim sum = 0 Dim pow = pows(le - 2) For ii = 1 To le Dim i = ii - 1 If i = idx Then Continue For End If sum += digits(i) * pow pow \= 10 Next Return sum End Function Sub Main() Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}} Dim count(5) As Integer Dim omitted(5, 10) As Integer Dim upperBound = lims.GetLength(0) For ii = 1 To upperBound Dim i = ii - 1 Dim nDigits(i + 2 - 1) As Integer Dim dDigits(i + 2 - 1) As Integer Dim blank(i + 2 - 1) As Integer For n = lims(i, 0) To lims(i, 1) blank.CopyTo(nDigits, 0) Dim nOk = GetDigits(n, i + 2, nDigits) If Not nOk Then Continue For End If For d = n + 1 To lims(i, 1) + 1 blank.CopyTo(dDigits, 0) Dim dOk = GetDigits(d, i + 2, dDigits) If Not dOk Then Continue For End If For nixt = 1 To nDigits.Length Dim nix = nixt - 1 Dim digit = nDigits(nix) Dim dix = IndexOf(digit, dDigits) If dix >= 0 Then Dim rn = RemoveDigit(nDigits, i + 2, nix) Dim rd = RemoveDigit(dDigits, i + 2, dix) If (n / d) = (rn / rd) Then count(i) += 1 omitted(i, digit) += 1 If count(i) <= 12 Then Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4} End If End If End If Next Next Next Console.WriteLine() Next For i = 2 To 5 Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i) For j = 1 To 9 If omitted(i - 2, j) = 0 Then Continue For End If Console.WriteLine("{0,6} have {1} Next Console.WriteLine() Next End Sub End Module
Generate an equivalent Go version of this Haskell code.
import Control.Monad (guard) import Data.List (intersect, unfoldr, delete, nub, group, sort) import Text.Printf (printf) type Fraction = (Int, Int) type Reduction = (Fraction, Fraction, Int) validIntegers :: [Int] -> [Int] validIntegers xs = [x | x <- xs, not $ hasZeros x, hasUniqueDigits x] where hasZeros = elem 0 . digits 10 hasUniqueDigits n = length ds == length ul where ds = digits 10 n ul = nub ds possibleFractions :: [Int] -> [Fraction] possibleFractions = (\ys -> [(n,d) | n <- ys, d <- ys, n < d, gcd n d /= 1]) . validIntegers digits :: Integral a => a -> a -> [a] digits b = unfoldr (\n -> guard (n /= 0) >> pure (n `mod` b, n `div` b)) digitsToIntegral :: Integral a => [a] -> a digitsToIntegral = sum . zipWith (*) (iterate (*10) 1) findReductions :: Fraction -> [Reduction] findReductions z@(n1, d1) = [ (z, (n2, d2), x) | x <- digits 10 n1 `intersect` digits 10 d1, let n2 = dropDigit x n1 d2 = dropDigit x d1 decimalWithDrop = realToFrac n2 / realToFrac d2, decimalWithDrop == decimal ] where dropDigit d = digitsToIntegral . delete d . digits 10 decimal = realToFrac n1 / realToFrac d1 findGroupReductions :: [Int] -> [Reduction] findGroupReductions = (findReductions =<<) . possibleFractions showReduction :: Reduction -> IO () showReduction ((n1,d1),(n2,d2),d) = printf "%d/%d = %d/%d by dropping %d\n" n1 d1 n2 d2 d showCount :: [Reduction] -> Int -> IO () showCount xs n = do printf "There are %d %d-digit fractions of which:\n" (length xs) n mapM_ (uncurry (printf "%5d have %d's omitted\n")) (countReductions xs) >> printf "\n" where countReductions = fmap ((,) . length <*> head) . group . sort . fmap (\(_, _, x) -> x) main :: IO () main = do mapM_ (\g -> mapM_ showReduction (take 12 g) >> printf "\n") groups mapM_ (uncurry showCount) $ zip groups [2..] where groups = [ findGroupReductions [10^1..99], findGroupReductions [10^2..999] , findGroupReductions [10^3..9999], findGroupReductions [10^4..99999] ]
package main import ( "fmt" "time" ) func indexOf(n int, s []int) int { for i, j := range s { if n == j { return i } } return -1 } func getDigits(n, le int, digits []int) bool { for n > 0 { r := n % 10 if r == 0 || indexOf(r, digits) >= 0 { return false } le-- digits[le] = r n /= 10 } return true } var pows = [5]int{1, 10, 100, 1000, 10000} func removeDigit(digits []int, le, idx int) int { sum := 0 pow := pows[le-2] for i := 0; i < le; i++ { if i == idx { continue } sum += digits[i] * pow pow /= 10 } return sum } func main() { start := time.Now() lims := [5][2]int{ {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}, {123456, 987653}, } var count [5]int var omitted [5][10]int for i, lim := range lims { nDigits := make([]int, i+2) dDigits := make([]int, i+2) blank := make([]int, i+2) for n := lim[0]; n <= lim[1]; n++ { copy(nDigits, blank) nOk := getDigits(n, i+2, nDigits) if !nOk { continue } for d := n + 1; d <= lim[1]+1; d++ { copy(dDigits, blank) dOk := getDigits(d, i+2, dDigits) if !dOk { continue } for nix, digit := range nDigits { if dix := indexOf(digit, dDigits); dix >= 0 { rn := removeDigit(nDigits, i+2, nix) rd := removeDigit(dDigits, i+2, dix) if float64(n)/float64(d) == float64(rn)/float64(rd) { count[i]++ omitted[i][digit]++ if count[i] <= 12 { fmt.Printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit) } } } } } } fmt.Println() } for i := 2; i <= 6; i++ { fmt.Printf("There are %d %d-digit fractions of which:\n", count[i-2], i) for j := 1; j <= 9; j++ { if omitted[i-2][j] == 0 { continue } fmt.Printf("%6d have %d's omitted\n", omitted[i-2][j], j) } fmt.Println() } fmt.Printf("Took %s\n", time.Since(start)) }
Please provide an equivalent version of this J code in C.
Filter=: (#~`)(`:6) assert 'ac' -: 1 0 1"_ Filter 'abc' intersect=:-.^:2 assert 'ab' -: 'abc'intersect'razb' odometer=: (4$.$.)@:($&1) Note 'odometer 2 3' 0 0 0 1 0 2 1 0 1 1 1 2 ) common=: 0 e. ~: assert common 1 2 1 assert -. common 1 2 3 o=: '123456789' {~ [: -.@:common"1 Filter odometer@:(#&9) f=: ,:"1/&g~ mask=: [: </~&i. # av=: (([: , mask) # ,/)@:f c=: [: common@:,/"2 Filter av fac=: [: ([: common ,&:~.&:q:&:"./)"2 Filter c cancellation=: monad define NDL =. c y ND =. ". NDL MASK=. ([: common ,&:~.&:q:/)"1 ND FRAC=. _2 x: MASK # ND CANDIDATES=. MASK # NDL rat=. , 'r'&, result=. 0 3 $ a: for_i. i. # CANDIDATES do. fraction =. i { FRAC pair=. i { CANDIDATES for_d. intersect/ pair do. trial=. pair -."1 d if. fraction = _2 x: ". trial do. result =. result , (rat/pair) ; (rat/trial) ; d end. end. end. result )
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }
Convert this J snippet to C# and keep its semantics consistent.
Filter=: (#~`)(`:6) assert 'ac' -: 1 0 1"_ Filter 'abc' intersect=:-.^:2 assert 'ab' -: 'abc'intersect'razb' odometer=: (4$.$.)@:($&1) Note 'odometer 2 3' 0 0 0 1 0 2 1 0 1 1 1 2 ) common=: 0 e. ~: assert common 1 2 1 assert -. common 1 2 3 o=: '123456789' {~ [: -.@:common"1 Filter odometer@:(#&9) f=: ,:"1/&g~ mask=: [: </~&i. # av=: (([: , mask) # ,/)@:f c=: [: common@:,/"2 Filter av fac=: [: ([: common ,&:~.&:q:&:"./)"2 Filter c cancellation=: monad define NDL =. c y ND =. ". NDL MASK=. ([: common ,&:~.&:q:/)"1 ND FRAC=. _2 x: MASK # ND CANDIDATES=. MASK # NDL rat=. , 'r'&, result=. 0 3 $ a: for_i. i. # CANDIDATES do. fraction =. i { FRAC pair=. i { CANDIDATES for_d. intersect/ pair do. trial=. pair -."1 d if. fraction = _2 x: ". trial do. result =. result , (rat/pair) ; (rat/trial) ; d end. end. end. result )
using System; namespace FractionReduction { class Program { static int IndexOf(int n, int[] s) { for (int i = 0; i < s.Length; i++) { if (s[i] == n) { return i; } } return -1; } static bool GetDigits(int n, int le, int[] digits) { while (n > 0) { var r = n % 10; if (r == 0 || IndexOf(r, digits) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } static int RemoveDigit(int[] digits, int le, int idx) { int[] pows = { 1, 10, 100, 1000, 10000 }; var sum = 0; var pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } static void Main() { var lims = new int[,] { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; var count = new int[5]; var omitted = new int[5, 10]; var upperBound = lims.GetLength(0); for (int i = 0; i < upperBound; i++) { var nDigits = new int[i + 2]; var dDigits = new int[i + 2]; var blank = new int[i + 2]; for (int n = lims[i, 0]; n <= lims[i, 1]; n++) { blank.CopyTo(nDigits, 0); var nOk = GetDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i, 1] + 1; d++) { blank.CopyTo(dDigits, 0); var dOk = GetDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.Length; nix++) { var digit = nDigits[nix]; var dix = IndexOf(digit, dDigits); if (dix >= 0) { var rn = RemoveDigit(nDigits, i + 2, nix); var rd = RemoveDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i, digit]++; if (count[i] <= 12) { Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4}'s", n, d, rn, rd, digit); } } } } } } Console.WriteLine(); } for (int i = 2; i <= 5; i++) { Console.WriteLine("There are {0} {1}-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2, j] == 0) { continue; } Console.WriteLine("{0,6} have {1}'s omitted", omitted[i - 2, j], j); } Console.WriteLine(); } } } }
Port the provided J code into C++ while preserving the original functionality.
Filter=: (#~`)(`:6) assert 'ac' -: 1 0 1"_ Filter 'abc' intersect=:-.^:2 assert 'ab' -: 'abc'intersect'razb' odometer=: (4$.$.)@:($&1) Note 'odometer 2 3' 0 0 0 1 0 2 1 0 1 1 1 2 ) common=: 0 e. ~: assert common 1 2 1 assert -. common 1 2 3 o=: '123456789' {~ [: -.@:common"1 Filter odometer@:(#&9) f=: ,:"1/&g~ mask=: [: </~&i. # av=: (([: , mask) # ,/)@:f c=: [: common@:,/"2 Filter av fac=: [: ([: common ,&:~.&:q:&:"./)"2 Filter c cancellation=: monad define NDL =. c y ND =. ". NDL MASK=. ([: common ,&:~.&:q:/)"1 ND FRAC=. _2 x: MASK # ND CANDIDATES=. MASK # NDL rat=. , 'r'&, result=. 0 3 $ a: for_i. i. # CANDIDATES do. fraction =. i { FRAC pair=. i { CANDIDATES for_d. intersect/ pair do. trial=. pair -."1 d if. fraction = _2 x: ". trial do. result =. result , (rat/pair) ; (rat/trial) ; d end. end. end. result )
#include <array> #include <iomanip> #include <iostream> #include <vector> int indexOf(const std::vector<int> &haystack, int needle) { auto it = haystack.cbegin(); auto end = haystack.cend(); int idx = 0; for (; it != end; it = std::next(it)) { if (*it == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, std::vector<int> &digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(const std::vector<int> &digits, int le, int idx) { static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 }; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } int main() { std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }; std::array<int, 5> count; std::array<std::array<int, 10>, 5> omitted; std::fill(count.begin(), count.end(), 0); std::for_each(omitted.begin(), omitted.end(), [](auto &a) { std::fill(a.begin(), a.end(), 0); } ); for (size_t i = 0; i < lims.size(); i++) { std::vector<int> nDigits(i + 2); std::vector<int> dDigits(i + 2); for (int n = lims[i].first; n <= lims[i].second; n++) { std::fill(nDigits.begin(), nDigits.end(), 0); bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i].second + 1; d++) { std::fill(dDigits.begin(), dDigits.end(), 0); bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (size_t nix = 0; nix < nDigits.size(); nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n"; } } } } } } std::cout << '\n'; } for (int i = 2; i <= 5; i++) { std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n"; for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n"; } std::cout << '\n'; } return 0; }
Port the following code from J to Java with equivalent syntax and logic.
Filter=: (#~`)(`:6) assert 'ac' -: 1 0 1"_ Filter 'abc' intersect=:-.^:2 assert 'ab' -: 'abc'intersect'razb' odometer=: (4$.$.)@:($&1) Note 'odometer 2 3' 0 0 0 1 0 2 1 0 1 1 1 2 ) common=: 0 e. ~: assert common 1 2 1 assert -. common 1 2 3 o=: '123456789' {~ [: -.@:common"1 Filter odometer@:(#&9) f=: ,:"1/&g~ mask=: [: </~&i. # av=: (([: , mask) # ,/)@:f c=: [: common@:,/"2 Filter av fac=: [: ([: common ,&:~.&:q:&:"./)"2 Filter c cancellation=: monad define NDL =. c y ND =. ". NDL MASK=. ([: common ,&:~.&:q:/)"1 ND FRAC=. _2 x: MASK # ND CANDIDATES=. MASK # NDL rat=. , 'r'&, result=. 0 3 $ a: for_i. i. # CANDIDATES do. fraction =. i { FRAC pair=. i { CANDIDATES for_d. intersect/ pair do. trial=. pair -."1 d if. fraction = _2 x: ". trial do. result =. result , (rat/pair) ; (rat/trial) ; d end. end. end. result )
import java.util.ArrayList; import java.util.Collections; import java.util.HashMap; import java.util.List; import java.util.Map; public class FractionReduction { public static void main(String[] args) { for ( int size = 2 ; size <= 5 ; size++ ) { reduce(size); } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits); int min = (int) Math.pow(10, numDigits-1); int max = (int) Math.pow(10, numDigits) - 1; List<Integer> values = new ArrayList<>(); for ( int number = min ; number <= max ; number++ ) { if ( isValid(number) ) { values.add(number); } } Map<Integer,Integer> cancelCount = new HashMap<>(); int size = values.size(); int solutions = 0; for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) { int numerator = values.get(nIndex); for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) { int denominator = values.get(dIndex); for ( int commonDigit : digitsInCommon(numerator, denominator) ) { int numRemoved = removeDigit(numerator, commonDigit); int denRemoved = removeDigit(denominator, commonDigit); if ( numerator * denRemoved == denominator * numRemoved ) { solutions++; cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2); if ( solutions <= 12 ) { System.out.printf(" When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved); } } } } } System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions); List<Integer> sorted = new ArrayList<>(cancelCount.keySet()); Collections.sort(sorted); for ( int removed : sorted ) { System.out.printf(" The digit %d was removed %d times.%n", removed, cancelCount.get(removed)); } System.out.println(); } private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000}; private static int removeDigit(int n, int removed) { int m = 0; int pow = 0; while ( n > 0 ) { int r = n % 10; if ( r != removed ) { m = m + r*powers[pow]; pow++; } n /= 10; } return m; } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10]; List<Integer> common = new ArrayList<>(); while ( n1 > 0 ) { int r = n1 % 10; count[r] += 1; n1 /= 10; } while ( n2 > 0 ) { int r = n2 % 10; if ( count[r] > 0 ) { common.add(r); } n2 /= 10; } return common; } private static boolean isValid(int num) { int[] count = new int[10]; while ( num > 0 ) { int r = num % 10; if ( r == 0 || count[r] == 1 ) { return false; } count[r] = 1; num /= 10; } return true; } }
Translate this program into Python but keep the logic exactly as in J.
Filter=: (#~`)(`:6) assert 'ac' -: 1 0 1"_ Filter 'abc' intersect=:-.^:2 assert 'ab' -: 'abc'intersect'razb' odometer=: (4$.$.)@:($&1) Note 'odometer 2 3' 0 0 0 1 0 2 1 0 1 1 1 2 ) common=: 0 e. ~: assert common 1 2 1 assert -. common 1 2 3 o=: '123456789' {~ [: -.@:common"1 Filter odometer@:(#&9) f=: ,:"1/&g~ mask=: [: </~&i. # av=: (([: , mask) # ,/)@:f c=: [: common@:,/"2 Filter av fac=: [: ([: common ,&:~.&:q:&:"./)"2 Filter c cancellation=: monad define NDL =. c y ND =. ". NDL MASK=. ([: common ,&:~.&:q:/)"1 ND FRAC=. _2 x: MASK # ND CANDIDATES=. MASK # NDL rat=. , 'r'&, result=. 0 3 $ a: for_i. i. # CANDIDATES do. fraction =. i { FRAC pair=. i { CANDIDATES for_d. intersect/ pair do. trial=. pair -."1 d if. fraction = _2 x: ". trial do. result =. result , (rat/pair) ; (rat/trial) ; d end. end. end. result )
def indexOf(haystack, needle): idx = 0 for straw in haystack: if straw == needle: return idx else: idx += 1 return -1 def getDigits(n, le, digits): while n > 0: r = n % 10 if r == 0 or indexOf(digits, r) >= 0: return False le -= 1 digits[le] = r n = int(n / 10) return True def removeDigit(digits, le, idx): pows = [1, 10, 100, 1000, 10000] sum = 0 pow = pows[le - 2] i = 0 while i < le: if i == idx: i += 1 continue sum = sum + digits[i] * pow pow = int(pow / 10) i += 1 return sum def main(): lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = [0 for i in range(5)] omitted = [[0 for i in range(10)] for j in range(5)] i = 0 while i < len(lims): n = lims[i][0] while n < lims[i][1]: nDigits = [0 for k in range(i + 2)] nOk = getDigits(n, i + 2, nDigits) if not nOk: n += 1 continue d = n + 1 while d <= lims[i][1] + 1: dDigits = [0 for k in range(i + 2)] dOk = getDigits(d, i + 2, dDigits) if not dOk: d += 1 continue nix = 0 while nix < len(nDigits): digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0: rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd): count[i] += 1 omitted[i][digit] += 1 if count[i] <= 12: print "%d/%d = %d/%d by omitting %d's" % (n, d, rn, rd, digit) nix += 1 d += 1 n += 1 print i += 1 i = 2 while i <= 5: print "There are %d %d-digit fractions of which:" % (count[i - 2], i) j = 1 while j <= 9: if omitted[i - 2][j] == 0: j += 1 continue print "%6s have %d's omitted" % (omitted[i - 2][j], j) j += 1 print i += 1 return None main()
Please provide an equivalent version of this J code in VB.
Filter=: (#~`)(`:6) assert 'ac' -: 1 0 1"_ Filter 'abc' intersect=:-.^:2 assert 'ab' -: 'abc'intersect'razb' odometer=: (4$.$.)@:($&1) Note 'odometer 2 3' 0 0 0 1 0 2 1 0 1 1 1 2 ) common=: 0 e. ~: assert common 1 2 1 assert -. common 1 2 3 o=: '123456789' {~ [: -.@:common"1 Filter odometer@:(#&9) f=: ,:"1/&g~ mask=: [: </~&i. # av=: (([: , mask) # ,/)@:f c=: [: common@:,/"2 Filter av fac=: [: ([: common ,&:~.&:q:&:"./)"2 Filter c cancellation=: monad define NDL =. c y ND =. ". NDL MASK=. ([: common ,&:~.&:q:/)"1 ND FRAC=. _2 x: MASK # ND CANDIDATES=. MASK # NDL rat=. , 'r'&, result=. 0 3 $ a: for_i. i. # CANDIDATES do. fraction =. i { FRAC pair=. i { CANDIDATES for_d. intersect/ pair do. trial=. pair -."1 d if. fraction = _2 x: ". trial do. result =. result , (rat/pair) ; (rat/trial) ; d end. end. end. result )
Module Module1 Function IndexOf(n As Integer, s As Integer()) As Integer For ii = 1 To s.Length Dim i = ii - 1 If s(i) = n Then Return i End If Next Return -1 End Function Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean While n > 0 Dim r = n Mod 10 If r = 0 OrElse IndexOf(r, digits) >= 0 Then Return False End If le -= 1 digits(le) = r n \= 10 End While Return True End Function Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer Dim pows = {1, 10, 100, 1000, 10000} Dim sum = 0 Dim pow = pows(le - 2) For ii = 1 To le Dim i = ii - 1 If i = idx Then Continue For End If sum += digits(i) * pow pow \= 10 Next Return sum End Function Sub Main() Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}} Dim count(5) As Integer Dim omitted(5, 10) As Integer Dim upperBound = lims.GetLength(0) For ii = 1 To upperBound Dim i = ii - 1 Dim nDigits(i + 2 - 1) As Integer Dim dDigits(i + 2 - 1) As Integer Dim blank(i + 2 - 1) As Integer For n = lims(i, 0) To lims(i, 1) blank.CopyTo(nDigits, 0) Dim nOk = GetDigits(n, i + 2, nDigits) If Not nOk Then Continue For End If For d = n + 1 To lims(i, 1) + 1 blank.CopyTo(dDigits, 0) Dim dOk = GetDigits(d, i + 2, dDigits) If Not dOk Then Continue For End If For nixt = 1 To nDigits.Length Dim nix = nixt - 1 Dim digit = nDigits(nix) Dim dix = IndexOf(digit, dDigits) If dix >= 0 Then Dim rn = RemoveDigit(nDigits, i + 2, nix) Dim rd = RemoveDigit(dDigits, i + 2, dix) If (n / d) = (rn / rd) Then count(i) += 1 omitted(i, digit) += 1 If count(i) <= 12 Then Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4} End If End If End If Next Next Next Console.WriteLine() Next For i = 2 To 5 Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i) For j = 1 To 9 If omitted(i - 2, j) = 0 Then Continue For End If Console.WriteLine("{0,6} have {1} Next Console.WriteLine() Next End Sub End Module
Write the same algorithm in Go as shown in this J implementation.
Filter=: (#~`)(`:6) assert 'ac' -: 1 0 1"_ Filter 'abc' intersect=:-.^:2 assert 'ab' -: 'abc'intersect'razb' odometer=: (4$.$.)@:($&1) Note 'odometer 2 3' 0 0 0 1 0 2 1 0 1 1 1 2 ) common=: 0 e. ~: assert common 1 2 1 assert -. common 1 2 3 o=: '123456789' {~ [: -.@:common"1 Filter odometer@:(#&9) f=: ,:"1/&g~ mask=: [: </~&i. # av=: (([: , mask) # ,/)@:f c=: [: common@:,/"2 Filter av fac=: [: ([: common ,&:~.&:q:&:"./)"2 Filter c cancellation=: monad define NDL =. c y ND =. ". NDL MASK=. ([: common ,&:~.&:q:/)"1 ND FRAC=. _2 x: MASK # ND CANDIDATES=. MASK # NDL rat=. , 'r'&, result=. 0 3 $ a: for_i. i. # CANDIDATES do. fraction =. i { FRAC pair=. i { CANDIDATES for_d. intersect/ pair do. trial=. pair -."1 d if. fraction = _2 x: ". trial do. result =. result , (rat/pair) ; (rat/trial) ; d end. end. end. result )
package main import ( "fmt" "time" ) func indexOf(n int, s []int) int { for i, j := range s { if n == j { return i } } return -1 } func getDigits(n, le int, digits []int) bool { for n > 0 { r := n % 10 if r == 0 || indexOf(r, digits) >= 0 { return false } le-- digits[le] = r n /= 10 } return true } var pows = [5]int{1, 10, 100, 1000, 10000} func removeDigit(digits []int, le, idx int) int { sum := 0 pow := pows[le-2] for i := 0; i < le; i++ { if i == idx { continue } sum += digits[i] * pow pow /= 10 } return sum } func main() { start := time.Now() lims := [5][2]int{ {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}, {123456, 987653}, } var count [5]int var omitted [5][10]int for i, lim := range lims { nDigits := make([]int, i+2) dDigits := make([]int, i+2) blank := make([]int, i+2) for n := lim[0]; n <= lim[1]; n++ { copy(nDigits, blank) nOk := getDigits(n, i+2, nDigits) if !nOk { continue } for d := n + 1; d <= lim[1]+1; d++ { copy(dDigits, blank) dOk := getDigits(d, i+2, dDigits) if !dOk { continue } for nix, digit := range nDigits { if dix := indexOf(digit, dDigits); dix >= 0 { rn := removeDigit(nDigits, i+2, nix) rd := removeDigit(dDigits, i+2, dix) if float64(n)/float64(d) == float64(rn)/float64(rd) { count[i]++ omitted[i][digit]++ if count[i] <= 12 { fmt.Printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit) } } } } } } fmt.Println() } for i := 2; i <= 6; i++ { fmt.Printf("There are %d %d-digit fractions of which:\n", count[i-2], i) for j := 1; j <= 9; j++ { if omitted[i-2][j] == 0 { continue } fmt.Printf("%6d have %d's omitted\n", omitted[i-2][j], j) } fmt.Println() } fmt.Printf("Took %s\n", time.Since(start)) }
Preserve the algorithm and functionality while converting the code from Julia to C.
using Combinatorics toi(set) = parse(Int, join(set, "")) drop1(c, set) = toi(filter(x -> x != c, set)) function anomalouscancellingfractions(numdigits) ret = Vector{Tuple{Int, Int, Int, Int, Int}}() for nset in permutations(1:9, numdigits), dset in permutations(1:9, numdigits) if nset < dset for c in nset if c in dset n, d, nn, dd = toi(nset), toi(dset), drop1(c, nset), drop1(c, dset) if n // d == nn // dd push!(ret, (n, d, nn, dd, c)) end end end end end ret end function testfractionreduction(maxdigits=5) for i in 2:maxdigits results = anomalouscancellingfractions(i) println("\nFor $i digits, there were ", length(results), " fractions with anomalous cancellation.") numcounts = zeros(Int, 9) for r in results numcounts[r[5]] += 1 end for (j, count) in enumerate(numcounts) count > 0 && println("The digit $j was crossed out $count times.") end println("Examples:") for j in 1:min(length(results), 12) r = results[j] println(r[1], "/", r[2], " = ", r[3], "/", r[4], " ($(r[5]) crossed out)") end end end testfractionreduction()
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }
Produce a language-to-language conversion: from Julia to C#, same semantics.
using Combinatorics toi(set) = parse(Int, join(set, "")) drop1(c, set) = toi(filter(x -> x != c, set)) function anomalouscancellingfractions(numdigits) ret = Vector{Tuple{Int, Int, Int, Int, Int}}() for nset in permutations(1:9, numdigits), dset in permutations(1:9, numdigits) if nset < dset for c in nset if c in dset n, d, nn, dd = toi(nset), toi(dset), drop1(c, nset), drop1(c, dset) if n // d == nn // dd push!(ret, (n, d, nn, dd, c)) end end end end end ret end function testfractionreduction(maxdigits=5) for i in 2:maxdigits results = anomalouscancellingfractions(i) println("\nFor $i digits, there were ", length(results), " fractions with anomalous cancellation.") numcounts = zeros(Int, 9) for r in results numcounts[r[5]] += 1 end for (j, count) in enumerate(numcounts) count > 0 && println("The digit $j was crossed out $count times.") end println("Examples:") for j in 1:min(length(results), 12) r = results[j] println(r[1], "/", r[2], " = ", r[3], "/", r[4], " ($(r[5]) crossed out)") end end end testfractionreduction()
using System; namespace FractionReduction { class Program { static int IndexOf(int n, int[] s) { for (int i = 0; i < s.Length; i++) { if (s[i] == n) { return i; } } return -1; } static bool GetDigits(int n, int le, int[] digits) { while (n > 0) { var r = n % 10; if (r == 0 || IndexOf(r, digits) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } static int RemoveDigit(int[] digits, int le, int idx) { int[] pows = { 1, 10, 100, 1000, 10000 }; var sum = 0; var pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } static void Main() { var lims = new int[,] { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; var count = new int[5]; var omitted = new int[5, 10]; var upperBound = lims.GetLength(0); for (int i = 0; i < upperBound; i++) { var nDigits = new int[i + 2]; var dDigits = new int[i + 2]; var blank = new int[i + 2]; for (int n = lims[i, 0]; n <= lims[i, 1]; n++) { blank.CopyTo(nDigits, 0); var nOk = GetDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i, 1] + 1; d++) { blank.CopyTo(dDigits, 0); var dOk = GetDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.Length; nix++) { var digit = nDigits[nix]; var dix = IndexOf(digit, dDigits); if (dix >= 0) { var rn = RemoveDigit(nDigits, i + 2, nix); var rd = RemoveDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i, digit]++; if (count[i] <= 12) { Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4}'s", n, d, rn, rd, digit); } } } } } } Console.WriteLine(); } for (int i = 2; i <= 5; i++) { Console.WriteLine("There are {0} {1}-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2, j] == 0) { continue; } Console.WriteLine("{0,6} have {1}'s omitted", omitted[i - 2, j], j); } Console.WriteLine(); } } } }
Maintain the same structure and functionality when rewriting this code in C++.
using Combinatorics toi(set) = parse(Int, join(set, "")) drop1(c, set) = toi(filter(x -> x != c, set)) function anomalouscancellingfractions(numdigits) ret = Vector{Tuple{Int, Int, Int, Int, Int}}() for nset in permutations(1:9, numdigits), dset in permutations(1:9, numdigits) if nset < dset for c in nset if c in dset n, d, nn, dd = toi(nset), toi(dset), drop1(c, nset), drop1(c, dset) if n // d == nn // dd push!(ret, (n, d, nn, dd, c)) end end end end end ret end function testfractionreduction(maxdigits=5) for i in 2:maxdigits results = anomalouscancellingfractions(i) println("\nFor $i digits, there were ", length(results), " fractions with anomalous cancellation.") numcounts = zeros(Int, 9) for r in results numcounts[r[5]] += 1 end for (j, count) in enumerate(numcounts) count > 0 && println("The digit $j was crossed out $count times.") end println("Examples:") for j in 1:min(length(results), 12) r = results[j] println(r[1], "/", r[2], " = ", r[3], "/", r[4], " ($(r[5]) crossed out)") end end end testfractionreduction()
#include <array> #include <iomanip> #include <iostream> #include <vector> int indexOf(const std::vector<int> &haystack, int needle) { auto it = haystack.cbegin(); auto end = haystack.cend(); int idx = 0; for (; it != end; it = std::next(it)) { if (*it == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, std::vector<int> &digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(const std::vector<int> &digits, int le, int idx) { static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 }; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } int main() { std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }; std::array<int, 5> count; std::array<std::array<int, 10>, 5> omitted; std::fill(count.begin(), count.end(), 0); std::for_each(omitted.begin(), omitted.end(), [](auto &a) { std::fill(a.begin(), a.end(), 0); } ); for (size_t i = 0; i < lims.size(); i++) { std::vector<int> nDigits(i + 2); std::vector<int> dDigits(i + 2); for (int n = lims[i].first; n <= lims[i].second; n++) { std::fill(nDigits.begin(), nDigits.end(), 0); bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i].second + 1; d++) { std::fill(dDigits.begin(), dDigits.end(), 0); bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (size_t nix = 0; nix < nDigits.size(); nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n"; } } } } } } std::cout << '\n'; } for (int i = 2; i <= 5; i++) { std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n"; for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n"; } std::cout << '\n'; } return 0; }
Generate a Java translation of this Julia snippet without changing its computational steps.
using Combinatorics toi(set) = parse(Int, join(set, "")) drop1(c, set) = toi(filter(x -> x != c, set)) function anomalouscancellingfractions(numdigits) ret = Vector{Tuple{Int, Int, Int, Int, Int}}() for nset in permutations(1:9, numdigits), dset in permutations(1:9, numdigits) if nset < dset for c in nset if c in dset n, d, nn, dd = toi(nset), toi(dset), drop1(c, nset), drop1(c, dset) if n // d == nn // dd push!(ret, (n, d, nn, dd, c)) end end end end end ret end function testfractionreduction(maxdigits=5) for i in 2:maxdigits results = anomalouscancellingfractions(i) println("\nFor $i digits, there were ", length(results), " fractions with anomalous cancellation.") numcounts = zeros(Int, 9) for r in results numcounts[r[5]] += 1 end for (j, count) in enumerate(numcounts) count > 0 && println("The digit $j was crossed out $count times.") end println("Examples:") for j in 1:min(length(results), 12) r = results[j] println(r[1], "/", r[2], " = ", r[3], "/", r[4], " ($(r[5]) crossed out)") end end end testfractionreduction()
import java.util.ArrayList; import java.util.Collections; import java.util.HashMap; import java.util.List; import java.util.Map; public class FractionReduction { public static void main(String[] args) { for ( int size = 2 ; size <= 5 ; size++ ) { reduce(size); } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits); int min = (int) Math.pow(10, numDigits-1); int max = (int) Math.pow(10, numDigits) - 1; List<Integer> values = new ArrayList<>(); for ( int number = min ; number <= max ; number++ ) { if ( isValid(number) ) { values.add(number); } } Map<Integer,Integer> cancelCount = new HashMap<>(); int size = values.size(); int solutions = 0; for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) { int numerator = values.get(nIndex); for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) { int denominator = values.get(dIndex); for ( int commonDigit : digitsInCommon(numerator, denominator) ) { int numRemoved = removeDigit(numerator, commonDigit); int denRemoved = removeDigit(denominator, commonDigit); if ( numerator * denRemoved == denominator * numRemoved ) { solutions++; cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2); if ( solutions <= 12 ) { System.out.printf(" When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved); } } } } } System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions); List<Integer> sorted = new ArrayList<>(cancelCount.keySet()); Collections.sort(sorted); for ( int removed : sorted ) { System.out.printf(" The digit %d was removed %d times.%n", removed, cancelCount.get(removed)); } System.out.println(); } private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000}; private static int removeDigit(int n, int removed) { int m = 0; int pow = 0; while ( n > 0 ) { int r = n % 10; if ( r != removed ) { m = m + r*powers[pow]; pow++; } n /= 10; } return m; } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10]; List<Integer> common = new ArrayList<>(); while ( n1 > 0 ) { int r = n1 % 10; count[r] += 1; n1 /= 10; } while ( n2 > 0 ) { int r = n2 % 10; if ( count[r] > 0 ) { common.add(r); } n2 /= 10; } return common; } private static boolean isValid(int num) { int[] count = new int[10]; while ( num > 0 ) { int r = num % 10; if ( r == 0 || count[r] == 1 ) { return false; } count[r] = 1; num /= 10; } return true; } }
Transform the following Julia implementation into Python, maintaining the same output and logic.
using Combinatorics toi(set) = parse(Int, join(set, "")) drop1(c, set) = toi(filter(x -> x != c, set)) function anomalouscancellingfractions(numdigits) ret = Vector{Tuple{Int, Int, Int, Int, Int}}() for nset in permutations(1:9, numdigits), dset in permutations(1:9, numdigits) if nset < dset for c in nset if c in dset n, d, nn, dd = toi(nset), toi(dset), drop1(c, nset), drop1(c, dset) if n // d == nn // dd push!(ret, (n, d, nn, dd, c)) end end end end end ret end function testfractionreduction(maxdigits=5) for i in 2:maxdigits results = anomalouscancellingfractions(i) println("\nFor $i digits, there were ", length(results), " fractions with anomalous cancellation.") numcounts = zeros(Int, 9) for r in results numcounts[r[5]] += 1 end for (j, count) in enumerate(numcounts) count > 0 && println("The digit $j was crossed out $count times.") end println("Examples:") for j in 1:min(length(results), 12) r = results[j] println(r[1], "/", r[2], " = ", r[3], "/", r[4], " ($(r[5]) crossed out)") end end end testfractionreduction()
def indexOf(haystack, needle): idx = 0 for straw in haystack: if straw == needle: return idx else: idx += 1 return -1 def getDigits(n, le, digits): while n > 0: r = n % 10 if r == 0 or indexOf(digits, r) >= 0: return False le -= 1 digits[le] = r n = int(n / 10) return True def removeDigit(digits, le, idx): pows = [1, 10, 100, 1000, 10000] sum = 0 pow = pows[le - 2] i = 0 while i < le: if i == idx: i += 1 continue sum = sum + digits[i] * pow pow = int(pow / 10) i += 1 return sum def main(): lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = [0 for i in range(5)] omitted = [[0 for i in range(10)] for j in range(5)] i = 0 while i < len(lims): n = lims[i][0] while n < lims[i][1]: nDigits = [0 for k in range(i + 2)] nOk = getDigits(n, i + 2, nDigits) if not nOk: n += 1 continue d = n + 1 while d <= lims[i][1] + 1: dDigits = [0 for k in range(i + 2)] dOk = getDigits(d, i + 2, dDigits) if not dOk: d += 1 continue nix = 0 while nix < len(nDigits): digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0: rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd): count[i] += 1 omitted[i][digit] += 1 if count[i] <= 12: print "%d/%d = %d/%d by omitting %d's" % (n, d, rn, rd, digit) nix += 1 d += 1 n += 1 print i += 1 i = 2 while i <= 5: print "There are %d %d-digit fractions of which:" % (count[i - 2], i) j = 1 while j <= 9: if omitted[i - 2][j] == 0: j += 1 continue print "%6s have %d's omitted" % (omitted[i - 2][j], j) j += 1 print i += 1 return None main()
Change the programming language of this snippet from Julia to VB without modifying what it does.
using Combinatorics toi(set) = parse(Int, join(set, "")) drop1(c, set) = toi(filter(x -> x != c, set)) function anomalouscancellingfractions(numdigits) ret = Vector{Tuple{Int, Int, Int, Int, Int}}() for nset in permutations(1:9, numdigits), dset in permutations(1:9, numdigits) if nset < dset for c in nset if c in dset n, d, nn, dd = toi(nset), toi(dset), drop1(c, nset), drop1(c, dset) if n // d == nn // dd push!(ret, (n, d, nn, dd, c)) end end end end end ret end function testfractionreduction(maxdigits=5) for i in 2:maxdigits results = anomalouscancellingfractions(i) println("\nFor $i digits, there were ", length(results), " fractions with anomalous cancellation.") numcounts = zeros(Int, 9) for r in results numcounts[r[5]] += 1 end for (j, count) in enumerate(numcounts) count > 0 && println("The digit $j was crossed out $count times.") end println("Examples:") for j in 1:min(length(results), 12) r = results[j] println(r[1], "/", r[2], " = ", r[3], "/", r[4], " ($(r[5]) crossed out)") end end end testfractionreduction()
Module Module1 Function IndexOf(n As Integer, s As Integer()) As Integer For ii = 1 To s.Length Dim i = ii - 1 If s(i) = n Then Return i End If Next Return -1 End Function Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean While n > 0 Dim r = n Mod 10 If r = 0 OrElse IndexOf(r, digits) >= 0 Then Return False End If le -= 1 digits(le) = r n \= 10 End While Return True End Function Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer Dim pows = {1, 10, 100, 1000, 10000} Dim sum = 0 Dim pow = pows(le - 2) For ii = 1 To le Dim i = ii - 1 If i = idx Then Continue For End If sum += digits(i) * pow pow \= 10 Next Return sum End Function Sub Main() Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}} Dim count(5) As Integer Dim omitted(5, 10) As Integer Dim upperBound = lims.GetLength(0) For ii = 1 To upperBound Dim i = ii - 1 Dim nDigits(i + 2 - 1) As Integer Dim dDigits(i + 2 - 1) As Integer Dim blank(i + 2 - 1) As Integer For n = lims(i, 0) To lims(i, 1) blank.CopyTo(nDigits, 0) Dim nOk = GetDigits(n, i + 2, nDigits) If Not nOk Then Continue For End If For d = n + 1 To lims(i, 1) + 1 blank.CopyTo(dDigits, 0) Dim dOk = GetDigits(d, i + 2, dDigits) If Not dOk Then Continue For End If For nixt = 1 To nDigits.Length Dim nix = nixt - 1 Dim digit = nDigits(nix) Dim dix = IndexOf(digit, dDigits) If dix >= 0 Then Dim rn = RemoveDigit(nDigits, i + 2, nix) Dim rd = RemoveDigit(dDigits, i + 2, dix) If (n / d) = (rn / rd) Then count(i) += 1 omitted(i, digit) += 1 If count(i) <= 12 Then Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4} End If End If End If Next Next Next Console.WriteLine() Next For i = 2 To 5 Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i) For j = 1 To 9 If omitted(i - 2, j) = 0 Then Continue For End If Console.WriteLine("{0,6} have {1} Next Console.WriteLine() Next End Sub End Module
Produce a functionally identical Go code for the snippet given in Julia.
using Combinatorics toi(set) = parse(Int, join(set, "")) drop1(c, set) = toi(filter(x -> x != c, set)) function anomalouscancellingfractions(numdigits) ret = Vector{Tuple{Int, Int, Int, Int, Int}}() for nset in permutations(1:9, numdigits), dset in permutations(1:9, numdigits) if nset < dset for c in nset if c in dset n, d, nn, dd = toi(nset), toi(dset), drop1(c, nset), drop1(c, dset) if n // d == nn // dd push!(ret, (n, d, nn, dd, c)) end end end end end ret end function testfractionreduction(maxdigits=5) for i in 2:maxdigits results = anomalouscancellingfractions(i) println("\nFor $i digits, there were ", length(results), " fractions with anomalous cancellation.") numcounts = zeros(Int, 9) for r in results numcounts[r[5]] += 1 end for (j, count) in enumerate(numcounts) count > 0 && println("The digit $j was crossed out $count times.") end println("Examples:") for j in 1:min(length(results), 12) r = results[j] println(r[1], "/", r[2], " = ", r[3], "/", r[4], " ($(r[5]) crossed out)") end end end testfractionreduction()
package main import ( "fmt" "time" ) func indexOf(n int, s []int) int { for i, j := range s { if n == j { return i } } return -1 } func getDigits(n, le int, digits []int) bool { for n > 0 { r := n % 10 if r == 0 || indexOf(r, digits) >= 0 { return false } le-- digits[le] = r n /= 10 } return true } var pows = [5]int{1, 10, 100, 1000, 10000} func removeDigit(digits []int, le, idx int) int { sum := 0 pow := pows[le-2] for i := 0; i < le; i++ { if i == idx { continue } sum += digits[i] * pow pow /= 10 } return sum } func main() { start := time.Now() lims := [5][2]int{ {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}, {123456, 987653}, } var count [5]int var omitted [5][10]int for i, lim := range lims { nDigits := make([]int, i+2) dDigits := make([]int, i+2) blank := make([]int, i+2) for n := lim[0]; n <= lim[1]; n++ { copy(nDigits, blank) nOk := getDigits(n, i+2, nDigits) if !nOk { continue } for d := n + 1; d <= lim[1]+1; d++ { copy(dDigits, blank) dOk := getDigits(d, i+2, dDigits) if !dOk { continue } for nix, digit := range nDigits { if dix := indexOf(digit, dDigits); dix >= 0 { rn := removeDigit(nDigits, i+2, nix) rd := removeDigit(dDigits, i+2, dix) if float64(n)/float64(d) == float64(rn)/float64(rd) { count[i]++ omitted[i][digit]++ if count[i] <= 12 { fmt.Printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit) } } } } } } fmt.Println() } for i := 2; i <= 6; i++ { fmt.Printf("There are %d %d-digit fractions of which:\n", count[i-2], i) for j := 1; j <= 9; j++ { if omitted[i-2][j] == 0 { continue } fmt.Printf("%6d have %d's omitted\n", omitted[i-2][j], j) } fmt.Println() } fmt.Printf("Took %s\n", time.Since(start)) }
Maintain the same structure and functionality when rewriting this code in C.
function indexOf(haystack, needle) for idx,straw in pairs(haystack) do if straw == needle then return idx end end return -1 end function getDigits(n, le, digits) while n > 0 do local r = n % 10 if r == 0 or indexOf(digits, r) > 0 then return false end le = le - 1 digits[le + 1] = r n = math.floor(n / 10) end return true end function removeDigit(digits, le, idx) local pows = { 1, 10, 100, 1000, 10000 } local sum = 0 local pow = pows[le - 2 + 1] for i = 1, le do if i ~= idx then sum = sum + digits[i] * pow pow = math.floor(pow / 10) end end return sum end function main() local lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} } local count = { 0, 0, 0, 0, 0 } local omitted = { { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, } for i,_ in pairs(lims) do local nDigits = {} local dDigits = {} for j = 1, i + 2 - 1 do nDigits[j] = -1 dDigits[j] = -1 end for n = lims[i][1], lims[i][2] do for j,_ in pairs(nDigits) do nDigits[j] = 0 end local nOk = getDigits(n, i + 2 - 1, nDigits) if nOk then for d = n + 1, lims[i][2] + 1 do for j,_ in pairs(dDigits) do dDigits[j] = 0 end local dOk = getDigits(d, i + 2 - 1, dDigits) if dOk then for nix,_ in pairs(nDigits) do local digit = nDigits[nix] local dix = indexOf(dDigits, digit) if dix >= 0 then local rn = removeDigit(nDigits, i + 2 - 1, nix) local rd = removeDigit(dDigits, i + 2 - 1, dix) if (n / d) == (rn / rd) then count[i] = count[i] + 1 omitted[i][digit + 1] = omitted[i][digit + 1] + 1 if count[i] <= 12 then print(string.format("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit)) end end end end end end end end print() end for i = 2, 5 do print("There are "..count[i - 2 + 1].." "..i.."-digit fractions of which:") for j = 1, 9 do if omitted[i - 2 + 1][j + 1] > 0 then print(string.format("%6d have %d's omitted", omitted[i - 2 + 1][j + 1], j)) end end print() end end main()
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }
Maintain the same structure and functionality when rewriting this code in C#.
function indexOf(haystack, needle) for idx,straw in pairs(haystack) do if straw == needle then return idx end end return -1 end function getDigits(n, le, digits) while n > 0 do local r = n % 10 if r == 0 or indexOf(digits, r) > 0 then return false end le = le - 1 digits[le + 1] = r n = math.floor(n / 10) end return true end function removeDigit(digits, le, idx) local pows = { 1, 10, 100, 1000, 10000 } local sum = 0 local pow = pows[le - 2 + 1] for i = 1, le do if i ~= idx then sum = sum + digits[i] * pow pow = math.floor(pow / 10) end end return sum end function main() local lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} } local count = { 0, 0, 0, 0, 0 } local omitted = { { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, } for i,_ in pairs(lims) do local nDigits = {} local dDigits = {} for j = 1, i + 2 - 1 do nDigits[j] = -1 dDigits[j] = -1 end for n = lims[i][1], lims[i][2] do for j,_ in pairs(nDigits) do nDigits[j] = 0 end local nOk = getDigits(n, i + 2 - 1, nDigits) if nOk then for d = n + 1, lims[i][2] + 1 do for j,_ in pairs(dDigits) do dDigits[j] = 0 end local dOk = getDigits(d, i + 2 - 1, dDigits) if dOk then for nix,_ in pairs(nDigits) do local digit = nDigits[nix] local dix = indexOf(dDigits, digit) if dix >= 0 then local rn = removeDigit(nDigits, i + 2 - 1, nix) local rd = removeDigit(dDigits, i + 2 - 1, dix) if (n / d) == (rn / rd) then count[i] = count[i] + 1 omitted[i][digit + 1] = omitted[i][digit + 1] + 1 if count[i] <= 12 then print(string.format("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit)) end end end end end end end end print() end for i = 2, 5 do print("There are "..count[i - 2 + 1].." "..i.."-digit fractions of which:") for j = 1, 9 do if omitted[i - 2 + 1][j + 1] > 0 then print(string.format("%6d have %d's omitted", omitted[i - 2 + 1][j + 1], j)) end end print() end end main()
using System; namespace FractionReduction { class Program { static int IndexOf(int n, int[] s) { for (int i = 0; i < s.Length; i++) { if (s[i] == n) { return i; } } return -1; } static bool GetDigits(int n, int le, int[] digits) { while (n > 0) { var r = n % 10; if (r == 0 || IndexOf(r, digits) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } static int RemoveDigit(int[] digits, int le, int idx) { int[] pows = { 1, 10, 100, 1000, 10000 }; var sum = 0; var pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } static void Main() { var lims = new int[,] { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; var count = new int[5]; var omitted = new int[5, 10]; var upperBound = lims.GetLength(0); for (int i = 0; i < upperBound; i++) { var nDigits = new int[i + 2]; var dDigits = new int[i + 2]; var blank = new int[i + 2]; for (int n = lims[i, 0]; n <= lims[i, 1]; n++) { blank.CopyTo(nDigits, 0); var nOk = GetDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i, 1] + 1; d++) { blank.CopyTo(dDigits, 0); var dOk = GetDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.Length; nix++) { var digit = nDigits[nix]; var dix = IndexOf(digit, dDigits); if (dix >= 0) { var rn = RemoveDigit(nDigits, i + 2, nix); var rd = RemoveDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i, digit]++; if (count[i] <= 12) { Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4}'s", n, d, rn, rd, digit); } } } } } } Console.WriteLine(); } for (int i = 2; i <= 5; i++) { Console.WriteLine("There are {0} {1}-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2, j] == 0) { continue; } Console.WriteLine("{0,6} have {1}'s omitted", omitted[i - 2, j], j); } Console.WriteLine(); } } } }
Rewrite the snippet below in C++ so it works the same as the original Lua code.
function indexOf(haystack, needle) for idx,straw in pairs(haystack) do if straw == needle then return idx end end return -1 end function getDigits(n, le, digits) while n > 0 do local r = n % 10 if r == 0 or indexOf(digits, r) > 0 then return false end le = le - 1 digits[le + 1] = r n = math.floor(n / 10) end return true end function removeDigit(digits, le, idx) local pows = { 1, 10, 100, 1000, 10000 } local sum = 0 local pow = pows[le - 2 + 1] for i = 1, le do if i ~= idx then sum = sum + digits[i] * pow pow = math.floor(pow / 10) end end return sum end function main() local lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} } local count = { 0, 0, 0, 0, 0 } local omitted = { { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, } for i,_ in pairs(lims) do local nDigits = {} local dDigits = {} for j = 1, i + 2 - 1 do nDigits[j] = -1 dDigits[j] = -1 end for n = lims[i][1], lims[i][2] do for j,_ in pairs(nDigits) do nDigits[j] = 0 end local nOk = getDigits(n, i + 2 - 1, nDigits) if nOk then for d = n + 1, lims[i][2] + 1 do for j,_ in pairs(dDigits) do dDigits[j] = 0 end local dOk = getDigits(d, i + 2 - 1, dDigits) if dOk then for nix,_ in pairs(nDigits) do local digit = nDigits[nix] local dix = indexOf(dDigits, digit) if dix >= 0 then local rn = removeDigit(nDigits, i + 2 - 1, nix) local rd = removeDigit(dDigits, i + 2 - 1, dix) if (n / d) == (rn / rd) then count[i] = count[i] + 1 omitted[i][digit + 1] = omitted[i][digit + 1] + 1 if count[i] <= 12 then print(string.format("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit)) end end end end end end end end print() end for i = 2, 5 do print("There are "..count[i - 2 + 1].." "..i.."-digit fractions of which:") for j = 1, 9 do if omitted[i - 2 + 1][j + 1] > 0 then print(string.format("%6d have %d's omitted", omitted[i - 2 + 1][j + 1], j)) end end print() end end main()
#include <array> #include <iomanip> #include <iostream> #include <vector> int indexOf(const std::vector<int> &haystack, int needle) { auto it = haystack.cbegin(); auto end = haystack.cend(); int idx = 0; for (; it != end; it = std::next(it)) { if (*it == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, std::vector<int> &digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(const std::vector<int> &digits, int le, int idx) { static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 }; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } int main() { std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }; std::array<int, 5> count; std::array<std::array<int, 10>, 5> omitted; std::fill(count.begin(), count.end(), 0); std::for_each(omitted.begin(), omitted.end(), [](auto &a) { std::fill(a.begin(), a.end(), 0); } ); for (size_t i = 0; i < lims.size(); i++) { std::vector<int> nDigits(i + 2); std::vector<int> dDigits(i + 2); for (int n = lims[i].first; n <= lims[i].second; n++) { std::fill(nDigits.begin(), nDigits.end(), 0); bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i].second + 1; d++) { std::fill(dDigits.begin(), dDigits.end(), 0); bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (size_t nix = 0; nix < nDigits.size(); nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n"; } } } } } } std::cout << '\n'; } for (int i = 2; i <= 5; i++) { std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n"; for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n"; } std::cout << '\n'; } return 0; }
Preserve the algorithm and functionality while converting the code from Lua to Java.
function indexOf(haystack, needle) for idx,straw in pairs(haystack) do if straw == needle then return idx end end return -1 end function getDigits(n, le, digits) while n > 0 do local r = n % 10 if r == 0 or indexOf(digits, r) > 0 then return false end le = le - 1 digits[le + 1] = r n = math.floor(n / 10) end return true end function removeDigit(digits, le, idx) local pows = { 1, 10, 100, 1000, 10000 } local sum = 0 local pow = pows[le - 2 + 1] for i = 1, le do if i ~= idx then sum = sum + digits[i] * pow pow = math.floor(pow / 10) end end return sum end function main() local lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} } local count = { 0, 0, 0, 0, 0 } local omitted = { { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, } for i,_ in pairs(lims) do local nDigits = {} local dDigits = {} for j = 1, i + 2 - 1 do nDigits[j] = -1 dDigits[j] = -1 end for n = lims[i][1], lims[i][2] do for j,_ in pairs(nDigits) do nDigits[j] = 0 end local nOk = getDigits(n, i + 2 - 1, nDigits) if nOk then for d = n + 1, lims[i][2] + 1 do for j,_ in pairs(dDigits) do dDigits[j] = 0 end local dOk = getDigits(d, i + 2 - 1, dDigits) if dOk then for nix,_ in pairs(nDigits) do local digit = nDigits[nix] local dix = indexOf(dDigits, digit) if dix >= 0 then local rn = removeDigit(nDigits, i + 2 - 1, nix) local rd = removeDigit(dDigits, i + 2 - 1, dix) if (n / d) == (rn / rd) then count[i] = count[i] + 1 omitted[i][digit + 1] = omitted[i][digit + 1] + 1 if count[i] <= 12 then print(string.format("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit)) end end end end end end end end print() end for i = 2, 5 do print("There are "..count[i - 2 + 1].." "..i.."-digit fractions of which:") for j = 1, 9 do if omitted[i - 2 + 1][j + 1] > 0 then print(string.format("%6d have %d's omitted", omitted[i - 2 + 1][j + 1], j)) end end print() end end main()
import java.util.ArrayList; import java.util.Collections; import java.util.HashMap; import java.util.List; import java.util.Map; public class FractionReduction { public static void main(String[] args) { for ( int size = 2 ; size <= 5 ; size++ ) { reduce(size); } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits); int min = (int) Math.pow(10, numDigits-1); int max = (int) Math.pow(10, numDigits) - 1; List<Integer> values = new ArrayList<>(); for ( int number = min ; number <= max ; number++ ) { if ( isValid(number) ) { values.add(number); } } Map<Integer,Integer> cancelCount = new HashMap<>(); int size = values.size(); int solutions = 0; for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) { int numerator = values.get(nIndex); for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) { int denominator = values.get(dIndex); for ( int commonDigit : digitsInCommon(numerator, denominator) ) { int numRemoved = removeDigit(numerator, commonDigit); int denRemoved = removeDigit(denominator, commonDigit); if ( numerator * denRemoved == denominator * numRemoved ) { solutions++; cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2); if ( solutions <= 12 ) { System.out.printf(" When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved); } } } } } System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions); List<Integer> sorted = new ArrayList<>(cancelCount.keySet()); Collections.sort(sorted); for ( int removed : sorted ) { System.out.printf(" The digit %d was removed %d times.%n", removed, cancelCount.get(removed)); } System.out.println(); } private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000}; private static int removeDigit(int n, int removed) { int m = 0; int pow = 0; while ( n > 0 ) { int r = n % 10; if ( r != removed ) { m = m + r*powers[pow]; pow++; } n /= 10; } return m; } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10]; List<Integer> common = new ArrayList<>(); while ( n1 > 0 ) { int r = n1 % 10; count[r] += 1; n1 /= 10; } while ( n2 > 0 ) { int r = n2 % 10; if ( count[r] > 0 ) { common.add(r); } n2 /= 10; } return common; } private static boolean isValid(int num) { int[] count = new int[10]; while ( num > 0 ) { int r = num % 10; if ( r == 0 || count[r] == 1 ) { return false; } count[r] = 1; num /= 10; } return true; } }
Please provide an equivalent version of this Lua code in Python.
function indexOf(haystack, needle) for idx,straw in pairs(haystack) do if straw == needle then return idx end end return -1 end function getDigits(n, le, digits) while n > 0 do local r = n % 10 if r == 0 or indexOf(digits, r) > 0 then return false end le = le - 1 digits[le + 1] = r n = math.floor(n / 10) end return true end function removeDigit(digits, le, idx) local pows = { 1, 10, 100, 1000, 10000 } local sum = 0 local pow = pows[le - 2 + 1] for i = 1, le do if i ~= idx then sum = sum + digits[i] * pow pow = math.floor(pow / 10) end end return sum end function main() local lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} } local count = { 0, 0, 0, 0, 0 } local omitted = { { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, } for i,_ in pairs(lims) do local nDigits = {} local dDigits = {} for j = 1, i + 2 - 1 do nDigits[j] = -1 dDigits[j] = -1 end for n = lims[i][1], lims[i][2] do for j,_ in pairs(nDigits) do nDigits[j] = 0 end local nOk = getDigits(n, i + 2 - 1, nDigits) if nOk then for d = n + 1, lims[i][2] + 1 do for j,_ in pairs(dDigits) do dDigits[j] = 0 end local dOk = getDigits(d, i + 2 - 1, dDigits) if dOk then for nix,_ in pairs(nDigits) do local digit = nDigits[nix] local dix = indexOf(dDigits, digit) if dix >= 0 then local rn = removeDigit(nDigits, i + 2 - 1, nix) local rd = removeDigit(dDigits, i + 2 - 1, dix) if (n / d) == (rn / rd) then count[i] = count[i] + 1 omitted[i][digit + 1] = omitted[i][digit + 1] + 1 if count[i] <= 12 then print(string.format("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit)) end end end end end end end end print() end for i = 2, 5 do print("There are "..count[i - 2 + 1].." "..i.."-digit fractions of which:") for j = 1, 9 do if omitted[i - 2 + 1][j + 1] > 0 then print(string.format("%6d have %d's omitted", omitted[i - 2 + 1][j + 1], j)) end end print() end end main()
def indexOf(haystack, needle): idx = 0 for straw in haystack: if straw == needle: return idx else: idx += 1 return -1 def getDigits(n, le, digits): while n > 0: r = n % 10 if r == 0 or indexOf(digits, r) >= 0: return False le -= 1 digits[le] = r n = int(n / 10) return True def removeDigit(digits, le, idx): pows = [1, 10, 100, 1000, 10000] sum = 0 pow = pows[le - 2] i = 0 while i < le: if i == idx: i += 1 continue sum = sum + digits[i] * pow pow = int(pow / 10) i += 1 return sum def main(): lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = [0 for i in range(5)] omitted = [[0 for i in range(10)] for j in range(5)] i = 0 while i < len(lims): n = lims[i][0] while n < lims[i][1]: nDigits = [0 for k in range(i + 2)] nOk = getDigits(n, i + 2, nDigits) if not nOk: n += 1 continue d = n + 1 while d <= lims[i][1] + 1: dDigits = [0 for k in range(i + 2)] dOk = getDigits(d, i + 2, dDigits) if not dOk: d += 1 continue nix = 0 while nix < len(nDigits): digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0: rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd): count[i] += 1 omitted[i][digit] += 1 if count[i] <= 12: print "%d/%d = %d/%d by omitting %d's" % (n, d, rn, rd, digit) nix += 1 d += 1 n += 1 print i += 1 i = 2 while i <= 5: print "There are %d %d-digit fractions of which:" % (count[i - 2], i) j = 1 while j <= 9: if omitted[i - 2][j] == 0: j += 1 continue print "%6s have %d's omitted" % (omitted[i - 2][j], j) j += 1 print i += 1 return None main()
Write the same code in VB as shown below in Lua.
function indexOf(haystack, needle) for idx,straw in pairs(haystack) do if straw == needle then return idx end end return -1 end function getDigits(n, le, digits) while n > 0 do local r = n % 10 if r == 0 or indexOf(digits, r) > 0 then return false end le = le - 1 digits[le + 1] = r n = math.floor(n / 10) end return true end function removeDigit(digits, le, idx) local pows = { 1, 10, 100, 1000, 10000 } local sum = 0 local pow = pows[le - 2 + 1] for i = 1, le do if i ~= idx then sum = sum + digits[i] * pow pow = math.floor(pow / 10) end end return sum end function main() local lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} } local count = { 0, 0, 0, 0, 0 } local omitted = { { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, } for i,_ in pairs(lims) do local nDigits = {} local dDigits = {} for j = 1, i + 2 - 1 do nDigits[j] = -1 dDigits[j] = -1 end for n = lims[i][1], lims[i][2] do for j,_ in pairs(nDigits) do nDigits[j] = 0 end local nOk = getDigits(n, i + 2 - 1, nDigits) if nOk then for d = n + 1, lims[i][2] + 1 do for j,_ in pairs(dDigits) do dDigits[j] = 0 end local dOk = getDigits(d, i + 2 - 1, dDigits) if dOk then for nix,_ in pairs(nDigits) do local digit = nDigits[nix] local dix = indexOf(dDigits, digit) if dix >= 0 then local rn = removeDigit(nDigits, i + 2 - 1, nix) local rd = removeDigit(dDigits, i + 2 - 1, dix) if (n / d) == (rn / rd) then count[i] = count[i] + 1 omitted[i][digit + 1] = omitted[i][digit + 1] + 1 if count[i] <= 12 then print(string.format("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit)) end end end end end end end end print() end for i = 2, 5 do print("There are "..count[i - 2 + 1].." "..i.."-digit fractions of which:") for j = 1, 9 do if omitted[i - 2 + 1][j + 1] > 0 then print(string.format("%6d have %d's omitted", omitted[i - 2 + 1][j + 1], j)) end end print() end end main()
Module Module1 Function IndexOf(n As Integer, s As Integer()) As Integer For ii = 1 To s.Length Dim i = ii - 1 If s(i) = n Then Return i End If Next Return -1 End Function Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean While n > 0 Dim r = n Mod 10 If r = 0 OrElse IndexOf(r, digits) >= 0 Then Return False End If le -= 1 digits(le) = r n \= 10 End While Return True End Function Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer Dim pows = {1, 10, 100, 1000, 10000} Dim sum = 0 Dim pow = pows(le - 2) For ii = 1 To le Dim i = ii - 1 If i = idx Then Continue For End If sum += digits(i) * pow pow \= 10 Next Return sum End Function Sub Main() Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}} Dim count(5) As Integer Dim omitted(5, 10) As Integer Dim upperBound = lims.GetLength(0) For ii = 1 To upperBound Dim i = ii - 1 Dim nDigits(i + 2 - 1) As Integer Dim dDigits(i + 2 - 1) As Integer Dim blank(i + 2 - 1) As Integer For n = lims(i, 0) To lims(i, 1) blank.CopyTo(nDigits, 0) Dim nOk = GetDigits(n, i + 2, nDigits) If Not nOk Then Continue For End If For d = n + 1 To lims(i, 1) + 1 blank.CopyTo(dDigits, 0) Dim dOk = GetDigits(d, i + 2, dDigits) If Not dOk Then Continue For End If For nixt = 1 To nDigits.Length Dim nix = nixt - 1 Dim digit = nDigits(nix) Dim dix = IndexOf(digit, dDigits) If dix >= 0 Then Dim rn = RemoveDigit(nDigits, i + 2, nix) Dim rd = RemoveDigit(dDigits, i + 2, dix) If (n / d) = (rn / rd) Then count(i) += 1 omitted(i, digit) += 1 If count(i) <= 12 Then Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4} End If End If End If Next Next Next Console.WriteLine() Next For i = 2 To 5 Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i) For j = 1 To 9 If omitted(i - 2, j) = 0 Then Continue For End If Console.WriteLine("{0,6} have {1} Next Console.WriteLine() Next End Sub End Module
Generate an equivalent Go version of this Lua code.
function indexOf(haystack, needle) for idx,straw in pairs(haystack) do if straw == needle then return idx end end return -1 end function getDigits(n, le, digits) while n > 0 do local r = n % 10 if r == 0 or indexOf(digits, r) > 0 then return false end le = le - 1 digits[le + 1] = r n = math.floor(n / 10) end return true end function removeDigit(digits, le, idx) local pows = { 1, 10, 100, 1000, 10000 } local sum = 0 local pow = pows[le - 2 + 1] for i = 1, le do if i ~= idx then sum = sum + digits[i] * pow pow = math.floor(pow / 10) end end return sum end function main() local lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} } local count = { 0, 0, 0, 0, 0 } local omitted = { { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, } for i,_ in pairs(lims) do local nDigits = {} local dDigits = {} for j = 1, i + 2 - 1 do nDigits[j] = -1 dDigits[j] = -1 end for n = lims[i][1], lims[i][2] do for j,_ in pairs(nDigits) do nDigits[j] = 0 end local nOk = getDigits(n, i + 2 - 1, nDigits) if nOk then for d = n + 1, lims[i][2] + 1 do for j,_ in pairs(dDigits) do dDigits[j] = 0 end local dOk = getDigits(d, i + 2 - 1, dDigits) if dOk then for nix,_ in pairs(nDigits) do local digit = nDigits[nix] local dix = indexOf(dDigits, digit) if dix >= 0 then local rn = removeDigit(nDigits, i + 2 - 1, nix) local rd = removeDigit(dDigits, i + 2 - 1, dix) if (n / d) == (rn / rd) then count[i] = count[i] + 1 omitted[i][digit + 1] = omitted[i][digit + 1] + 1 if count[i] <= 12 then print(string.format("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit)) end end end end end end end end print() end for i = 2, 5 do print("There are "..count[i - 2 + 1].." "..i.."-digit fractions of which:") for j = 1, 9 do if omitted[i - 2 + 1][j + 1] > 0 then print(string.format("%6d have %d's omitted", omitted[i - 2 + 1][j + 1], j)) end end print() end end main()
package main import ( "fmt" "time" ) func indexOf(n int, s []int) int { for i, j := range s { if n == j { return i } } return -1 } func getDigits(n, le int, digits []int) bool { for n > 0 { r := n % 10 if r == 0 || indexOf(r, digits) >= 0 { return false } le-- digits[le] = r n /= 10 } return true } var pows = [5]int{1, 10, 100, 1000, 10000} func removeDigit(digits []int, le, idx int) int { sum := 0 pow := pows[le-2] for i := 0; i < le; i++ { if i == idx { continue } sum += digits[i] * pow pow /= 10 } return sum } func main() { start := time.Now() lims := [5][2]int{ {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}, {123456, 987653}, } var count [5]int var omitted [5][10]int for i, lim := range lims { nDigits := make([]int, i+2) dDigits := make([]int, i+2) blank := make([]int, i+2) for n := lim[0]; n <= lim[1]; n++ { copy(nDigits, blank) nOk := getDigits(n, i+2, nDigits) if !nOk { continue } for d := n + 1; d <= lim[1]+1; d++ { copy(dDigits, blank) dOk := getDigits(d, i+2, dDigits) if !dOk { continue } for nix, digit := range nDigits { if dix := indexOf(digit, dDigits); dix >= 0 { rn := removeDigit(nDigits, i+2, nix) rd := removeDigit(dDigits, i+2, dix) if float64(n)/float64(d) == float64(rn)/float64(rd) { count[i]++ omitted[i][digit]++ if count[i] <= 12 { fmt.Printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit) } } } } } } fmt.Println() } for i := 2; i <= 6; i++ { fmt.Printf("There are %d %d-digit fractions of which:\n", count[i-2], i) for j := 1; j <= 9; j++ { if omitted[i-2][j] == 0 { continue } fmt.Printf("%6d have %d's omitted\n", omitted[i-2][j], j) } fmt.Println() } fmt.Printf("Took %s\n", time.Since(start)) }
Preserve the algorithm and functionality while converting the code from Mathematica to C.
ClearAll[AnomalousCancellationQ2] AnomalousCancellationQ2[frac : {i_?Positive, j_?Positive}] := Module[{samedigits, idig, jdig, ff, p, q, r, tmp}, idig = IntegerDigits[i]; jdig = IntegerDigits[j]; samedigits = Intersection[idig, jdig]; ff = i/j; If[samedigits != {}, r = {}; Do[ p = Flatten[Position[idig, s]]; q = Flatten[Position[jdig, s]]; p = FromDigits[Delete[idig, #]] & /@ p; q = FromDigits[Delete[jdig, #]] & /@ q; tmp = Select[Tuples[{p, q}], #[[1]]/#[[2]] == ff &]; If[Length[tmp] > 0, r = Join[r, Join[#, {i, j, s}] & /@ tmp]; ]; , {s, samedigits} ]; r , {} ] ] ijs = Select[Select[Range[1, 9999], IntegerDigits /* FreeQ[0]], IntegerDigits /* DuplicateFreeQ]; res = Reap[ Do[ Do[ num = ijs[[i]]; den = ijs[[j]]; out = AnomalousCancellationQ2[{num, den}]; If[Length[out] > 0, Sow[out] ] , {i, 1, j - 1} ] , {j, Length[ijs]} ] ][[2, 1]]; tmp = Catenate[res]; sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 2 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First] sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 3 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First] sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 4 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First]
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }
Rewrite this program in C++ while keeping its functionality equivalent to the Mathematica version.
ClearAll[AnomalousCancellationQ2] AnomalousCancellationQ2[frac : {i_?Positive, j_?Positive}] := Module[{samedigits, idig, jdig, ff, p, q, r, tmp}, idig = IntegerDigits[i]; jdig = IntegerDigits[j]; samedigits = Intersection[idig, jdig]; ff = i/j; If[samedigits != {}, r = {}; Do[ p = Flatten[Position[idig, s]]; q = Flatten[Position[jdig, s]]; p = FromDigits[Delete[idig, #]] & /@ p; q = FromDigits[Delete[jdig, #]] & /@ q; tmp = Select[Tuples[{p, q}], #[[1]]/#[[2]] == ff &]; If[Length[tmp] > 0, r = Join[r, Join[#, {i, j, s}] & /@ tmp]; ]; , {s, samedigits} ]; r , {} ] ] ijs = Select[Select[Range[1, 9999], IntegerDigits /* FreeQ[0]], IntegerDigits /* DuplicateFreeQ]; res = Reap[ Do[ Do[ num = ijs[[i]]; den = ijs[[j]]; out = AnomalousCancellationQ2[{num, den}]; If[Length[out] > 0, Sow[out] ] , {i, 1, j - 1} ] , {j, Length[ijs]} ] ][[2, 1]]; tmp = Catenate[res]; sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 2 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First] sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 3 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First] sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 4 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First]
#include <array> #include <iomanip> #include <iostream> #include <vector> int indexOf(const std::vector<int> &haystack, int needle) { auto it = haystack.cbegin(); auto end = haystack.cend(); int idx = 0; for (; it != end; it = std::next(it)) { if (*it == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, std::vector<int> &digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(const std::vector<int> &digits, int le, int idx) { static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 }; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } int main() { std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }; std::array<int, 5> count; std::array<std::array<int, 10>, 5> omitted; std::fill(count.begin(), count.end(), 0); std::for_each(omitted.begin(), omitted.end(), [](auto &a) { std::fill(a.begin(), a.end(), 0); } ); for (size_t i = 0; i < lims.size(); i++) { std::vector<int> nDigits(i + 2); std::vector<int> dDigits(i + 2); for (int n = lims[i].first; n <= lims[i].second; n++) { std::fill(nDigits.begin(), nDigits.end(), 0); bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i].second + 1; d++) { std::fill(dDigits.begin(), dDigits.end(), 0); bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (size_t nix = 0; nix < nDigits.size(); nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n"; } } } } } } std::cout << '\n'; } for (int i = 2; i <= 5; i++) { std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n"; for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n"; } std::cout << '\n'; } return 0; }
Ensure the translated Java code behaves exactly like the original Mathematica snippet.
ClearAll[AnomalousCancellationQ2] AnomalousCancellationQ2[frac : {i_?Positive, j_?Positive}] := Module[{samedigits, idig, jdig, ff, p, q, r, tmp}, idig = IntegerDigits[i]; jdig = IntegerDigits[j]; samedigits = Intersection[idig, jdig]; ff = i/j; If[samedigits != {}, r = {}; Do[ p = Flatten[Position[idig, s]]; q = Flatten[Position[jdig, s]]; p = FromDigits[Delete[idig, #]] & /@ p; q = FromDigits[Delete[jdig, #]] & /@ q; tmp = Select[Tuples[{p, q}], #[[1]]/#[[2]] == ff &]; If[Length[tmp] > 0, r = Join[r, Join[#, {i, j, s}] & /@ tmp]; ]; , {s, samedigits} ]; r , {} ] ] ijs = Select[Select[Range[1, 9999], IntegerDigits /* FreeQ[0]], IntegerDigits /* DuplicateFreeQ]; res = Reap[ Do[ Do[ num = ijs[[i]]; den = ijs[[j]]; out = AnomalousCancellationQ2[{num, den}]; If[Length[out] > 0, Sow[out] ] , {i, 1, j - 1} ] , {j, Length[ijs]} ] ][[2, 1]]; tmp = Catenate[res]; sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 2 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First] sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 3 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First] sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 4 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First]
import java.util.ArrayList; import java.util.Collections; import java.util.HashMap; import java.util.List; import java.util.Map; public class FractionReduction { public static void main(String[] args) { for ( int size = 2 ; size <= 5 ; size++ ) { reduce(size); } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits); int min = (int) Math.pow(10, numDigits-1); int max = (int) Math.pow(10, numDigits) - 1; List<Integer> values = new ArrayList<>(); for ( int number = min ; number <= max ; number++ ) { if ( isValid(number) ) { values.add(number); } } Map<Integer,Integer> cancelCount = new HashMap<>(); int size = values.size(); int solutions = 0; for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) { int numerator = values.get(nIndex); for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) { int denominator = values.get(dIndex); for ( int commonDigit : digitsInCommon(numerator, denominator) ) { int numRemoved = removeDigit(numerator, commonDigit); int denRemoved = removeDigit(denominator, commonDigit); if ( numerator * denRemoved == denominator * numRemoved ) { solutions++; cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2); if ( solutions <= 12 ) { System.out.printf(" When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved); } } } } } System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions); List<Integer> sorted = new ArrayList<>(cancelCount.keySet()); Collections.sort(sorted); for ( int removed : sorted ) { System.out.printf(" The digit %d was removed %d times.%n", removed, cancelCount.get(removed)); } System.out.println(); } private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000}; private static int removeDigit(int n, int removed) { int m = 0; int pow = 0; while ( n > 0 ) { int r = n % 10; if ( r != removed ) { m = m + r*powers[pow]; pow++; } n /= 10; } return m; } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10]; List<Integer> common = new ArrayList<>(); while ( n1 > 0 ) { int r = n1 % 10; count[r] += 1; n1 /= 10; } while ( n2 > 0 ) { int r = n2 % 10; if ( count[r] > 0 ) { common.add(r); } n2 /= 10; } return common; } private static boolean isValid(int num) { int[] count = new int[10]; while ( num > 0 ) { int r = num % 10; if ( r == 0 || count[r] == 1 ) { return false; } count[r] = 1; num /= 10; } return true; } }
Rewrite the snippet below in Python so it works the same as the original Mathematica code.
ClearAll[AnomalousCancellationQ2] AnomalousCancellationQ2[frac : {i_?Positive, j_?Positive}] := Module[{samedigits, idig, jdig, ff, p, q, r, tmp}, idig = IntegerDigits[i]; jdig = IntegerDigits[j]; samedigits = Intersection[idig, jdig]; ff = i/j; If[samedigits != {}, r = {}; Do[ p = Flatten[Position[idig, s]]; q = Flatten[Position[jdig, s]]; p = FromDigits[Delete[idig, #]] & /@ p; q = FromDigits[Delete[jdig, #]] & /@ q; tmp = Select[Tuples[{p, q}], #[[1]]/#[[2]] == ff &]; If[Length[tmp] > 0, r = Join[r, Join[#, {i, j, s}] & /@ tmp]; ]; , {s, samedigits} ]; r , {} ] ] ijs = Select[Select[Range[1, 9999], IntegerDigits /* FreeQ[0]], IntegerDigits /* DuplicateFreeQ]; res = Reap[ Do[ Do[ num = ijs[[i]]; den = ijs[[j]]; out = AnomalousCancellationQ2[{num, den}]; If[Length[out] > 0, Sow[out] ] , {i, 1, j - 1} ] , {j, Length[ijs]} ] ][[2, 1]]; tmp = Catenate[res]; sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 2 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First] sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 3 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First] sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 4 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First]
def indexOf(haystack, needle): idx = 0 for straw in haystack: if straw == needle: return idx else: idx += 1 return -1 def getDigits(n, le, digits): while n > 0: r = n % 10 if r == 0 or indexOf(digits, r) >= 0: return False le -= 1 digits[le] = r n = int(n / 10) return True def removeDigit(digits, le, idx): pows = [1, 10, 100, 1000, 10000] sum = 0 pow = pows[le - 2] i = 0 while i < le: if i == idx: i += 1 continue sum = sum + digits[i] * pow pow = int(pow / 10) i += 1 return sum def main(): lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = [0 for i in range(5)] omitted = [[0 for i in range(10)] for j in range(5)] i = 0 while i < len(lims): n = lims[i][0] while n < lims[i][1]: nDigits = [0 for k in range(i + 2)] nOk = getDigits(n, i + 2, nDigits) if not nOk: n += 1 continue d = n + 1 while d <= lims[i][1] + 1: dDigits = [0 for k in range(i + 2)] dOk = getDigits(d, i + 2, dDigits) if not dOk: d += 1 continue nix = 0 while nix < len(nDigits): digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0: rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd): count[i] += 1 omitted[i][digit] += 1 if count[i] <= 12: print "%d/%d = %d/%d by omitting %d's" % (n, d, rn, rd, digit) nix += 1 d += 1 n += 1 print i += 1 i = 2 while i <= 5: print "There are %d %d-digit fractions of which:" % (count[i - 2], i) j = 1 while j <= 9: if omitted[i - 2][j] == 0: j += 1 continue print "%6s have %d's omitted" % (omitted[i - 2][j], j) j += 1 print i += 1 return None main()
Maintain the same structure and functionality when rewriting this code in VB.
ClearAll[AnomalousCancellationQ2] AnomalousCancellationQ2[frac : {i_?Positive, j_?Positive}] := Module[{samedigits, idig, jdig, ff, p, q, r, tmp}, idig = IntegerDigits[i]; jdig = IntegerDigits[j]; samedigits = Intersection[idig, jdig]; ff = i/j; If[samedigits != {}, r = {}; Do[ p = Flatten[Position[idig, s]]; q = Flatten[Position[jdig, s]]; p = FromDigits[Delete[idig, #]] & /@ p; q = FromDigits[Delete[jdig, #]] & /@ q; tmp = Select[Tuples[{p, q}], #[[1]]/#[[2]] == ff &]; If[Length[tmp] > 0, r = Join[r, Join[#, {i, j, s}] & /@ tmp]; ]; , {s, samedigits} ]; r , {} ] ] ijs = Select[Select[Range[1, 9999], IntegerDigits /* FreeQ[0]], IntegerDigits /* DuplicateFreeQ]; res = Reap[ Do[ Do[ num = ijs[[i]]; den = ijs[[j]]; out = AnomalousCancellationQ2[{num, den}]; If[Length[out] > 0, Sow[out] ] , {i, 1, j - 1} ] , {j, Length[ijs]} ] ][[2, 1]]; tmp = Catenate[res]; sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 2 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First] sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 3 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First] sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 4 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First]
Module Module1 Function IndexOf(n As Integer, s As Integer()) As Integer For ii = 1 To s.Length Dim i = ii - 1 If s(i) = n Then Return i End If Next Return -1 End Function Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean While n > 0 Dim r = n Mod 10 If r = 0 OrElse IndexOf(r, digits) >= 0 Then Return False End If le -= 1 digits(le) = r n \= 10 End While Return True End Function Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer Dim pows = {1, 10, 100, 1000, 10000} Dim sum = 0 Dim pow = pows(le - 2) For ii = 1 To le Dim i = ii - 1 If i = idx Then Continue For End If sum += digits(i) * pow pow \= 10 Next Return sum End Function Sub Main() Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}} Dim count(5) As Integer Dim omitted(5, 10) As Integer Dim upperBound = lims.GetLength(0) For ii = 1 To upperBound Dim i = ii - 1 Dim nDigits(i + 2 - 1) As Integer Dim dDigits(i + 2 - 1) As Integer Dim blank(i + 2 - 1) As Integer For n = lims(i, 0) To lims(i, 1) blank.CopyTo(nDigits, 0) Dim nOk = GetDigits(n, i + 2, nDigits) If Not nOk Then Continue For End If For d = n + 1 To lims(i, 1) + 1 blank.CopyTo(dDigits, 0) Dim dOk = GetDigits(d, i + 2, dDigits) If Not dOk Then Continue For End If For nixt = 1 To nDigits.Length Dim nix = nixt - 1 Dim digit = nDigits(nix) Dim dix = IndexOf(digit, dDigits) If dix >= 0 Then Dim rn = RemoveDigit(nDigits, i + 2, nix) Dim rd = RemoveDigit(dDigits, i + 2, dix) If (n / d) = (rn / rd) Then count(i) += 1 omitted(i, digit) += 1 If count(i) <= 12 Then Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4} End If End If End If Next Next Next Console.WriteLine() Next For i = 2 To 5 Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i) For j = 1 To 9 If omitted(i - 2, j) = 0 Then Continue For End If Console.WriteLine("{0,6} have {1} Next Console.WriteLine() Next End Sub End Module
Rewrite the snippet below in Go so it works the same as the original Mathematica code.
ClearAll[AnomalousCancellationQ2] AnomalousCancellationQ2[frac : {i_?Positive, j_?Positive}] := Module[{samedigits, idig, jdig, ff, p, q, r, tmp}, idig = IntegerDigits[i]; jdig = IntegerDigits[j]; samedigits = Intersection[idig, jdig]; ff = i/j; If[samedigits != {}, r = {}; Do[ p = Flatten[Position[idig, s]]; q = Flatten[Position[jdig, s]]; p = FromDigits[Delete[idig, #]] & /@ p; q = FromDigits[Delete[jdig, #]] & /@ q; tmp = Select[Tuples[{p, q}], #[[1]]/#[[2]] == ff &]; If[Length[tmp] > 0, r = Join[r, Join[#, {i, j, s}] & /@ tmp]; ]; , {s, samedigits} ]; r , {} ] ] ijs = Select[Select[Range[1, 9999], IntegerDigits /* FreeQ[0]], IntegerDigits /* DuplicateFreeQ]; res = Reap[ Do[ Do[ num = ijs[[i]]; den = ijs[[j]]; out = AnomalousCancellationQ2[{num, den}]; If[Length[out] > 0, Sow[out] ] , {i, 1, j - 1} ] , {j, Length[ijs]} ] ][[2, 1]]; tmp = Catenate[res]; sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 2 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First] sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 3 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First] sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 4 &]; Length[sel] t = Take[sel, UpTo[12]]; Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t] SortBy[Tally[sel[[All, -1]]], First]
package main import ( "fmt" "time" ) func indexOf(n int, s []int) int { for i, j := range s { if n == j { return i } } return -1 } func getDigits(n, le int, digits []int) bool { for n > 0 { r := n % 10 if r == 0 || indexOf(r, digits) >= 0 { return false } le-- digits[le] = r n /= 10 } return true } var pows = [5]int{1, 10, 100, 1000, 10000} func removeDigit(digits []int, le, idx int) int { sum := 0 pow := pows[le-2] for i := 0; i < le; i++ { if i == idx { continue } sum += digits[i] * pow pow /= 10 } return sum } func main() { start := time.Now() lims := [5][2]int{ {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}, {123456, 987653}, } var count [5]int var omitted [5][10]int for i, lim := range lims { nDigits := make([]int, i+2) dDigits := make([]int, i+2) blank := make([]int, i+2) for n := lim[0]; n <= lim[1]; n++ { copy(nDigits, blank) nOk := getDigits(n, i+2, nDigits) if !nOk { continue } for d := n + 1; d <= lim[1]+1; d++ { copy(dDigits, blank) dOk := getDigits(d, i+2, dDigits) if !dOk { continue } for nix, digit := range nDigits { if dix := indexOf(digit, dDigits); dix >= 0 { rn := removeDigit(nDigits, i+2, nix) rd := removeDigit(dDigits, i+2, dix) if float64(n)/float64(d) == float64(rn)/float64(rd) { count[i]++ omitted[i][digit]++ if count[i] <= 12 { fmt.Printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit) } } } } } } fmt.Println() } for i := 2; i <= 6; i++ { fmt.Printf("There are %d %d-digit fractions of which:\n", count[i-2], i) for j := 1; j <= 9; j++ { if omitted[i-2][j] == 0 { continue } fmt.Printf("%6d have %d's omitted\n", omitted[i-2][j], j) } fmt.Println() } fmt.Printf("Took %s\n", time.Since(start)) }
Change the following Nim code into C without altering its purpose.
import strformat import times type Result = tuple[n: int, nine: array[1..9, int]] template find[T; N: static int](a: array[1..N, T]; value: T): int = system.find(a, value) + 1 func toNumber(digits: seq[int]; removeDigit: int = 0): int = var digits = digits if removeDigit != 0: let idx = digits.find(removeDigit) digits.delete(idx) for d in digits: result = 10 * result + d func nDigits(n: int): seq[Result] = var digits = newSeq[int](n + 1) var used: array[1..9, bool] for i in 1..n: digits[i] = i used[i] = true var terminated = false while not terminated: var nine: array[1..9, int] for i in 1..9: if used[i]: nine[i] = digits.toNumber(i) result &= (n: digits.toNumber(), nine: nine) block searchLoop: terminated = true for i in countdown(n, 1): let d = digits[i] doAssert(used[d], "Encountered an inconsistency with 'used' array") used[d] = false for j in (d + 1)..9: if not used[j]: used[j] = true digits[i] = j for k in (i + 1)..n: digits[k] = used.find(false) used[digits[k]] = true terminated = false break searchLoop let start = gettime() for n in 2..6: let rs = nDigits(n) var count = 0 var omitted: array[1..9, int] for i in 1..<rs.high: let (xn, rn) = rs[i] for j in (i + 1)..rs.high: let (xd, rd) = rs[j] for k in 1..9: let yn = rn[k] let yd = rd[k] if yn != 0 and yd != 0 and xn * yd == yn * xd: inc count inc omitted[k] if count <= 12: echo &"{xn}/{xd} => {yn}/{yd} (removed {k})" echo &"{n}-digit fractions found: {count}, omitted {omitted}\n" echo &"Took {gettime() - start}"
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }
Rewrite the snippet below in C# so it works the same as the original Nim code.
import strformat import times type Result = tuple[n: int, nine: array[1..9, int]] template find[T; N: static int](a: array[1..N, T]; value: T): int = system.find(a, value) + 1 func toNumber(digits: seq[int]; removeDigit: int = 0): int = var digits = digits if removeDigit != 0: let idx = digits.find(removeDigit) digits.delete(idx) for d in digits: result = 10 * result + d func nDigits(n: int): seq[Result] = var digits = newSeq[int](n + 1) var used: array[1..9, bool] for i in 1..n: digits[i] = i used[i] = true var terminated = false while not terminated: var nine: array[1..9, int] for i in 1..9: if used[i]: nine[i] = digits.toNumber(i) result &= (n: digits.toNumber(), nine: nine) block searchLoop: terminated = true for i in countdown(n, 1): let d = digits[i] doAssert(used[d], "Encountered an inconsistency with 'used' array") used[d] = false for j in (d + 1)..9: if not used[j]: used[j] = true digits[i] = j for k in (i + 1)..n: digits[k] = used.find(false) used[digits[k]] = true terminated = false break searchLoop let start = gettime() for n in 2..6: let rs = nDigits(n) var count = 0 var omitted: array[1..9, int] for i in 1..<rs.high: let (xn, rn) = rs[i] for j in (i + 1)..rs.high: let (xd, rd) = rs[j] for k in 1..9: let yn = rn[k] let yd = rd[k] if yn != 0 and yd != 0 and xn * yd == yn * xd: inc count inc omitted[k] if count <= 12: echo &"{xn}/{xd} => {yn}/{yd} (removed {k})" echo &"{n}-digit fractions found: {count}, omitted {omitted}\n" echo &"Took {gettime() - start}"
using System; namespace FractionReduction { class Program { static int IndexOf(int n, int[] s) { for (int i = 0; i < s.Length; i++) { if (s[i] == n) { return i; } } return -1; } static bool GetDigits(int n, int le, int[] digits) { while (n > 0) { var r = n % 10; if (r == 0 || IndexOf(r, digits) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } static int RemoveDigit(int[] digits, int le, int idx) { int[] pows = { 1, 10, 100, 1000, 10000 }; var sum = 0; var pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } static void Main() { var lims = new int[,] { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; var count = new int[5]; var omitted = new int[5, 10]; var upperBound = lims.GetLength(0); for (int i = 0; i < upperBound; i++) { var nDigits = new int[i + 2]; var dDigits = new int[i + 2]; var blank = new int[i + 2]; for (int n = lims[i, 0]; n <= lims[i, 1]; n++) { blank.CopyTo(nDigits, 0); var nOk = GetDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i, 1] + 1; d++) { blank.CopyTo(dDigits, 0); var dOk = GetDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.Length; nix++) { var digit = nDigits[nix]; var dix = IndexOf(digit, dDigits); if (dix >= 0) { var rn = RemoveDigit(nDigits, i + 2, nix); var rd = RemoveDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i, digit]++; if (count[i] <= 12) { Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4}'s", n, d, rn, rd, digit); } } } } } } Console.WriteLine(); } for (int i = 2; i <= 5; i++) { Console.WriteLine("There are {0} {1}-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2, j] == 0) { continue; } Console.WriteLine("{0,6} have {1}'s omitted", omitted[i - 2, j], j); } Console.WriteLine(); } } } }
Generate an equivalent C++ version of this Nim code.
import strformat import times type Result = tuple[n: int, nine: array[1..9, int]] template find[T; N: static int](a: array[1..N, T]; value: T): int = system.find(a, value) + 1 func toNumber(digits: seq[int]; removeDigit: int = 0): int = var digits = digits if removeDigit != 0: let idx = digits.find(removeDigit) digits.delete(idx) for d in digits: result = 10 * result + d func nDigits(n: int): seq[Result] = var digits = newSeq[int](n + 1) var used: array[1..9, bool] for i in 1..n: digits[i] = i used[i] = true var terminated = false while not terminated: var nine: array[1..9, int] for i in 1..9: if used[i]: nine[i] = digits.toNumber(i) result &= (n: digits.toNumber(), nine: nine) block searchLoop: terminated = true for i in countdown(n, 1): let d = digits[i] doAssert(used[d], "Encountered an inconsistency with 'used' array") used[d] = false for j in (d + 1)..9: if not used[j]: used[j] = true digits[i] = j for k in (i + 1)..n: digits[k] = used.find(false) used[digits[k]] = true terminated = false break searchLoop let start = gettime() for n in 2..6: let rs = nDigits(n) var count = 0 var omitted: array[1..9, int] for i in 1..<rs.high: let (xn, rn) = rs[i] for j in (i + 1)..rs.high: let (xd, rd) = rs[j] for k in 1..9: let yn = rn[k] let yd = rd[k] if yn != 0 and yd != 0 and xn * yd == yn * xd: inc count inc omitted[k] if count <= 12: echo &"{xn}/{xd} => {yn}/{yd} (removed {k})" echo &"{n}-digit fractions found: {count}, omitted {omitted}\n" echo &"Took {gettime() - start}"
#include <array> #include <iomanip> #include <iostream> #include <vector> int indexOf(const std::vector<int> &haystack, int needle) { auto it = haystack.cbegin(); auto end = haystack.cend(); int idx = 0; for (; it != end; it = std::next(it)) { if (*it == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, std::vector<int> &digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(const std::vector<int> &digits, int le, int idx) { static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 }; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } int main() { std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }; std::array<int, 5> count; std::array<std::array<int, 10>, 5> omitted; std::fill(count.begin(), count.end(), 0); std::for_each(omitted.begin(), omitted.end(), [](auto &a) { std::fill(a.begin(), a.end(), 0); } ); for (size_t i = 0; i < lims.size(); i++) { std::vector<int> nDigits(i + 2); std::vector<int> dDigits(i + 2); for (int n = lims[i].first; n <= lims[i].second; n++) { std::fill(nDigits.begin(), nDigits.end(), 0); bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i].second + 1; d++) { std::fill(dDigits.begin(), dDigits.end(), 0); bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (size_t nix = 0; nix < nDigits.size(); nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n"; } } } } } } std::cout << '\n'; } for (int i = 2; i <= 5; i++) { std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n"; for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n"; } std::cout << '\n'; } return 0; }
Generate an equivalent Java version of this Nim code.
import strformat import times type Result = tuple[n: int, nine: array[1..9, int]] template find[T; N: static int](a: array[1..N, T]; value: T): int = system.find(a, value) + 1 func toNumber(digits: seq[int]; removeDigit: int = 0): int = var digits = digits if removeDigit != 0: let idx = digits.find(removeDigit) digits.delete(idx) for d in digits: result = 10 * result + d func nDigits(n: int): seq[Result] = var digits = newSeq[int](n + 1) var used: array[1..9, bool] for i in 1..n: digits[i] = i used[i] = true var terminated = false while not terminated: var nine: array[1..9, int] for i in 1..9: if used[i]: nine[i] = digits.toNumber(i) result &= (n: digits.toNumber(), nine: nine) block searchLoop: terminated = true for i in countdown(n, 1): let d = digits[i] doAssert(used[d], "Encountered an inconsistency with 'used' array") used[d] = false for j in (d + 1)..9: if not used[j]: used[j] = true digits[i] = j for k in (i + 1)..n: digits[k] = used.find(false) used[digits[k]] = true terminated = false break searchLoop let start = gettime() for n in 2..6: let rs = nDigits(n) var count = 0 var omitted: array[1..9, int] for i in 1..<rs.high: let (xn, rn) = rs[i] for j in (i + 1)..rs.high: let (xd, rd) = rs[j] for k in 1..9: let yn = rn[k] let yd = rd[k] if yn != 0 and yd != 0 and xn * yd == yn * xd: inc count inc omitted[k] if count <= 12: echo &"{xn}/{xd} => {yn}/{yd} (removed {k})" echo &"{n}-digit fractions found: {count}, omitted {omitted}\n" echo &"Took {gettime() - start}"
import java.util.ArrayList; import java.util.Collections; import java.util.HashMap; import java.util.List; import java.util.Map; public class FractionReduction { public static void main(String[] args) { for ( int size = 2 ; size <= 5 ; size++ ) { reduce(size); } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits); int min = (int) Math.pow(10, numDigits-1); int max = (int) Math.pow(10, numDigits) - 1; List<Integer> values = new ArrayList<>(); for ( int number = min ; number <= max ; number++ ) { if ( isValid(number) ) { values.add(number); } } Map<Integer,Integer> cancelCount = new HashMap<>(); int size = values.size(); int solutions = 0; for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) { int numerator = values.get(nIndex); for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) { int denominator = values.get(dIndex); for ( int commonDigit : digitsInCommon(numerator, denominator) ) { int numRemoved = removeDigit(numerator, commonDigit); int denRemoved = removeDigit(denominator, commonDigit); if ( numerator * denRemoved == denominator * numRemoved ) { solutions++; cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2); if ( solutions <= 12 ) { System.out.printf(" When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved); } } } } } System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions); List<Integer> sorted = new ArrayList<>(cancelCount.keySet()); Collections.sort(sorted); for ( int removed : sorted ) { System.out.printf(" The digit %d was removed %d times.%n", removed, cancelCount.get(removed)); } System.out.println(); } private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000}; private static int removeDigit(int n, int removed) { int m = 0; int pow = 0; while ( n > 0 ) { int r = n % 10; if ( r != removed ) { m = m + r*powers[pow]; pow++; } n /= 10; } return m; } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10]; List<Integer> common = new ArrayList<>(); while ( n1 > 0 ) { int r = n1 % 10; count[r] += 1; n1 /= 10; } while ( n2 > 0 ) { int r = n2 % 10; if ( count[r] > 0 ) { common.add(r); } n2 /= 10; } return common; } private static boolean isValid(int num) { int[] count = new int[10]; while ( num > 0 ) { int r = num % 10; if ( r == 0 || count[r] == 1 ) { return false; } count[r] = 1; num /= 10; } return true; } }
Convert the following code from Nim to Python, ensuring the logic remains intact.
import strformat import times type Result = tuple[n: int, nine: array[1..9, int]] template find[T; N: static int](a: array[1..N, T]; value: T): int = system.find(a, value) + 1 func toNumber(digits: seq[int]; removeDigit: int = 0): int = var digits = digits if removeDigit != 0: let idx = digits.find(removeDigit) digits.delete(idx) for d in digits: result = 10 * result + d func nDigits(n: int): seq[Result] = var digits = newSeq[int](n + 1) var used: array[1..9, bool] for i in 1..n: digits[i] = i used[i] = true var terminated = false while not terminated: var nine: array[1..9, int] for i in 1..9: if used[i]: nine[i] = digits.toNumber(i) result &= (n: digits.toNumber(), nine: nine) block searchLoop: terminated = true for i in countdown(n, 1): let d = digits[i] doAssert(used[d], "Encountered an inconsistency with 'used' array") used[d] = false for j in (d + 1)..9: if not used[j]: used[j] = true digits[i] = j for k in (i + 1)..n: digits[k] = used.find(false) used[digits[k]] = true terminated = false break searchLoop let start = gettime() for n in 2..6: let rs = nDigits(n) var count = 0 var omitted: array[1..9, int] for i in 1..<rs.high: let (xn, rn) = rs[i] for j in (i + 1)..rs.high: let (xd, rd) = rs[j] for k in 1..9: let yn = rn[k] let yd = rd[k] if yn != 0 and yd != 0 and xn * yd == yn * xd: inc count inc omitted[k] if count <= 12: echo &"{xn}/{xd} => {yn}/{yd} (removed {k})" echo &"{n}-digit fractions found: {count}, omitted {omitted}\n" echo &"Took {gettime() - start}"
def indexOf(haystack, needle): idx = 0 for straw in haystack: if straw == needle: return idx else: idx += 1 return -1 def getDigits(n, le, digits): while n > 0: r = n % 10 if r == 0 or indexOf(digits, r) >= 0: return False le -= 1 digits[le] = r n = int(n / 10) return True def removeDigit(digits, le, idx): pows = [1, 10, 100, 1000, 10000] sum = 0 pow = pows[le - 2] i = 0 while i < le: if i == idx: i += 1 continue sum = sum + digits[i] * pow pow = int(pow / 10) i += 1 return sum def main(): lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = [0 for i in range(5)] omitted = [[0 for i in range(10)] for j in range(5)] i = 0 while i < len(lims): n = lims[i][0] while n < lims[i][1]: nDigits = [0 for k in range(i + 2)] nOk = getDigits(n, i + 2, nDigits) if not nOk: n += 1 continue d = n + 1 while d <= lims[i][1] + 1: dDigits = [0 for k in range(i + 2)] dOk = getDigits(d, i + 2, dDigits) if not dOk: d += 1 continue nix = 0 while nix < len(nDigits): digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0: rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd): count[i] += 1 omitted[i][digit] += 1 if count[i] <= 12: print "%d/%d = %d/%d by omitting %d's" % (n, d, rn, rd, digit) nix += 1 d += 1 n += 1 print i += 1 i = 2 while i <= 5: print "There are %d %d-digit fractions of which:" % (count[i - 2], i) j = 1 while j <= 9: if omitted[i - 2][j] == 0: j += 1 continue print "%6s have %d's omitted" % (omitted[i - 2][j], j) j += 1 print i += 1 return None main()
Convert the following code from Nim to VB, ensuring the logic remains intact.
import strformat import times type Result = tuple[n: int, nine: array[1..9, int]] template find[T; N: static int](a: array[1..N, T]; value: T): int = system.find(a, value) + 1 func toNumber(digits: seq[int]; removeDigit: int = 0): int = var digits = digits if removeDigit != 0: let idx = digits.find(removeDigit) digits.delete(idx) for d in digits: result = 10 * result + d func nDigits(n: int): seq[Result] = var digits = newSeq[int](n + 1) var used: array[1..9, bool] for i in 1..n: digits[i] = i used[i] = true var terminated = false while not terminated: var nine: array[1..9, int] for i in 1..9: if used[i]: nine[i] = digits.toNumber(i) result &= (n: digits.toNumber(), nine: nine) block searchLoop: terminated = true for i in countdown(n, 1): let d = digits[i] doAssert(used[d], "Encountered an inconsistency with 'used' array") used[d] = false for j in (d + 1)..9: if not used[j]: used[j] = true digits[i] = j for k in (i + 1)..n: digits[k] = used.find(false) used[digits[k]] = true terminated = false break searchLoop let start = gettime() for n in 2..6: let rs = nDigits(n) var count = 0 var omitted: array[1..9, int] for i in 1..<rs.high: let (xn, rn) = rs[i] for j in (i + 1)..rs.high: let (xd, rd) = rs[j] for k in 1..9: let yn = rn[k] let yd = rd[k] if yn != 0 and yd != 0 and xn * yd == yn * xd: inc count inc omitted[k] if count <= 12: echo &"{xn}/{xd} => {yn}/{yd} (removed {k})" echo &"{n}-digit fractions found: {count}, omitted {omitted}\n" echo &"Took {gettime() - start}"
Module Module1 Function IndexOf(n As Integer, s As Integer()) As Integer For ii = 1 To s.Length Dim i = ii - 1 If s(i) = n Then Return i End If Next Return -1 End Function Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean While n > 0 Dim r = n Mod 10 If r = 0 OrElse IndexOf(r, digits) >= 0 Then Return False End If le -= 1 digits(le) = r n \= 10 End While Return True End Function Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer Dim pows = {1, 10, 100, 1000, 10000} Dim sum = 0 Dim pow = pows(le - 2) For ii = 1 To le Dim i = ii - 1 If i = idx Then Continue For End If sum += digits(i) * pow pow \= 10 Next Return sum End Function Sub Main() Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}} Dim count(5) As Integer Dim omitted(5, 10) As Integer Dim upperBound = lims.GetLength(0) For ii = 1 To upperBound Dim i = ii - 1 Dim nDigits(i + 2 - 1) As Integer Dim dDigits(i + 2 - 1) As Integer Dim blank(i + 2 - 1) As Integer For n = lims(i, 0) To lims(i, 1) blank.CopyTo(nDigits, 0) Dim nOk = GetDigits(n, i + 2, nDigits) If Not nOk Then Continue For End If For d = n + 1 To lims(i, 1) + 1 blank.CopyTo(dDigits, 0) Dim dOk = GetDigits(d, i + 2, dDigits) If Not dOk Then Continue For End If For nixt = 1 To nDigits.Length Dim nix = nixt - 1 Dim digit = nDigits(nix) Dim dix = IndexOf(digit, dDigits) If dix >= 0 Then Dim rn = RemoveDigit(nDigits, i + 2, nix) Dim rd = RemoveDigit(dDigits, i + 2, dix) If (n / d) = (rn / rd) Then count(i) += 1 omitted(i, digit) += 1 If count(i) <= 12 Then Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4} End If End If End If Next Next Next Console.WriteLine() Next For i = 2 To 5 Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i) For j = 1 To 9 If omitted(i - 2, j) = 0 Then Continue For End If Console.WriteLine("{0,6} have {1} Next Console.WriteLine() Next End Sub End Module
Write the same code in Go as shown below in Nim.
import strformat import times type Result = tuple[n: int, nine: array[1..9, int]] template find[T; N: static int](a: array[1..N, T]; value: T): int = system.find(a, value) + 1 func toNumber(digits: seq[int]; removeDigit: int = 0): int = var digits = digits if removeDigit != 0: let idx = digits.find(removeDigit) digits.delete(idx) for d in digits: result = 10 * result + d func nDigits(n: int): seq[Result] = var digits = newSeq[int](n + 1) var used: array[1..9, bool] for i in 1..n: digits[i] = i used[i] = true var terminated = false while not terminated: var nine: array[1..9, int] for i in 1..9: if used[i]: nine[i] = digits.toNumber(i) result &= (n: digits.toNumber(), nine: nine) block searchLoop: terminated = true for i in countdown(n, 1): let d = digits[i] doAssert(used[d], "Encountered an inconsistency with 'used' array") used[d] = false for j in (d + 1)..9: if not used[j]: used[j] = true digits[i] = j for k in (i + 1)..n: digits[k] = used.find(false) used[digits[k]] = true terminated = false break searchLoop let start = gettime() for n in 2..6: let rs = nDigits(n) var count = 0 var omitted: array[1..9, int] for i in 1..<rs.high: let (xn, rn) = rs[i] for j in (i + 1)..rs.high: let (xd, rd) = rs[j] for k in 1..9: let yn = rn[k] let yd = rd[k] if yn != 0 and yd != 0 and xn * yd == yn * xd: inc count inc omitted[k] if count <= 12: echo &"{xn}/{xd} => {yn}/{yd} (removed {k})" echo &"{n}-digit fractions found: {count}, omitted {omitted}\n" echo &"Took {gettime() - start}"
package main import ( "fmt" "time" ) func indexOf(n int, s []int) int { for i, j := range s { if n == j { return i } } return -1 } func getDigits(n, le int, digits []int) bool { for n > 0 { r := n % 10 if r == 0 || indexOf(r, digits) >= 0 { return false } le-- digits[le] = r n /= 10 } return true } var pows = [5]int{1, 10, 100, 1000, 10000} func removeDigit(digits []int, le, idx int) int { sum := 0 pow := pows[le-2] for i := 0; i < le; i++ { if i == idx { continue } sum += digits[i] * pow pow /= 10 } return sum } func main() { start := time.Now() lims := [5][2]int{ {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}, {123456, 987653}, } var count [5]int var omitted [5][10]int for i, lim := range lims { nDigits := make([]int, i+2) dDigits := make([]int, i+2) blank := make([]int, i+2) for n := lim[0]; n <= lim[1]; n++ { copy(nDigits, blank) nOk := getDigits(n, i+2, nDigits) if !nOk { continue } for d := n + 1; d <= lim[1]+1; d++ { copy(dDigits, blank) dOk := getDigits(d, i+2, dDigits) if !dOk { continue } for nix, digit := range nDigits { if dix := indexOf(digit, dDigits); dix >= 0 { rn := removeDigit(nDigits, i+2, nix) rd := removeDigit(dDigits, i+2, dix) if float64(n)/float64(d) == float64(rn)/float64(rd) { count[i]++ omitted[i][digit]++ if count[i] <= 12 { fmt.Printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit) } } } } } } fmt.Println() } for i := 2; i <= 6; i++ { fmt.Printf("There are %d %d-digit fractions of which:\n", count[i-2], i) for j := 1; j <= 9; j++ { if omitted[i-2][j] == 0 { continue } fmt.Printf("%6d have %d's omitted\n", omitted[i-2][j], j) } fmt.Println() } fmt.Printf("Took %s\n", time.Since(start)) }
Ensure the translated C code behaves exactly like the original Pascal snippet.
program FracRedu; uses SysUtils; type tdigit = 0..9; const cMaskDgt: array [tdigit] of Uint32 = (1, 2, 4, 8, 16, 32, 64, 128, 256, 512 ); cMaxDigits = High(tdigit); type tPermfield = array[tdigit] of uint32; tpPermfield = ^tPermfield; tDigitCnt = array[tdigit] of Uint32; tErg = record numUsedDigits : Uint32; numUnusedDigit : array[tdigit] of Uint32; numNormal : Uint64; dummy : array[0..7] of byte; end; tpErg = ^tErg; var Erg: array of tErg; pf_x, pf_y: tPermfield; DigitCnt :tDigitCnt; permcnt, UsedDigits,Anzahl: NativeUint; function Fakultaet(i: integer): integer; begin Result := 1; while i > 1 do begin Result := Result * i; Dec(i); end; end; procedure OutErg(dgt: Uint32;pi,pJ:tpErg); begin writeln(dgt:3,' ', pi^.numUnusedDigit[dgt],'/',pj^.numUnusedDigit[dgt] ,' = ',pi^.numNormal,'/',pj^.numNormal); end; function Check(pI,pJ : tpErg;Nud :Word):integer; var dgt: NativeInt; Begin result := 0; dgt := 1; NUD := NUD SHR 1; repeat IF NUD AND 1 <> 0 then Begin If pI^.numNormal*pJ^.numUnusedDigit[dgt] = pJ^.numNormal*pI^.numUnusedDigit[dgt] then Begin inc(result); inc(DigitCnt[dgt]); IF Anzahl < 110 then OutErg(dgt,pI,pJ); end; end; inc(dgt); NUD := NUD SHR 1; until NUD = 0; end; procedure CheckWithOne(pI : tpErg;j,Nud:Uint32); var pJ : tpErg; l : NativeUInt; Begin pJ := pI; if UsedDigits <5 then Begin for j := j+1 to permcnt do begin inc(pJ); l := NUD AND pJ^.numUsedDigits; IF l <> 0 then inc(Anzahl,Check(pI,pJ,l)); end; end else Begin for j := j+1 to permcnt do begin inc(pJ); l := NUD AND pJ^.numUsedDigits; inc(Anzahl,Check(pI,pJ,l)); end; end; end; procedure SearchMultiple; var pI : tpErg; i : NativeUInt; begin pI := @Erg[0]; for i := 0 to permcnt do Begin CheckWithOne(pI,i,pI^.numUsedDigits); inc(pI); end; end; function BinomCoeff(n, k: byte): longint; var i: longint; begin if k > n div 2 then k := n - k; Result := 1; if k <= n then for i := 1 to k do Result := Result * (n - i + 1) div i; end; procedure InsertToErg(var E: tErg; const x: tPermfield); var n : Uint64; k,i,j,dgt,nud: NativeInt; begin k := UsedDigits; n := 0; nud := 0; for i := 1 to k do begin dgt := x[i]; nud := nud or cMaskDgt[dgt]; n := n * 10 + dgt; end; with E do begin numUsedDigits := nud; numNormal := n; end; For J := k downto 1 do Begin n := 0; for i := 1 to j-1 do n := n * 10 + x[i]; for i := j+1 to k do n := n * 10 + x[i]; E.numUnusedDigit[x[j]] := n; end; end; procedure PermKoutofN(k, n: nativeInt); var x, y: tpPermfield; i, yi, tmp: NativeInt; begin x := @pf_x; y := @pf_y; permcnt := 0; if k > n then k := n; if k = n then k := k - 1; for i := 1 to n do x^[i] := i; for i := 1 to k do y^[i] := i; InserttoErg(Erg[permcnt], x^); i := k; repeat yi := y^[i]; if yi < n then begin Inc(permcnt); Inc(yi); y^[i] := yi; tmp := x^[i]; x^[i] := x^[yi]; x^[yi] := tmp; i := k; InserttoErg(Erg[permcnt], x^); end else begin repeat tmp := x^[i]; x^[i] := x^[yi]; x^[yi] := tmp; Dec(yi); until yi <= i; y^[i] := yi; Dec(i); end; until (i = 0); end; procedure OutDigitCount; var i : tDigit; Begin writeln('omitted digits 1 to 9'); For i := 1 to 9do write(DigitCnt[i]:UsedDigits); writeln; end; procedure ClearDigitCount; var i : tDigit; Begin For i := low(DigitCnt) to high(DigitCnt) do DigitCnt[i] := 0; end; var t1, t0: TDateTime; begin For UsedDigits := 8 to 9 do Begin writeln('Used digits ',UsedDigits); T0 := now; ClearDigitCount; setlength(Erg, Fakultaet(UsedDigits) * BinomCoeff(cMaxDigits, UsedDigits)); Anzahl := 0; permcnt := 0; PermKoutOfN(UsedDigits, cMaxDigits); SearchMultiple; T1 := now; writeln('Found solutions ',Anzahl); OutDigitCount; writeln('time taken ',FormatDateTime('HH:NN:SS.zzz', T1 - T0)); setlength(Erg, 0); writeln; end; end.
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }
Write the same code in C# as shown below in Pascal.
program FracRedu; uses SysUtils; type tdigit = 0..9; const cMaskDgt: array [tdigit] of Uint32 = (1, 2, 4, 8, 16, 32, 64, 128, 256, 512 ); cMaxDigits = High(tdigit); type tPermfield = array[tdigit] of uint32; tpPermfield = ^tPermfield; tDigitCnt = array[tdigit] of Uint32; tErg = record numUsedDigits : Uint32; numUnusedDigit : array[tdigit] of Uint32; numNormal : Uint64; dummy : array[0..7] of byte; end; tpErg = ^tErg; var Erg: array of tErg; pf_x, pf_y: tPermfield; DigitCnt :tDigitCnt; permcnt, UsedDigits,Anzahl: NativeUint; function Fakultaet(i: integer): integer; begin Result := 1; while i > 1 do begin Result := Result * i; Dec(i); end; end; procedure OutErg(dgt: Uint32;pi,pJ:tpErg); begin writeln(dgt:3,' ', pi^.numUnusedDigit[dgt],'/',pj^.numUnusedDigit[dgt] ,' = ',pi^.numNormal,'/',pj^.numNormal); end; function Check(pI,pJ : tpErg;Nud :Word):integer; var dgt: NativeInt; Begin result := 0; dgt := 1; NUD := NUD SHR 1; repeat IF NUD AND 1 <> 0 then Begin If pI^.numNormal*pJ^.numUnusedDigit[dgt] = pJ^.numNormal*pI^.numUnusedDigit[dgt] then Begin inc(result); inc(DigitCnt[dgt]); IF Anzahl < 110 then OutErg(dgt,pI,pJ); end; end; inc(dgt); NUD := NUD SHR 1; until NUD = 0; end; procedure CheckWithOne(pI : tpErg;j,Nud:Uint32); var pJ : tpErg; l : NativeUInt; Begin pJ := pI; if UsedDigits <5 then Begin for j := j+1 to permcnt do begin inc(pJ); l := NUD AND pJ^.numUsedDigits; IF l <> 0 then inc(Anzahl,Check(pI,pJ,l)); end; end else Begin for j := j+1 to permcnt do begin inc(pJ); l := NUD AND pJ^.numUsedDigits; inc(Anzahl,Check(pI,pJ,l)); end; end; end; procedure SearchMultiple; var pI : tpErg; i : NativeUInt; begin pI := @Erg[0]; for i := 0 to permcnt do Begin CheckWithOne(pI,i,pI^.numUsedDigits); inc(pI); end; end; function BinomCoeff(n, k: byte): longint; var i: longint; begin if k > n div 2 then k := n - k; Result := 1; if k <= n then for i := 1 to k do Result := Result * (n - i + 1) div i; end; procedure InsertToErg(var E: tErg; const x: tPermfield); var n : Uint64; k,i,j,dgt,nud: NativeInt; begin k := UsedDigits; n := 0; nud := 0; for i := 1 to k do begin dgt := x[i]; nud := nud or cMaskDgt[dgt]; n := n * 10 + dgt; end; with E do begin numUsedDigits := nud; numNormal := n; end; For J := k downto 1 do Begin n := 0; for i := 1 to j-1 do n := n * 10 + x[i]; for i := j+1 to k do n := n * 10 + x[i]; E.numUnusedDigit[x[j]] := n; end; end; procedure PermKoutofN(k, n: nativeInt); var x, y: tpPermfield; i, yi, tmp: NativeInt; begin x := @pf_x; y := @pf_y; permcnt := 0; if k > n then k := n; if k = n then k := k - 1; for i := 1 to n do x^[i] := i; for i := 1 to k do y^[i] := i; InserttoErg(Erg[permcnt], x^); i := k; repeat yi := y^[i]; if yi < n then begin Inc(permcnt); Inc(yi); y^[i] := yi; tmp := x^[i]; x^[i] := x^[yi]; x^[yi] := tmp; i := k; InserttoErg(Erg[permcnt], x^); end else begin repeat tmp := x^[i]; x^[i] := x^[yi]; x^[yi] := tmp; Dec(yi); until yi <= i; y^[i] := yi; Dec(i); end; until (i = 0); end; procedure OutDigitCount; var i : tDigit; Begin writeln('omitted digits 1 to 9'); For i := 1 to 9do write(DigitCnt[i]:UsedDigits); writeln; end; procedure ClearDigitCount; var i : tDigit; Begin For i := low(DigitCnt) to high(DigitCnt) do DigitCnt[i] := 0; end; var t1, t0: TDateTime; begin For UsedDigits := 8 to 9 do Begin writeln('Used digits ',UsedDigits); T0 := now; ClearDigitCount; setlength(Erg, Fakultaet(UsedDigits) * BinomCoeff(cMaxDigits, UsedDigits)); Anzahl := 0; permcnt := 0; PermKoutOfN(UsedDigits, cMaxDigits); SearchMultiple; T1 := now; writeln('Found solutions ',Anzahl); OutDigitCount; writeln('time taken ',FormatDateTime('HH:NN:SS.zzz', T1 - T0)); setlength(Erg, 0); writeln; end; end.
using System; namespace FractionReduction { class Program { static int IndexOf(int n, int[] s) { for (int i = 0; i < s.Length; i++) { if (s[i] == n) { return i; } } return -1; } static bool GetDigits(int n, int le, int[] digits) { while (n > 0) { var r = n % 10; if (r == 0 || IndexOf(r, digits) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } static int RemoveDigit(int[] digits, int le, int idx) { int[] pows = { 1, 10, 100, 1000, 10000 }; var sum = 0; var pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } static void Main() { var lims = new int[,] { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; var count = new int[5]; var omitted = new int[5, 10]; var upperBound = lims.GetLength(0); for (int i = 0; i < upperBound; i++) { var nDigits = new int[i + 2]; var dDigits = new int[i + 2]; var blank = new int[i + 2]; for (int n = lims[i, 0]; n <= lims[i, 1]; n++) { blank.CopyTo(nDigits, 0); var nOk = GetDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i, 1] + 1; d++) { blank.CopyTo(dDigits, 0); var dOk = GetDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.Length; nix++) { var digit = nDigits[nix]; var dix = IndexOf(digit, dDigits); if (dix >= 0) { var rn = RemoveDigit(nDigits, i + 2, nix); var rd = RemoveDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i, digit]++; if (count[i] <= 12) { Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4}'s", n, d, rn, rd, digit); } } } } } } Console.WriteLine(); } for (int i = 2; i <= 5; i++) { Console.WriteLine("There are {0} {1}-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2, j] == 0) { continue; } Console.WriteLine("{0,6} have {1}'s omitted", omitted[i - 2, j], j); } Console.WriteLine(); } } } }
Generate an equivalent C++ version of this Pascal code.
program FracRedu; uses SysUtils; type tdigit = 0..9; const cMaskDgt: array [tdigit] of Uint32 = (1, 2, 4, 8, 16, 32, 64, 128, 256, 512 ); cMaxDigits = High(tdigit); type tPermfield = array[tdigit] of uint32; tpPermfield = ^tPermfield; tDigitCnt = array[tdigit] of Uint32; tErg = record numUsedDigits : Uint32; numUnusedDigit : array[tdigit] of Uint32; numNormal : Uint64; dummy : array[0..7] of byte; end; tpErg = ^tErg; var Erg: array of tErg; pf_x, pf_y: tPermfield; DigitCnt :tDigitCnt; permcnt, UsedDigits,Anzahl: NativeUint; function Fakultaet(i: integer): integer; begin Result := 1; while i > 1 do begin Result := Result * i; Dec(i); end; end; procedure OutErg(dgt: Uint32;pi,pJ:tpErg); begin writeln(dgt:3,' ', pi^.numUnusedDigit[dgt],'/',pj^.numUnusedDigit[dgt] ,' = ',pi^.numNormal,'/',pj^.numNormal); end; function Check(pI,pJ : tpErg;Nud :Word):integer; var dgt: NativeInt; Begin result := 0; dgt := 1; NUD := NUD SHR 1; repeat IF NUD AND 1 <> 0 then Begin If pI^.numNormal*pJ^.numUnusedDigit[dgt] = pJ^.numNormal*pI^.numUnusedDigit[dgt] then Begin inc(result); inc(DigitCnt[dgt]); IF Anzahl < 110 then OutErg(dgt,pI,pJ); end; end; inc(dgt); NUD := NUD SHR 1; until NUD = 0; end; procedure CheckWithOne(pI : tpErg;j,Nud:Uint32); var pJ : tpErg; l : NativeUInt; Begin pJ := pI; if UsedDigits <5 then Begin for j := j+1 to permcnt do begin inc(pJ); l := NUD AND pJ^.numUsedDigits; IF l <> 0 then inc(Anzahl,Check(pI,pJ,l)); end; end else Begin for j := j+1 to permcnt do begin inc(pJ); l := NUD AND pJ^.numUsedDigits; inc(Anzahl,Check(pI,pJ,l)); end; end; end; procedure SearchMultiple; var pI : tpErg; i : NativeUInt; begin pI := @Erg[0]; for i := 0 to permcnt do Begin CheckWithOne(pI,i,pI^.numUsedDigits); inc(pI); end; end; function BinomCoeff(n, k: byte): longint; var i: longint; begin if k > n div 2 then k := n - k; Result := 1; if k <= n then for i := 1 to k do Result := Result * (n - i + 1) div i; end; procedure InsertToErg(var E: tErg; const x: tPermfield); var n : Uint64; k,i,j,dgt,nud: NativeInt; begin k := UsedDigits; n := 0; nud := 0; for i := 1 to k do begin dgt := x[i]; nud := nud or cMaskDgt[dgt]; n := n * 10 + dgt; end; with E do begin numUsedDigits := nud; numNormal := n; end; For J := k downto 1 do Begin n := 0; for i := 1 to j-1 do n := n * 10 + x[i]; for i := j+1 to k do n := n * 10 + x[i]; E.numUnusedDigit[x[j]] := n; end; end; procedure PermKoutofN(k, n: nativeInt); var x, y: tpPermfield; i, yi, tmp: NativeInt; begin x := @pf_x; y := @pf_y; permcnt := 0; if k > n then k := n; if k = n then k := k - 1; for i := 1 to n do x^[i] := i; for i := 1 to k do y^[i] := i; InserttoErg(Erg[permcnt], x^); i := k; repeat yi := y^[i]; if yi < n then begin Inc(permcnt); Inc(yi); y^[i] := yi; tmp := x^[i]; x^[i] := x^[yi]; x^[yi] := tmp; i := k; InserttoErg(Erg[permcnt], x^); end else begin repeat tmp := x^[i]; x^[i] := x^[yi]; x^[yi] := tmp; Dec(yi); until yi <= i; y^[i] := yi; Dec(i); end; until (i = 0); end; procedure OutDigitCount; var i : tDigit; Begin writeln('omitted digits 1 to 9'); For i := 1 to 9do write(DigitCnt[i]:UsedDigits); writeln; end; procedure ClearDigitCount; var i : tDigit; Begin For i := low(DigitCnt) to high(DigitCnt) do DigitCnt[i] := 0; end; var t1, t0: TDateTime; begin For UsedDigits := 8 to 9 do Begin writeln('Used digits ',UsedDigits); T0 := now; ClearDigitCount; setlength(Erg, Fakultaet(UsedDigits) * BinomCoeff(cMaxDigits, UsedDigits)); Anzahl := 0; permcnt := 0; PermKoutOfN(UsedDigits, cMaxDigits); SearchMultiple; T1 := now; writeln('Found solutions ',Anzahl); OutDigitCount; writeln('time taken ',FormatDateTime('HH:NN:SS.zzz', T1 - T0)); setlength(Erg, 0); writeln; end; end.
#include <array> #include <iomanip> #include <iostream> #include <vector> int indexOf(const std::vector<int> &haystack, int needle) { auto it = haystack.cbegin(); auto end = haystack.cend(); int idx = 0; for (; it != end; it = std::next(it)) { if (*it == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, std::vector<int> &digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(const std::vector<int> &digits, int le, int idx) { static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 }; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } int main() { std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }; std::array<int, 5> count; std::array<std::array<int, 10>, 5> omitted; std::fill(count.begin(), count.end(), 0); std::for_each(omitted.begin(), omitted.end(), [](auto &a) { std::fill(a.begin(), a.end(), 0); } ); for (size_t i = 0; i < lims.size(); i++) { std::vector<int> nDigits(i + 2); std::vector<int> dDigits(i + 2); for (int n = lims[i].first; n <= lims[i].second; n++) { std::fill(nDigits.begin(), nDigits.end(), 0); bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i].second + 1; d++) { std::fill(dDigits.begin(), dDigits.end(), 0); bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (size_t nix = 0; nix < nDigits.size(); nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n"; } } } } } } std::cout << '\n'; } for (int i = 2; i <= 5; i++) { std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n"; for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n"; } std::cout << '\n'; } return 0; }
Rewrite this program in Java while keeping its functionality equivalent to the Pascal version.
program FracRedu; uses SysUtils; type tdigit = 0..9; const cMaskDgt: array [tdigit] of Uint32 = (1, 2, 4, 8, 16, 32, 64, 128, 256, 512 ); cMaxDigits = High(tdigit); type tPermfield = array[tdigit] of uint32; tpPermfield = ^tPermfield; tDigitCnt = array[tdigit] of Uint32; tErg = record numUsedDigits : Uint32; numUnusedDigit : array[tdigit] of Uint32; numNormal : Uint64; dummy : array[0..7] of byte; end; tpErg = ^tErg; var Erg: array of tErg; pf_x, pf_y: tPermfield; DigitCnt :tDigitCnt; permcnt, UsedDigits,Anzahl: NativeUint; function Fakultaet(i: integer): integer; begin Result := 1; while i > 1 do begin Result := Result * i; Dec(i); end; end; procedure OutErg(dgt: Uint32;pi,pJ:tpErg); begin writeln(dgt:3,' ', pi^.numUnusedDigit[dgt],'/',pj^.numUnusedDigit[dgt] ,' = ',pi^.numNormal,'/',pj^.numNormal); end; function Check(pI,pJ : tpErg;Nud :Word):integer; var dgt: NativeInt; Begin result := 0; dgt := 1; NUD := NUD SHR 1; repeat IF NUD AND 1 <> 0 then Begin If pI^.numNormal*pJ^.numUnusedDigit[dgt] = pJ^.numNormal*pI^.numUnusedDigit[dgt] then Begin inc(result); inc(DigitCnt[dgt]); IF Anzahl < 110 then OutErg(dgt,pI,pJ); end; end; inc(dgt); NUD := NUD SHR 1; until NUD = 0; end; procedure CheckWithOne(pI : tpErg;j,Nud:Uint32); var pJ : tpErg; l : NativeUInt; Begin pJ := pI; if UsedDigits <5 then Begin for j := j+1 to permcnt do begin inc(pJ); l := NUD AND pJ^.numUsedDigits; IF l <> 0 then inc(Anzahl,Check(pI,pJ,l)); end; end else Begin for j := j+1 to permcnt do begin inc(pJ); l := NUD AND pJ^.numUsedDigits; inc(Anzahl,Check(pI,pJ,l)); end; end; end; procedure SearchMultiple; var pI : tpErg; i : NativeUInt; begin pI := @Erg[0]; for i := 0 to permcnt do Begin CheckWithOne(pI,i,pI^.numUsedDigits); inc(pI); end; end; function BinomCoeff(n, k: byte): longint; var i: longint; begin if k > n div 2 then k := n - k; Result := 1; if k <= n then for i := 1 to k do Result := Result * (n - i + 1) div i; end; procedure InsertToErg(var E: tErg; const x: tPermfield); var n : Uint64; k,i,j,dgt,nud: NativeInt; begin k := UsedDigits; n := 0; nud := 0; for i := 1 to k do begin dgt := x[i]; nud := nud or cMaskDgt[dgt]; n := n * 10 + dgt; end; with E do begin numUsedDigits := nud; numNormal := n; end; For J := k downto 1 do Begin n := 0; for i := 1 to j-1 do n := n * 10 + x[i]; for i := j+1 to k do n := n * 10 + x[i]; E.numUnusedDigit[x[j]] := n; end; end; procedure PermKoutofN(k, n: nativeInt); var x, y: tpPermfield; i, yi, tmp: NativeInt; begin x := @pf_x; y := @pf_y; permcnt := 0; if k > n then k := n; if k = n then k := k - 1; for i := 1 to n do x^[i] := i; for i := 1 to k do y^[i] := i; InserttoErg(Erg[permcnt], x^); i := k; repeat yi := y^[i]; if yi < n then begin Inc(permcnt); Inc(yi); y^[i] := yi; tmp := x^[i]; x^[i] := x^[yi]; x^[yi] := tmp; i := k; InserttoErg(Erg[permcnt], x^); end else begin repeat tmp := x^[i]; x^[i] := x^[yi]; x^[yi] := tmp; Dec(yi); until yi <= i; y^[i] := yi; Dec(i); end; until (i = 0); end; procedure OutDigitCount; var i : tDigit; Begin writeln('omitted digits 1 to 9'); For i := 1 to 9do write(DigitCnt[i]:UsedDigits); writeln; end; procedure ClearDigitCount; var i : tDigit; Begin For i := low(DigitCnt) to high(DigitCnt) do DigitCnt[i] := 0; end; var t1, t0: TDateTime; begin For UsedDigits := 8 to 9 do Begin writeln('Used digits ',UsedDigits); T0 := now; ClearDigitCount; setlength(Erg, Fakultaet(UsedDigits) * BinomCoeff(cMaxDigits, UsedDigits)); Anzahl := 0; permcnt := 0; PermKoutOfN(UsedDigits, cMaxDigits); SearchMultiple; T1 := now; writeln('Found solutions ',Anzahl); OutDigitCount; writeln('time taken ',FormatDateTime('HH:NN:SS.zzz', T1 - T0)); setlength(Erg, 0); writeln; end; end.
import java.util.ArrayList; import java.util.Collections; import java.util.HashMap; import java.util.List; import java.util.Map; public class FractionReduction { public static void main(String[] args) { for ( int size = 2 ; size <= 5 ; size++ ) { reduce(size); } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits); int min = (int) Math.pow(10, numDigits-1); int max = (int) Math.pow(10, numDigits) - 1; List<Integer> values = new ArrayList<>(); for ( int number = min ; number <= max ; number++ ) { if ( isValid(number) ) { values.add(number); } } Map<Integer,Integer> cancelCount = new HashMap<>(); int size = values.size(); int solutions = 0; for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) { int numerator = values.get(nIndex); for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) { int denominator = values.get(dIndex); for ( int commonDigit : digitsInCommon(numerator, denominator) ) { int numRemoved = removeDigit(numerator, commonDigit); int denRemoved = removeDigit(denominator, commonDigit); if ( numerator * denRemoved == denominator * numRemoved ) { solutions++; cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2); if ( solutions <= 12 ) { System.out.printf(" When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved); } } } } } System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions); List<Integer> sorted = new ArrayList<>(cancelCount.keySet()); Collections.sort(sorted); for ( int removed : sorted ) { System.out.printf(" The digit %d was removed %d times.%n", removed, cancelCount.get(removed)); } System.out.println(); } private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000}; private static int removeDigit(int n, int removed) { int m = 0; int pow = 0; while ( n > 0 ) { int r = n % 10; if ( r != removed ) { m = m + r*powers[pow]; pow++; } n /= 10; } return m; } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10]; List<Integer> common = new ArrayList<>(); while ( n1 > 0 ) { int r = n1 % 10; count[r] += 1; n1 /= 10; } while ( n2 > 0 ) { int r = n2 % 10; if ( count[r] > 0 ) { common.add(r); } n2 /= 10; } return common; } private static boolean isValid(int num) { int[] count = new int[10]; while ( num > 0 ) { int r = num % 10; if ( r == 0 || count[r] == 1 ) { return false; } count[r] = 1; num /= 10; } return true; } }
Can you help me rewrite this code in Python instead of Pascal, keeping it the same logically?
program FracRedu; uses SysUtils; type tdigit = 0..9; const cMaskDgt: array [tdigit] of Uint32 = (1, 2, 4, 8, 16, 32, 64, 128, 256, 512 ); cMaxDigits = High(tdigit); type tPermfield = array[tdigit] of uint32; tpPermfield = ^tPermfield; tDigitCnt = array[tdigit] of Uint32; tErg = record numUsedDigits : Uint32; numUnusedDigit : array[tdigit] of Uint32; numNormal : Uint64; dummy : array[0..7] of byte; end; tpErg = ^tErg; var Erg: array of tErg; pf_x, pf_y: tPermfield; DigitCnt :tDigitCnt; permcnt, UsedDigits,Anzahl: NativeUint; function Fakultaet(i: integer): integer; begin Result := 1; while i > 1 do begin Result := Result * i; Dec(i); end; end; procedure OutErg(dgt: Uint32;pi,pJ:tpErg); begin writeln(dgt:3,' ', pi^.numUnusedDigit[dgt],'/',pj^.numUnusedDigit[dgt] ,' = ',pi^.numNormal,'/',pj^.numNormal); end; function Check(pI,pJ : tpErg;Nud :Word):integer; var dgt: NativeInt; Begin result := 0; dgt := 1; NUD := NUD SHR 1; repeat IF NUD AND 1 <> 0 then Begin If pI^.numNormal*pJ^.numUnusedDigit[dgt] = pJ^.numNormal*pI^.numUnusedDigit[dgt] then Begin inc(result); inc(DigitCnt[dgt]); IF Anzahl < 110 then OutErg(dgt,pI,pJ); end; end; inc(dgt); NUD := NUD SHR 1; until NUD = 0; end; procedure CheckWithOne(pI : tpErg;j,Nud:Uint32); var pJ : tpErg; l : NativeUInt; Begin pJ := pI; if UsedDigits <5 then Begin for j := j+1 to permcnt do begin inc(pJ); l := NUD AND pJ^.numUsedDigits; IF l <> 0 then inc(Anzahl,Check(pI,pJ,l)); end; end else Begin for j := j+1 to permcnt do begin inc(pJ); l := NUD AND pJ^.numUsedDigits; inc(Anzahl,Check(pI,pJ,l)); end; end; end; procedure SearchMultiple; var pI : tpErg; i : NativeUInt; begin pI := @Erg[0]; for i := 0 to permcnt do Begin CheckWithOne(pI,i,pI^.numUsedDigits); inc(pI); end; end; function BinomCoeff(n, k: byte): longint; var i: longint; begin if k > n div 2 then k := n - k; Result := 1; if k <= n then for i := 1 to k do Result := Result * (n - i + 1) div i; end; procedure InsertToErg(var E: tErg; const x: tPermfield); var n : Uint64; k,i,j,dgt,nud: NativeInt; begin k := UsedDigits; n := 0; nud := 0; for i := 1 to k do begin dgt := x[i]; nud := nud or cMaskDgt[dgt]; n := n * 10 + dgt; end; with E do begin numUsedDigits := nud; numNormal := n; end; For J := k downto 1 do Begin n := 0; for i := 1 to j-1 do n := n * 10 + x[i]; for i := j+1 to k do n := n * 10 + x[i]; E.numUnusedDigit[x[j]] := n; end; end; procedure PermKoutofN(k, n: nativeInt); var x, y: tpPermfield; i, yi, tmp: NativeInt; begin x := @pf_x; y := @pf_y; permcnt := 0; if k > n then k := n; if k = n then k := k - 1; for i := 1 to n do x^[i] := i; for i := 1 to k do y^[i] := i; InserttoErg(Erg[permcnt], x^); i := k; repeat yi := y^[i]; if yi < n then begin Inc(permcnt); Inc(yi); y^[i] := yi; tmp := x^[i]; x^[i] := x^[yi]; x^[yi] := tmp; i := k; InserttoErg(Erg[permcnt], x^); end else begin repeat tmp := x^[i]; x^[i] := x^[yi]; x^[yi] := tmp; Dec(yi); until yi <= i; y^[i] := yi; Dec(i); end; until (i = 0); end; procedure OutDigitCount; var i : tDigit; Begin writeln('omitted digits 1 to 9'); For i := 1 to 9do write(DigitCnt[i]:UsedDigits); writeln; end; procedure ClearDigitCount; var i : tDigit; Begin For i := low(DigitCnt) to high(DigitCnt) do DigitCnt[i] := 0; end; var t1, t0: TDateTime; begin For UsedDigits := 8 to 9 do Begin writeln('Used digits ',UsedDigits); T0 := now; ClearDigitCount; setlength(Erg, Fakultaet(UsedDigits) * BinomCoeff(cMaxDigits, UsedDigits)); Anzahl := 0; permcnt := 0; PermKoutOfN(UsedDigits, cMaxDigits); SearchMultiple; T1 := now; writeln('Found solutions ',Anzahl); OutDigitCount; writeln('time taken ',FormatDateTime('HH:NN:SS.zzz', T1 - T0)); setlength(Erg, 0); writeln; end; end.
def indexOf(haystack, needle): idx = 0 for straw in haystack: if straw == needle: return idx else: idx += 1 return -1 def getDigits(n, le, digits): while n > 0: r = n % 10 if r == 0 or indexOf(digits, r) >= 0: return False le -= 1 digits[le] = r n = int(n / 10) return True def removeDigit(digits, le, idx): pows = [1, 10, 100, 1000, 10000] sum = 0 pow = pows[le - 2] i = 0 while i < le: if i == idx: i += 1 continue sum = sum + digits[i] * pow pow = int(pow / 10) i += 1 return sum def main(): lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = [0 for i in range(5)] omitted = [[0 for i in range(10)] for j in range(5)] i = 0 while i < len(lims): n = lims[i][0] while n < lims[i][1]: nDigits = [0 for k in range(i + 2)] nOk = getDigits(n, i + 2, nDigits) if not nOk: n += 1 continue d = n + 1 while d <= lims[i][1] + 1: dDigits = [0 for k in range(i + 2)] dOk = getDigits(d, i + 2, dDigits) if not dOk: d += 1 continue nix = 0 while nix < len(nDigits): digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0: rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd): count[i] += 1 omitted[i][digit] += 1 if count[i] <= 12: print "%d/%d = %d/%d by omitting %d's" % (n, d, rn, rd, digit) nix += 1 d += 1 n += 1 print i += 1 i = 2 while i <= 5: print "There are %d %d-digit fractions of which:" % (count[i - 2], i) j = 1 while j <= 9: if omitted[i - 2][j] == 0: j += 1 continue print "%6s have %d's omitted" % (omitted[i - 2][j], j) j += 1 print i += 1 return None main()
Translate this program into VB but keep the logic exactly as in Pascal.
program FracRedu; uses SysUtils; type tdigit = 0..9; const cMaskDgt: array [tdigit] of Uint32 = (1, 2, 4, 8, 16, 32, 64, 128, 256, 512 ); cMaxDigits = High(tdigit); type tPermfield = array[tdigit] of uint32; tpPermfield = ^tPermfield; tDigitCnt = array[tdigit] of Uint32; tErg = record numUsedDigits : Uint32; numUnusedDigit : array[tdigit] of Uint32; numNormal : Uint64; dummy : array[0..7] of byte; end; tpErg = ^tErg; var Erg: array of tErg; pf_x, pf_y: tPermfield; DigitCnt :tDigitCnt; permcnt, UsedDigits,Anzahl: NativeUint; function Fakultaet(i: integer): integer; begin Result := 1; while i > 1 do begin Result := Result * i; Dec(i); end; end; procedure OutErg(dgt: Uint32;pi,pJ:tpErg); begin writeln(dgt:3,' ', pi^.numUnusedDigit[dgt],'/',pj^.numUnusedDigit[dgt] ,' = ',pi^.numNormal,'/',pj^.numNormal); end; function Check(pI,pJ : tpErg;Nud :Word):integer; var dgt: NativeInt; Begin result := 0; dgt := 1; NUD := NUD SHR 1; repeat IF NUD AND 1 <> 0 then Begin If pI^.numNormal*pJ^.numUnusedDigit[dgt] = pJ^.numNormal*pI^.numUnusedDigit[dgt] then Begin inc(result); inc(DigitCnt[dgt]); IF Anzahl < 110 then OutErg(dgt,pI,pJ); end; end; inc(dgt); NUD := NUD SHR 1; until NUD = 0; end; procedure CheckWithOne(pI : tpErg;j,Nud:Uint32); var pJ : tpErg; l : NativeUInt; Begin pJ := pI; if UsedDigits <5 then Begin for j := j+1 to permcnt do begin inc(pJ); l := NUD AND pJ^.numUsedDigits; IF l <> 0 then inc(Anzahl,Check(pI,pJ,l)); end; end else Begin for j := j+1 to permcnt do begin inc(pJ); l := NUD AND pJ^.numUsedDigits; inc(Anzahl,Check(pI,pJ,l)); end; end; end; procedure SearchMultiple; var pI : tpErg; i : NativeUInt; begin pI := @Erg[0]; for i := 0 to permcnt do Begin CheckWithOne(pI,i,pI^.numUsedDigits); inc(pI); end; end; function BinomCoeff(n, k: byte): longint; var i: longint; begin if k > n div 2 then k := n - k; Result := 1; if k <= n then for i := 1 to k do Result := Result * (n - i + 1) div i; end; procedure InsertToErg(var E: tErg; const x: tPermfield); var n : Uint64; k,i,j,dgt,nud: NativeInt; begin k := UsedDigits; n := 0; nud := 0; for i := 1 to k do begin dgt := x[i]; nud := nud or cMaskDgt[dgt]; n := n * 10 + dgt; end; with E do begin numUsedDigits := nud; numNormal := n; end; For J := k downto 1 do Begin n := 0; for i := 1 to j-1 do n := n * 10 + x[i]; for i := j+1 to k do n := n * 10 + x[i]; E.numUnusedDigit[x[j]] := n; end; end; procedure PermKoutofN(k, n: nativeInt); var x, y: tpPermfield; i, yi, tmp: NativeInt; begin x := @pf_x; y := @pf_y; permcnt := 0; if k > n then k := n; if k = n then k := k - 1; for i := 1 to n do x^[i] := i; for i := 1 to k do y^[i] := i; InserttoErg(Erg[permcnt], x^); i := k; repeat yi := y^[i]; if yi < n then begin Inc(permcnt); Inc(yi); y^[i] := yi; tmp := x^[i]; x^[i] := x^[yi]; x^[yi] := tmp; i := k; InserttoErg(Erg[permcnt], x^); end else begin repeat tmp := x^[i]; x^[i] := x^[yi]; x^[yi] := tmp; Dec(yi); until yi <= i; y^[i] := yi; Dec(i); end; until (i = 0); end; procedure OutDigitCount; var i : tDigit; Begin writeln('omitted digits 1 to 9'); For i := 1 to 9do write(DigitCnt[i]:UsedDigits); writeln; end; procedure ClearDigitCount; var i : tDigit; Begin For i := low(DigitCnt) to high(DigitCnt) do DigitCnt[i] := 0; end; var t1, t0: TDateTime; begin For UsedDigits := 8 to 9 do Begin writeln('Used digits ',UsedDigits); T0 := now; ClearDigitCount; setlength(Erg, Fakultaet(UsedDigits) * BinomCoeff(cMaxDigits, UsedDigits)); Anzahl := 0; permcnt := 0; PermKoutOfN(UsedDigits, cMaxDigits); SearchMultiple; T1 := now; writeln('Found solutions ',Anzahl); OutDigitCount; writeln('time taken ',FormatDateTime('HH:NN:SS.zzz', T1 - T0)); setlength(Erg, 0); writeln; end; end.
Module Module1 Function IndexOf(n As Integer, s As Integer()) As Integer For ii = 1 To s.Length Dim i = ii - 1 If s(i) = n Then Return i End If Next Return -1 End Function Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean While n > 0 Dim r = n Mod 10 If r = 0 OrElse IndexOf(r, digits) >= 0 Then Return False End If le -= 1 digits(le) = r n \= 10 End While Return True End Function Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer Dim pows = {1, 10, 100, 1000, 10000} Dim sum = 0 Dim pow = pows(le - 2) For ii = 1 To le Dim i = ii - 1 If i = idx Then Continue For End If sum += digits(i) * pow pow \= 10 Next Return sum End Function Sub Main() Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}} Dim count(5) As Integer Dim omitted(5, 10) As Integer Dim upperBound = lims.GetLength(0) For ii = 1 To upperBound Dim i = ii - 1 Dim nDigits(i + 2 - 1) As Integer Dim dDigits(i + 2 - 1) As Integer Dim blank(i + 2 - 1) As Integer For n = lims(i, 0) To lims(i, 1) blank.CopyTo(nDigits, 0) Dim nOk = GetDigits(n, i + 2, nDigits) If Not nOk Then Continue For End If For d = n + 1 To lims(i, 1) + 1 blank.CopyTo(dDigits, 0) Dim dOk = GetDigits(d, i + 2, dDigits) If Not dOk Then Continue For End If For nixt = 1 To nDigits.Length Dim nix = nixt - 1 Dim digit = nDigits(nix) Dim dix = IndexOf(digit, dDigits) If dix >= 0 Then Dim rn = RemoveDigit(nDigits, i + 2, nix) Dim rd = RemoveDigit(dDigits, i + 2, dix) If (n / d) = (rn / rd) Then count(i) += 1 omitted(i, digit) += 1 If count(i) <= 12 Then Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4} End If End If End If Next Next Next Console.WriteLine() Next For i = 2 To 5 Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i) For j = 1 To 9 If omitted(i - 2, j) = 0 Then Continue For End If Console.WriteLine("{0,6} have {1} Next Console.WriteLine() Next End Sub End Module
Convert this Pascal block to Go, preserving its control flow and logic.
program FracRedu; uses SysUtils; type tdigit = 0..9; const cMaskDgt: array [tdigit] of Uint32 = (1, 2, 4, 8, 16, 32, 64, 128, 256, 512 ); cMaxDigits = High(tdigit); type tPermfield = array[tdigit] of uint32; tpPermfield = ^tPermfield; tDigitCnt = array[tdigit] of Uint32; tErg = record numUsedDigits : Uint32; numUnusedDigit : array[tdigit] of Uint32; numNormal : Uint64; dummy : array[0..7] of byte; end; tpErg = ^tErg; var Erg: array of tErg; pf_x, pf_y: tPermfield; DigitCnt :tDigitCnt; permcnt, UsedDigits,Anzahl: NativeUint; function Fakultaet(i: integer): integer; begin Result := 1; while i > 1 do begin Result := Result * i; Dec(i); end; end; procedure OutErg(dgt: Uint32;pi,pJ:tpErg); begin writeln(dgt:3,' ', pi^.numUnusedDigit[dgt],'/',pj^.numUnusedDigit[dgt] ,' = ',pi^.numNormal,'/',pj^.numNormal); end; function Check(pI,pJ : tpErg;Nud :Word):integer; var dgt: NativeInt; Begin result := 0; dgt := 1; NUD := NUD SHR 1; repeat IF NUD AND 1 <> 0 then Begin If pI^.numNormal*pJ^.numUnusedDigit[dgt] = pJ^.numNormal*pI^.numUnusedDigit[dgt] then Begin inc(result); inc(DigitCnt[dgt]); IF Anzahl < 110 then OutErg(dgt,pI,pJ); end; end; inc(dgt); NUD := NUD SHR 1; until NUD = 0; end; procedure CheckWithOne(pI : tpErg;j,Nud:Uint32); var pJ : tpErg; l : NativeUInt; Begin pJ := pI; if UsedDigits <5 then Begin for j := j+1 to permcnt do begin inc(pJ); l := NUD AND pJ^.numUsedDigits; IF l <> 0 then inc(Anzahl,Check(pI,pJ,l)); end; end else Begin for j := j+1 to permcnt do begin inc(pJ); l := NUD AND pJ^.numUsedDigits; inc(Anzahl,Check(pI,pJ,l)); end; end; end; procedure SearchMultiple; var pI : tpErg; i : NativeUInt; begin pI := @Erg[0]; for i := 0 to permcnt do Begin CheckWithOne(pI,i,pI^.numUsedDigits); inc(pI); end; end; function BinomCoeff(n, k: byte): longint; var i: longint; begin if k > n div 2 then k := n - k; Result := 1; if k <= n then for i := 1 to k do Result := Result * (n - i + 1) div i; end; procedure InsertToErg(var E: tErg; const x: tPermfield); var n : Uint64; k,i,j,dgt,nud: NativeInt; begin k := UsedDigits; n := 0; nud := 0; for i := 1 to k do begin dgt := x[i]; nud := nud or cMaskDgt[dgt]; n := n * 10 + dgt; end; with E do begin numUsedDigits := nud; numNormal := n; end; For J := k downto 1 do Begin n := 0; for i := 1 to j-1 do n := n * 10 + x[i]; for i := j+1 to k do n := n * 10 + x[i]; E.numUnusedDigit[x[j]] := n; end; end; procedure PermKoutofN(k, n: nativeInt); var x, y: tpPermfield; i, yi, tmp: NativeInt; begin x := @pf_x; y := @pf_y; permcnt := 0; if k > n then k := n; if k = n then k := k - 1; for i := 1 to n do x^[i] := i; for i := 1 to k do y^[i] := i; InserttoErg(Erg[permcnt], x^); i := k; repeat yi := y^[i]; if yi < n then begin Inc(permcnt); Inc(yi); y^[i] := yi; tmp := x^[i]; x^[i] := x^[yi]; x^[yi] := tmp; i := k; InserttoErg(Erg[permcnt], x^); end else begin repeat tmp := x^[i]; x^[i] := x^[yi]; x^[yi] := tmp; Dec(yi); until yi <= i; y^[i] := yi; Dec(i); end; until (i = 0); end; procedure OutDigitCount; var i : tDigit; Begin writeln('omitted digits 1 to 9'); For i := 1 to 9do write(DigitCnt[i]:UsedDigits); writeln; end; procedure ClearDigitCount; var i : tDigit; Begin For i := low(DigitCnt) to high(DigitCnt) do DigitCnt[i] := 0; end; var t1, t0: TDateTime; begin For UsedDigits := 8 to 9 do Begin writeln('Used digits ',UsedDigits); T0 := now; ClearDigitCount; setlength(Erg, Fakultaet(UsedDigits) * BinomCoeff(cMaxDigits, UsedDigits)); Anzahl := 0; permcnt := 0; PermKoutOfN(UsedDigits, cMaxDigits); SearchMultiple; T1 := now; writeln('Found solutions ',Anzahl); OutDigitCount; writeln('time taken ',FormatDateTime('HH:NN:SS.zzz', T1 - T0)); setlength(Erg, 0); writeln; end; end.
package main import ( "fmt" "time" ) func indexOf(n int, s []int) int { for i, j := range s { if n == j { return i } } return -1 } func getDigits(n, le int, digits []int) bool { for n > 0 { r := n % 10 if r == 0 || indexOf(r, digits) >= 0 { return false } le-- digits[le] = r n /= 10 } return true } var pows = [5]int{1, 10, 100, 1000, 10000} func removeDigit(digits []int, le, idx int) int { sum := 0 pow := pows[le-2] for i := 0; i < le; i++ { if i == idx { continue } sum += digits[i] * pow pow /= 10 } return sum } func main() { start := time.Now() lims := [5][2]int{ {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}, {123456, 987653}, } var count [5]int var omitted [5][10]int for i, lim := range lims { nDigits := make([]int, i+2) dDigits := make([]int, i+2) blank := make([]int, i+2) for n := lim[0]; n <= lim[1]; n++ { copy(nDigits, blank) nOk := getDigits(n, i+2, nDigits) if !nOk { continue } for d := n + 1; d <= lim[1]+1; d++ { copy(dDigits, blank) dOk := getDigits(d, i+2, dDigits) if !dOk { continue } for nix, digit := range nDigits { if dix := indexOf(digit, dDigits); dix >= 0 { rn := removeDigit(nDigits, i+2, nix) rd := removeDigit(dDigits, i+2, dix) if float64(n)/float64(d) == float64(rn)/float64(rd) { count[i]++ omitted[i][digit]++ if count[i] <= 12 { fmt.Printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit) } } } } } } fmt.Println() } for i := 2; i <= 6; i++ { fmt.Printf("There are %d %d-digit fractions of which:\n", count[i-2], i) for j := 1; j <= 9; j++ { if omitted[i-2][j] == 0 { continue } fmt.Printf("%6d have %d's omitted\n", omitted[i-2][j], j) } fmt.Println() } fmt.Printf("Took %s\n", time.Since(start)) }
Translate the given Perl code snippet into C without altering its behavior.
use strict; use warnings; use feature 'say'; use List::Util qw<sum uniq uniqnum head tail>; for my $exp (map { $_ - 1 } <2 3 4>) { my %reduced; my $start = sum map { 10 ** $_ * ($exp - $_ + 1) } 0..$exp; my $end = 10**($exp+1) - -1 + sum map { 10 ** $_ * ($exp - $_) } 0..$exp-1; for my $den ($start .. $end-1) { next if $den =~ /0/ or (uniqnum split '', $den) <= $exp; for my $num ($start .. $den-1) { next if $num =~ /0/ or (uniqnum split '', $num) <= $exp; my %i; map { $i{$_}++ } (uniq head -1, split '',$den), uniq tail -1, split '',$num; my @set = grep { $_ if $i{$_} > 1 } keys %i; next if @set < 1; for (@set) { (my $ne = $num) =~ s/$_//; (my $de = $den) =~ s/$_//; if ($ne/$de == $num/$den) { $reduced{"$num/$den:$_"} = "$ne/$de"; } } } } my $digit = $exp + 1; say "\n" . +%reduced . " $digit-digit reducible fractions:"; for my $n (1..9) { my $cnt = scalar grep { /:$n/ } keys %reduced; say "$cnt with removed $n" if $cnt; } say "\n 12 (or all, if less) $digit-digit reducible fractions:"; for my $f (head 12, sort keys %reduced) { printf " %s => %s removed %s\n", substr($f,0,$digit*2+1), $reduced{$f}, substr($f,-1) } }
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }
Generate a C# translation of this Perl snippet without changing its computational steps.
use strict; use warnings; use feature 'say'; use List::Util qw<sum uniq uniqnum head tail>; for my $exp (map { $_ - 1 } <2 3 4>) { my %reduced; my $start = sum map { 10 ** $_ * ($exp - $_ + 1) } 0..$exp; my $end = 10**($exp+1) - -1 + sum map { 10 ** $_ * ($exp - $_) } 0..$exp-1; for my $den ($start .. $end-1) { next if $den =~ /0/ or (uniqnum split '', $den) <= $exp; for my $num ($start .. $den-1) { next if $num =~ /0/ or (uniqnum split '', $num) <= $exp; my %i; map { $i{$_}++ } (uniq head -1, split '',$den), uniq tail -1, split '',$num; my @set = grep { $_ if $i{$_} > 1 } keys %i; next if @set < 1; for (@set) { (my $ne = $num) =~ s/$_//; (my $de = $den) =~ s/$_//; if ($ne/$de == $num/$den) { $reduced{"$num/$den:$_"} = "$ne/$de"; } } } } my $digit = $exp + 1; say "\n" . +%reduced . " $digit-digit reducible fractions:"; for my $n (1..9) { my $cnt = scalar grep { /:$n/ } keys %reduced; say "$cnt with removed $n" if $cnt; } say "\n 12 (or all, if less) $digit-digit reducible fractions:"; for my $f (head 12, sort keys %reduced) { printf " %s => %s removed %s\n", substr($f,0,$digit*2+1), $reduced{$f}, substr($f,-1) } }
using System; namespace FractionReduction { class Program { static int IndexOf(int n, int[] s) { for (int i = 0; i < s.Length; i++) { if (s[i] == n) { return i; } } return -1; } static bool GetDigits(int n, int le, int[] digits) { while (n > 0) { var r = n % 10; if (r == 0 || IndexOf(r, digits) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } static int RemoveDigit(int[] digits, int le, int idx) { int[] pows = { 1, 10, 100, 1000, 10000 }; var sum = 0; var pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } static void Main() { var lims = new int[,] { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; var count = new int[5]; var omitted = new int[5, 10]; var upperBound = lims.GetLength(0); for (int i = 0; i < upperBound; i++) { var nDigits = new int[i + 2]; var dDigits = new int[i + 2]; var blank = new int[i + 2]; for (int n = lims[i, 0]; n <= lims[i, 1]; n++) { blank.CopyTo(nDigits, 0); var nOk = GetDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i, 1] + 1; d++) { blank.CopyTo(dDigits, 0); var dOk = GetDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.Length; nix++) { var digit = nDigits[nix]; var dix = IndexOf(digit, dDigits); if (dix >= 0) { var rn = RemoveDigit(nDigits, i + 2, nix); var rd = RemoveDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i, digit]++; if (count[i] <= 12) { Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4}'s", n, d, rn, rd, digit); } } } } } } Console.WriteLine(); } for (int i = 2; i <= 5; i++) { Console.WriteLine("There are {0} {1}-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2, j] == 0) { continue; } Console.WriteLine("{0,6} have {1}'s omitted", omitted[i - 2, j], j); } Console.WriteLine(); } } } }
Write the same code in C++ as shown below in Perl.
use strict; use warnings; use feature 'say'; use List::Util qw<sum uniq uniqnum head tail>; for my $exp (map { $_ - 1 } <2 3 4>) { my %reduced; my $start = sum map { 10 ** $_ * ($exp - $_ + 1) } 0..$exp; my $end = 10**($exp+1) - -1 + sum map { 10 ** $_ * ($exp - $_) } 0..$exp-1; for my $den ($start .. $end-1) { next if $den =~ /0/ or (uniqnum split '', $den) <= $exp; for my $num ($start .. $den-1) { next if $num =~ /0/ or (uniqnum split '', $num) <= $exp; my %i; map { $i{$_}++ } (uniq head -1, split '',$den), uniq tail -1, split '',$num; my @set = grep { $_ if $i{$_} > 1 } keys %i; next if @set < 1; for (@set) { (my $ne = $num) =~ s/$_//; (my $de = $den) =~ s/$_//; if ($ne/$de == $num/$den) { $reduced{"$num/$den:$_"} = "$ne/$de"; } } } } my $digit = $exp + 1; say "\n" . +%reduced . " $digit-digit reducible fractions:"; for my $n (1..9) { my $cnt = scalar grep { /:$n/ } keys %reduced; say "$cnt with removed $n" if $cnt; } say "\n 12 (or all, if less) $digit-digit reducible fractions:"; for my $f (head 12, sort keys %reduced) { printf " %s => %s removed %s\n", substr($f,0,$digit*2+1), $reduced{$f}, substr($f,-1) } }
#include <array> #include <iomanip> #include <iostream> #include <vector> int indexOf(const std::vector<int> &haystack, int needle) { auto it = haystack.cbegin(); auto end = haystack.cend(); int idx = 0; for (; it != end; it = std::next(it)) { if (*it == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, std::vector<int> &digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(const std::vector<int> &digits, int le, int idx) { static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 }; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } int main() { std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }; std::array<int, 5> count; std::array<std::array<int, 10>, 5> omitted; std::fill(count.begin(), count.end(), 0); std::for_each(omitted.begin(), omitted.end(), [](auto &a) { std::fill(a.begin(), a.end(), 0); } ); for (size_t i = 0; i < lims.size(); i++) { std::vector<int> nDigits(i + 2); std::vector<int> dDigits(i + 2); for (int n = lims[i].first; n <= lims[i].second; n++) { std::fill(nDigits.begin(), nDigits.end(), 0); bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i].second + 1; d++) { std::fill(dDigits.begin(), dDigits.end(), 0); bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (size_t nix = 0; nix < nDigits.size(); nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n"; } } } } } } std::cout << '\n'; } for (int i = 2; i <= 5; i++) { std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n"; for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n"; } std::cout << '\n'; } return 0; }
Translate this program into Java but keep the logic exactly as in Perl.
use strict; use warnings; use feature 'say'; use List::Util qw<sum uniq uniqnum head tail>; for my $exp (map { $_ - 1 } <2 3 4>) { my %reduced; my $start = sum map { 10 ** $_ * ($exp - $_ + 1) } 0..$exp; my $end = 10**($exp+1) - -1 + sum map { 10 ** $_ * ($exp - $_) } 0..$exp-1; for my $den ($start .. $end-1) { next if $den =~ /0/ or (uniqnum split '', $den) <= $exp; for my $num ($start .. $den-1) { next if $num =~ /0/ or (uniqnum split '', $num) <= $exp; my %i; map { $i{$_}++ } (uniq head -1, split '',$den), uniq tail -1, split '',$num; my @set = grep { $_ if $i{$_} > 1 } keys %i; next if @set < 1; for (@set) { (my $ne = $num) =~ s/$_//; (my $de = $den) =~ s/$_//; if ($ne/$de == $num/$den) { $reduced{"$num/$den:$_"} = "$ne/$de"; } } } } my $digit = $exp + 1; say "\n" . +%reduced . " $digit-digit reducible fractions:"; for my $n (1..9) { my $cnt = scalar grep { /:$n/ } keys %reduced; say "$cnt with removed $n" if $cnt; } say "\n 12 (or all, if less) $digit-digit reducible fractions:"; for my $f (head 12, sort keys %reduced) { printf " %s => %s removed %s\n", substr($f,0,$digit*2+1), $reduced{$f}, substr($f,-1) } }
import java.util.ArrayList; import java.util.Collections; import java.util.HashMap; import java.util.List; import java.util.Map; public class FractionReduction { public static void main(String[] args) { for ( int size = 2 ; size <= 5 ; size++ ) { reduce(size); } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits); int min = (int) Math.pow(10, numDigits-1); int max = (int) Math.pow(10, numDigits) - 1; List<Integer> values = new ArrayList<>(); for ( int number = min ; number <= max ; number++ ) { if ( isValid(number) ) { values.add(number); } } Map<Integer,Integer> cancelCount = new HashMap<>(); int size = values.size(); int solutions = 0; for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) { int numerator = values.get(nIndex); for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) { int denominator = values.get(dIndex); for ( int commonDigit : digitsInCommon(numerator, denominator) ) { int numRemoved = removeDigit(numerator, commonDigit); int denRemoved = removeDigit(denominator, commonDigit); if ( numerator * denRemoved == denominator * numRemoved ) { solutions++; cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2); if ( solutions <= 12 ) { System.out.printf(" When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved); } } } } } System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions); List<Integer> sorted = new ArrayList<>(cancelCount.keySet()); Collections.sort(sorted); for ( int removed : sorted ) { System.out.printf(" The digit %d was removed %d times.%n", removed, cancelCount.get(removed)); } System.out.println(); } private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000}; private static int removeDigit(int n, int removed) { int m = 0; int pow = 0; while ( n > 0 ) { int r = n % 10; if ( r != removed ) { m = m + r*powers[pow]; pow++; } n /= 10; } return m; } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10]; List<Integer> common = new ArrayList<>(); while ( n1 > 0 ) { int r = n1 % 10; count[r] += 1; n1 /= 10; } while ( n2 > 0 ) { int r = n2 % 10; if ( count[r] > 0 ) { common.add(r); } n2 /= 10; } return common; } private static boolean isValid(int num) { int[] count = new int[10]; while ( num > 0 ) { int r = num % 10; if ( r == 0 || count[r] == 1 ) { return false; } count[r] = 1; num /= 10; } return true; } }
Port the following code from Perl to Python with equivalent syntax and logic.
use strict; use warnings; use feature 'say'; use List::Util qw<sum uniq uniqnum head tail>; for my $exp (map { $_ - 1 } <2 3 4>) { my %reduced; my $start = sum map { 10 ** $_ * ($exp - $_ + 1) } 0..$exp; my $end = 10**($exp+1) - -1 + sum map { 10 ** $_ * ($exp - $_) } 0..$exp-1; for my $den ($start .. $end-1) { next if $den =~ /0/ or (uniqnum split '', $den) <= $exp; for my $num ($start .. $den-1) { next if $num =~ /0/ or (uniqnum split '', $num) <= $exp; my %i; map { $i{$_}++ } (uniq head -1, split '',$den), uniq tail -1, split '',$num; my @set = grep { $_ if $i{$_} > 1 } keys %i; next if @set < 1; for (@set) { (my $ne = $num) =~ s/$_//; (my $de = $den) =~ s/$_//; if ($ne/$de == $num/$den) { $reduced{"$num/$den:$_"} = "$ne/$de"; } } } } my $digit = $exp + 1; say "\n" . +%reduced . " $digit-digit reducible fractions:"; for my $n (1..9) { my $cnt = scalar grep { /:$n/ } keys %reduced; say "$cnt with removed $n" if $cnt; } say "\n 12 (or all, if less) $digit-digit reducible fractions:"; for my $f (head 12, sort keys %reduced) { printf " %s => %s removed %s\n", substr($f,0,$digit*2+1), $reduced{$f}, substr($f,-1) } }
def indexOf(haystack, needle): idx = 0 for straw in haystack: if straw == needle: return idx else: idx += 1 return -1 def getDigits(n, le, digits): while n > 0: r = n % 10 if r == 0 or indexOf(digits, r) >= 0: return False le -= 1 digits[le] = r n = int(n / 10) return True def removeDigit(digits, le, idx): pows = [1, 10, 100, 1000, 10000] sum = 0 pow = pows[le - 2] i = 0 while i < le: if i == idx: i += 1 continue sum = sum + digits[i] * pow pow = int(pow / 10) i += 1 return sum def main(): lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = [0 for i in range(5)] omitted = [[0 for i in range(10)] for j in range(5)] i = 0 while i < len(lims): n = lims[i][0] while n < lims[i][1]: nDigits = [0 for k in range(i + 2)] nOk = getDigits(n, i + 2, nDigits) if not nOk: n += 1 continue d = n + 1 while d <= lims[i][1] + 1: dDigits = [0 for k in range(i + 2)] dOk = getDigits(d, i + 2, dDigits) if not dOk: d += 1 continue nix = 0 while nix < len(nDigits): digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0: rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd): count[i] += 1 omitted[i][digit] += 1 if count[i] <= 12: print "%d/%d = %d/%d by omitting %d's" % (n, d, rn, rd, digit) nix += 1 d += 1 n += 1 print i += 1 i = 2 while i <= 5: print "There are %d %d-digit fractions of which:" % (count[i - 2], i) j = 1 while j <= 9: if omitted[i - 2][j] == 0: j += 1 continue print "%6s have %d's omitted" % (omitted[i - 2][j], j) j += 1 print i += 1 return None main()
Keep all operations the same but rewrite the snippet in VB.
use strict; use warnings; use feature 'say'; use List::Util qw<sum uniq uniqnum head tail>; for my $exp (map { $_ - 1 } <2 3 4>) { my %reduced; my $start = sum map { 10 ** $_ * ($exp - $_ + 1) } 0..$exp; my $end = 10**($exp+1) - -1 + sum map { 10 ** $_ * ($exp - $_) } 0..$exp-1; for my $den ($start .. $end-1) { next if $den =~ /0/ or (uniqnum split '', $den) <= $exp; for my $num ($start .. $den-1) { next if $num =~ /0/ or (uniqnum split '', $num) <= $exp; my %i; map { $i{$_}++ } (uniq head -1, split '',$den), uniq tail -1, split '',$num; my @set = grep { $_ if $i{$_} > 1 } keys %i; next if @set < 1; for (@set) { (my $ne = $num) =~ s/$_//; (my $de = $den) =~ s/$_//; if ($ne/$de == $num/$den) { $reduced{"$num/$den:$_"} = "$ne/$de"; } } } } my $digit = $exp + 1; say "\n" . +%reduced . " $digit-digit reducible fractions:"; for my $n (1..9) { my $cnt = scalar grep { /:$n/ } keys %reduced; say "$cnt with removed $n" if $cnt; } say "\n 12 (or all, if less) $digit-digit reducible fractions:"; for my $f (head 12, sort keys %reduced) { printf " %s => %s removed %s\n", substr($f,0,$digit*2+1), $reduced{$f}, substr($f,-1) } }
Module Module1 Function IndexOf(n As Integer, s As Integer()) As Integer For ii = 1 To s.Length Dim i = ii - 1 If s(i) = n Then Return i End If Next Return -1 End Function Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean While n > 0 Dim r = n Mod 10 If r = 0 OrElse IndexOf(r, digits) >= 0 Then Return False End If le -= 1 digits(le) = r n \= 10 End While Return True End Function Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer Dim pows = {1, 10, 100, 1000, 10000} Dim sum = 0 Dim pow = pows(le - 2) For ii = 1 To le Dim i = ii - 1 If i = idx Then Continue For End If sum += digits(i) * pow pow \= 10 Next Return sum End Function Sub Main() Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}} Dim count(5) As Integer Dim omitted(5, 10) As Integer Dim upperBound = lims.GetLength(0) For ii = 1 To upperBound Dim i = ii - 1 Dim nDigits(i + 2 - 1) As Integer Dim dDigits(i + 2 - 1) As Integer Dim blank(i + 2 - 1) As Integer For n = lims(i, 0) To lims(i, 1) blank.CopyTo(nDigits, 0) Dim nOk = GetDigits(n, i + 2, nDigits) If Not nOk Then Continue For End If For d = n + 1 To lims(i, 1) + 1 blank.CopyTo(dDigits, 0) Dim dOk = GetDigits(d, i + 2, dDigits) If Not dOk Then Continue For End If For nixt = 1 To nDigits.Length Dim nix = nixt - 1 Dim digit = nDigits(nix) Dim dix = IndexOf(digit, dDigits) If dix >= 0 Then Dim rn = RemoveDigit(nDigits, i + 2, nix) Dim rd = RemoveDigit(dDigits, i + 2, dix) If (n / d) = (rn / rd) Then count(i) += 1 omitted(i, digit) += 1 If count(i) <= 12 Then Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4} End If End If End If Next Next Next Console.WriteLine() Next For i = 2 To 5 Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i) For j = 1 To 9 If omitted(i - 2, j) = 0 Then Continue For End If Console.WriteLine("{0,6} have {1} Next Console.WriteLine() Next End Sub End Module
Transform the following Perl implementation into Go, maintaining the same output and logic.
use strict; use warnings; use feature 'say'; use List::Util qw<sum uniq uniqnum head tail>; for my $exp (map { $_ - 1 } <2 3 4>) { my %reduced; my $start = sum map { 10 ** $_ * ($exp - $_ + 1) } 0..$exp; my $end = 10**($exp+1) - -1 + sum map { 10 ** $_ * ($exp - $_) } 0..$exp-1; for my $den ($start .. $end-1) { next if $den =~ /0/ or (uniqnum split '', $den) <= $exp; for my $num ($start .. $den-1) { next if $num =~ /0/ or (uniqnum split '', $num) <= $exp; my %i; map { $i{$_}++ } (uniq head -1, split '',$den), uniq tail -1, split '',$num; my @set = grep { $_ if $i{$_} > 1 } keys %i; next if @set < 1; for (@set) { (my $ne = $num) =~ s/$_//; (my $de = $den) =~ s/$_//; if ($ne/$de == $num/$den) { $reduced{"$num/$den:$_"} = "$ne/$de"; } } } } my $digit = $exp + 1; say "\n" . +%reduced . " $digit-digit reducible fractions:"; for my $n (1..9) { my $cnt = scalar grep { /:$n/ } keys %reduced; say "$cnt with removed $n" if $cnt; } say "\n 12 (or all, if less) $digit-digit reducible fractions:"; for my $f (head 12, sort keys %reduced) { printf " %s => %s removed %s\n", substr($f,0,$digit*2+1), $reduced{$f}, substr($f,-1) } }
package main import ( "fmt" "time" ) func indexOf(n int, s []int) int { for i, j := range s { if n == j { return i } } return -1 } func getDigits(n, le int, digits []int) bool { for n > 0 { r := n % 10 if r == 0 || indexOf(r, digits) >= 0 { return false } le-- digits[le] = r n /= 10 } return true } var pows = [5]int{1, 10, 100, 1000, 10000} func removeDigit(digits []int, le, idx int) int { sum := 0 pow := pows[le-2] for i := 0; i < le; i++ { if i == idx { continue } sum += digits[i] * pow pow /= 10 } return sum } func main() { start := time.Now() lims := [5][2]int{ {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}, {123456, 987653}, } var count [5]int var omitted [5][10]int for i, lim := range lims { nDigits := make([]int, i+2) dDigits := make([]int, i+2) blank := make([]int, i+2) for n := lim[0]; n <= lim[1]; n++ { copy(nDigits, blank) nOk := getDigits(n, i+2, nDigits) if !nOk { continue } for d := n + 1; d <= lim[1]+1; d++ { copy(dDigits, blank) dOk := getDigits(d, i+2, dDigits) if !dOk { continue } for nix, digit := range nDigits { if dix := indexOf(digit, dDigits); dix >= 0 { rn := removeDigit(nDigits, i+2, nix) rd := removeDigit(dDigits, i+2, dix) if float64(n)/float64(d) == float64(rn)/float64(rd) { count[i]++ omitted[i][digit]++ if count[i] <= 12 { fmt.Printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit) } } } } } } fmt.Println() } for i := 2; i <= 6; i++ { fmt.Printf("There are %d %d-digit fractions of which:\n", count[i-2], i) for j := 1; j <= 9; j++ { if omitted[i-2][j] == 0 { continue } fmt.Printf("%6d have %d's omitted\n", omitted[i-2][j], j) } fmt.Println() } fmt.Printf("Took %s\n", time.Since(start)) }
Produce a functionally identical C code for the snippet given in Racket.
#lang racket (require racket/generator syntax/parse/define) (define-syntax-parser for** [(_ [x:id {~datum <-} (e ...)] rst ...) #'(e ... (λ (x) (for** rst ...)))] [(_ e ...) #'(begin e ...)]) (define (permutations xs n yield #:lower [lower #f]) (let loop ([xs xs] [n n] [acc '()] [lower lower]) (cond [(= n 0) (yield (reverse acc))] [else (for ([x (in-list xs)] #:when (or (not lower) (>= x (first lower)))) (loop (remove x xs) (sub1 n) (cons x acc) (and lower (= x (first lower)) (rest lower))))]))) (define (list->number xs) (foldl (λ (e acc) (+ (* 10 acc) e)) 0 xs)) (define (calc n) (define rng (range 1 10)) (in-generator (for** [numer <- (permutations rng n)] [denom <- (permutations rng n #:lower numer)] (for* (#:when (not (equal? numer denom)) [crossed (in-list numer)] #:when (member crossed denom) [numer* (in-value (list->number (remove crossed numer)))] [denom* (in-value (list->number (remove crossed denom)))] [numer** (in-value (list->number numer))] [denom** (in-value (list->number denom))] #:when (= (* numer** denom*) (* numer* denom**))) (yield (list numer** denom** numer* denom* crossed)))))) (define (enumerate n) (for ([x (calc n)] [i (in-range 12)]) (apply printf "~a/~a = ~a/~a (~a crossed out)\n" x)) (newline)) (define (stats n) (define digits (make-hash)) (for ([x (calc n)]) (hash-update! digits (last x) add1 0)) (printf "There are ~a ~a-digit fractions of which:\n" (for/sum ([(k v) (in-hash digits)]) v) n) (for ([digit (in-list (sort (hash->list digits) < #:key car))]) (printf " The digit ~a was crossed out ~a times\n" (car digit) (cdr digit))) (newline)) (define (main) (enumerate 2) (enumerate 3) (enumerate 4) (enumerate 5) (stats 2) (stats 3) (stats 4) (stats 5)) (main)
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }
Can you help me rewrite this code in C# instead of Racket, keeping it the same logically?
#lang racket (require racket/generator syntax/parse/define) (define-syntax-parser for** [(_ [x:id {~datum <-} (e ...)] rst ...) #'(e ... (λ (x) (for** rst ...)))] [(_ e ...) #'(begin e ...)]) (define (permutations xs n yield #:lower [lower #f]) (let loop ([xs xs] [n n] [acc '()] [lower lower]) (cond [(= n 0) (yield (reverse acc))] [else (for ([x (in-list xs)] #:when (or (not lower) (>= x (first lower)))) (loop (remove x xs) (sub1 n) (cons x acc) (and lower (= x (first lower)) (rest lower))))]))) (define (list->number xs) (foldl (λ (e acc) (+ (* 10 acc) e)) 0 xs)) (define (calc n) (define rng (range 1 10)) (in-generator (for** [numer <- (permutations rng n)] [denom <- (permutations rng n #:lower numer)] (for* (#:when (not (equal? numer denom)) [crossed (in-list numer)] #:when (member crossed denom) [numer* (in-value (list->number (remove crossed numer)))] [denom* (in-value (list->number (remove crossed denom)))] [numer** (in-value (list->number numer))] [denom** (in-value (list->number denom))] #:when (= (* numer** denom*) (* numer* denom**))) (yield (list numer** denom** numer* denom* crossed)))))) (define (enumerate n) (for ([x (calc n)] [i (in-range 12)]) (apply printf "~a/~a = ~a/~a (~a crossed out)\n" x)) (newline)) (define (stats n) (define digits (make-hash)) (for ([x (calc n)]) (hash-update! digits (last x) add1 0)) (printf "There are ~a ~a-digit fractions of which:\n" (for/sum ([(k v) (in-hash digits)]) v) n) (for ([digit (in-list (sort (hash->list digits) < #:key car))]) (printf " The digit ~a was crossed out ~a times\n" (car digit) (cdr digit))) (newline)) (define (main) (enumerate 2) (enumerate 3) (enumerate 4) (enumerate 5) (stats 2) (stats 3) (stats 4) (stats 5)) (main)
using System; namespace FractionReduction { class Program { static int IndexOf(int n, int[] s) { for (int i = 0; i < s.Length; i++) { if (s[i] == n) { return i; } } return -1; } static bool GetDigits(int n, int le, int[] digits) { while (n > 0) { var r = n % 10; if (r == 0 || IndexOf(r, digits) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } static int RemoveDigit(int[] digits, int le, int idx) { int[] pows = { 1, 10, 100, 1000, 10000 }; var sum = 0; var pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } static void Main() { var lims = new int[,] { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; var count = new int[5]; var omitted = new int[5, 10]; var upperBound = lims.GetLength(0); for (int i = 0; i < upperBound; i++) { var nDigits = new int[i + 2]; var dDigits = new int[i + 2]; var blank = new int[i + 2]; for (int n = lims[i, 0]; n <= lims[i, 1]; n++) { blank.CopyTo(nDigits, 0); var nOk = GetDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i, 1] + 1; d++) { blank.CopyTo(dDigits, 0); var dOk = GetDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.Length; nix++) { var digit = nDigits[nix]; var dix = IndexOf(digit, dDigits); if (dix >= 0) { var rn = RemoveDigit(nDigits, i + 2, nix); var rd = RemoveDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i, digit]++; if (count[i] <= 12) { Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4}'s", n, d, rn, rd, digit); } } } } } } Console.WriteLine(); } for (int i = 2; i <= 5; i++) { Console.WriteLine("There are {0} {1}-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2, j] == 0) { continue; } Console.WriteLine("{0,6} have {1}'s omitted", omitted[i - 2, j], j); } Console.WriteLine(); } } } }
Please provide an equivalent version of this Racket code in C++.
#lang racket (require racket/generator syntax/parse/define) (define-syntax-parser for** [(_ [x:id {~datum <-} (e ...)] rst ...) #'(e ... (λ (x) (for** rst ...)))] [(_ e ...) #'(begin e ...)]) (define (permutations xs n yield #:lower [lower #f]) (let loop ([xs xs] [n n] [acc '()] [lower lower]) (cond [(= n 0) (yield (reverse acc))] [else (for ([x (in-list xs)] #:when (or (not lower) (>= x (first lower)))) (loop (remove x xs) (sub1 n) (cons x acc) (and lower (= x (first lower)) (rest lower))))]))) (define (list->number xs) (foldl (λ (e acc) (+ (* 10 acc) e)) 0 xs)) (define (calc n) (define rng (range 1 10)) (in-generator (for** [numer <- (permutations rng n)] [denom <- (permutations rng n #:lower numer)] (for* (#:when (not (equal? numer denom)) [crossed (in-list numer)] #:when (member crossed denom) [numer* (in-value (list->number (remove crossed numer)))] [denom* (in-value (list->number (remove crossed denom)))] [numer** (in-value (list->number numer))] [denom** (in-value (list->number denom))] #:when (= (* numer** denom*) (* numer* denom**))) (yield (list numer** denom** numer* denom* crossed)))))) (define (enumerate n) (for ([x (calc n)] [i (in-range 12)]) (apply printf "~a/~a = ~a/~a (~a crossed out)\n" x)) (newline)) (define (stats n) (define digits (make-hash)) (for ([x (calc n)]) (hash-update! digits (last x) add1 0)) (printf "There are ~a ~a-digit fractions of which:\n" (for/sum ([(k v) (in-hash digits)]) v) n) (for ([digit (in-list (sort (hash->list digits) < #:key car))]) (printf " The digit ~a was crossed out ~a times\n" (car digit) (cdr digit))) (newline)) (define (main) (enumerate 2) (enumerate 3) (enumerate 4) (enumerate 5) (stats 2) (stats 3) (stats 4) (stats 5)) (main)
#include <array> #include <iomanip> #include <iostream> #include <vector> int indexOf(const std::vector<int> &haystack, int needle) { auto it = haystack.cbegin(); auto end = haystack.cend(); int idx = 0; for (; it != end; it = std::next(it)) { if (*it == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, std::vector<int> &digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(const std::vector<int> &digits, int le, int idx) { static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 }; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } int main() { std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }; std::array<int, 5> count; std::array<std::array<int, 10>, 5> omitted; std::fill(count.begin(), count.end(), 0); std::for_each(omitted.begin(), omitted.end(), [](auto &a) { std::fill(a.begin(), a.end(), 0); } ); for (size_t i = 0; i < lims.size(); i++) { std::vector<int> nDigits(i + 2); std::vector<int> dDigits(i + 2); for (int n = lims[i].first; n <= lims[i].second; n++) { std::fill(nDigits.begin(), nDigits.end(), 0); bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i].second + 1; d++) { std::fill(dDigits.begin(), dDigits.end(), 0); bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (size_t nix = 0; nix < nDigits.size(); nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n"; } } } } } } std::cout << '\n'; } for (int i = 2; i <= 5; i++) { std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n"; for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n"; } std::cout << '\n'; } return 0; }
Change the following Racket code into Java without altering its purpose.
#lang racket (require racket/generator syntax/parse/define) (define-syntax-parser for** [(_ [x:id {~datum <-} (e ...)] rst ...) #'(e ... (λ (x) (for** rst ...)))] [(_ e ...) #'(begin e ...)]) (define (permutations xs n yield #:lower [lower #f]) (let loop ([xs xs] [n n] [acc '()] [lower lower]) (cond [(= n 0) (yield (reverse acc))] [else (for ([x (in-list xs)] #:when (or (not lower) (>= x (first lower)))) (loop (remove x xs) (sub1 n) (cons x acc) (and lower (= x (first lower)) (rest lower))))]))) (define (list->number xs) (foldl (λ (e acc) (+ (* 10 acc) e)) 0 xs)) (define (calc n) (define rng (range 1 10)) (in-generator (for** [numer <- (permutations rng n)] [denom <- (permutations rng n #:lower numer)] (for* (#:when (not (equal? numer denom)) [crossed (in-list numer)] #:when (member crossed denom) [numer* (in-value (list->number (remove crossed numer)))] [denom* (in-value (list->number (remove crossed denom)))] [numer** (in-value (list->number numer))] [denom** (in-value (list->number denom))] #:when (= (* numer** denom*) (* numer* denom**))) (yield (list numer** denom** numer* denom* crossed)))))) (define (enumerate n) (for ([x (calc n)] [i (in-range 12)]) (apply printf "~a/~a = ~a/~a (~a crossed out)\n" x)) (newline)) (define (stats n) (define digits (make-hash)) (for ([x (calc n)]) (hash-update! digits (last x) add1 0)) (printf "There are ~a ~a-digit fractions of which:\n" (for/sum ([(k v) (in-hash digits)]) v) n) (for ([digit (in-list (sort (hash->list digits) < #:key car))]) (printf " The digit ~a was crossed out ~a times\n" (car digit) (cdr digit))) (newline)) (define (main) (enumerate 2) (enumerate 3) (enumerate 4) (enumerate 5) (stats 2) (stats 3) (stats 4) (stats 5)) (main)
import java.util.ArrayList; import java.util.Collections; import java.util.HashMap; import java.util.List; import java.util.Map; public class FractionReduction { public static void main(String[] args) { for ( int size = 2 ; size <= 5 ; size++ ) { reduce(size); } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits); int min = (int) Math.pow(10, numDigits-1); int max = (int) Math.pow(10, numDigits) - 1; List<Integer> values = new ArrayList<>(); for ( int number = min ; number <= max ; number++ ) { if ( isValid(number) ) { values.add(number); } } Map<Integer,Integer> cancelCount = new HashMap<>(); int size = values.size(); int solutions = 0; for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) { int numerator = values.get(nIndex); for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) { int denominator = values.get(dIndex); for ( int commonDigit : digitsInCommon(numerator, denominator) ) { int numRemoved = removeDigit(numerator, commonDigit); int denRemoved = removeDigit(denominator, commonDigit); if ( numerator * denRemoved == denominator * numRemoved ) { solutions++; cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2); if ( solutions <= 12 ) { System.out.printf(" When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved); } } } } } System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions); List<Integer> sorted = new ArrayList<>(cancelCount.keySet()); Collections.sort(sorted); for ( int removed : sorted ) { System.out.printf(" The digit %d was removed %d times.%n", removed, cancelCount.get(removed)); } System.out.println(); } private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000}; private static int removeDigit(int n, int removed) { int m = 0; int pow = 0; while ( n > 0 ) { int r = n % 10; if ( r != removed ) { m = m + r*powers[pow]; pow++; } n /= 10; } return m; } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10]; List<Integer> common = new ArrayList<>(); while ( n1 > 0 ) { int r = n1 % 10; count[r] += 1; n1 /= 10; } while ( n2 > 0 ) { int r = n2 % 10; if ( count[r] > 0 ) { common.add(r); } n2 /= 10; } return common; } private static boolean isValid(int num) { int[] count = new int[10]; while ( num > 0 ) { int r = num % 10; if ( r == 0 || count[r] == 1 ) { return false; } count[r] = 1; num /= 10; } return true; } }
Can you help me rewrite this code in Python instead of Racket, keeping it the same logically?
#lang racket (require racket/generator syntax/parse/define) (define-syntax-parser for** [(_ [x:id {~datum <-} (e ...)] rst ...) #'(e ... (λ (x) (for** rst ...)))] [(_ e ...) #'(begin e ...)]) (define (permutations xs n yield #:lower [lower #f]) (let loop ([xs xs] [n n] [acc '()] [lower lower]) (cond [(= n 0) (yield (reverse acc))] [else (for ([x (in-list xs)] #:when (or (not lower) (>= x (first lower)))) (loop (remove x xs) (sub1 n) (cons x acc) (and lower (= x (first lower)) (rest lower))))]))) (define (list->number xs) (foldl (λ (e acc) (+ (* 10 acc) e)) 0 xs)) (define (calc n) (define rng (range 1 10)) (in-generator (for** [numer <- (permutations rng n)] [denom <- (permutations rng n #:lower numer)] (for* (#:when (not (equal? numer denom)) [crossed (in-list numer)] #:when (member crossed denom) [numer* (in-value (list->number (remove crossed numer)))] [denom* (in-value (list->number (remove crossed denom)))] [numer** (in-value (list->number numer))] [denom** (in-value (list->number denom))] #:when (= (* numer** denom*) (* numer* denom**))) (yield (list numer** denom** numer* denom* crossed)))))) (define (enumerate n) (for ([x (calc n)] [i (in-range 12)]) (apply printf "~a/~a = ~a/~a (~a crossed out)\n" x)) (newline)) (define (stats n) (define digits (make-hash)) (for ([x (calc n)]) (hash-update! digits (last x) add1 0)) (printf "There are ~a ~a-digit fractions of which:\n" (for/sum ([(k v) (in-hash digits)]) v) n) (for ([digit (in-list (sort (hash->list digits) < #:key car))]) (printf " The digit ~a was crossed out ~a times\n" (car digit) (cdr digit))) (newline)) (define (main) (enumerate 2) (enumerate 3) (enumerate 4) (enumerate 5) (stats 2) (stats 3) (stats 4) (stats 5)) (main)
def indexOf(haystack, needle): idx = 0 for straw in haystack: if straw == needle: return idx else: idx += 1 return -1 def getDigits(n, le, digits): while n > 0: r = n % 10 if r == 0 or indexOf(digits, r) >= 0: return False le -= 1 digits[le] = r n = int(n / 10) return True def removeDigit(digits, le, idx): pows = [1, 10, 100, 1000, 10000] sum = 0 pow = pows[le - 2] i = 0 while i < le: if i == idx: i += 1 continue sum = sum + digits[i] * pow pow = int(pow / 10) i += 1 return sum def main(): lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = [0 for i in range(5)] omitted = [[0 for i in range(10)] for j in range(5)] i = 0 while i < len(lims): n = lims[i][0] while n < lims[i][1]: nDigits = [0 for k in range(i + 2)] nOk = getDigits(n, i + 2, nDigits) if not nOk: n += 1 continue d = n + 1 while d <= lims[i][1] + 1: dDigits = [0 for k in range(i + 2)] dOk = getDigits(d, i + 2, dDigits) if not dOk: d += 1 continue nix = 0 while nix < len(nDigits): digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0: rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd): count[i] += 1 omitted[i][digit] += 1 if count[i] <= 12: print "%d/%d = %d/%d by omitting %d's" % (n, d, rn, rd, digit) nix += 1 d += 1 n += 1 print i += 1 i = 2 while i <= 5: print "There are %d %d-digit fractions of which:" % (count[i - 2], i) j = 1 while j <= 9: if omitted[i - 2][j] == 0: j += 1 continue print "%6s have %d's omitted" % (omitted[i - 2][j], j) j += 1 print i += 1 return None main()
Translate this program into VB but keep the logic exactly as in Racket.
#lang racket (require racket/generator syntax/parse/define) (define-syntax-parser for** [(_ [x:id {~datum <-} (e ...)] rst ...) #'(e ... (λ (x) (for** rst ...)))] [(_ e ...) #'(begin e ...)]) (define (permutations xs n yield #:lower [lower #f]) (let loop ([xs xs] [n n] [acc '()] [lower lower]) (cond [(= n 0) (yield (reverse acc))] [else (for ([x (in-list xs)] #:when (or (not lower) (>= x (first lower)))) (loop (remove x xs) (sub1 n) (cons x acc) (and lower (= x (first lower)) (rest lower))))]))) (define (list->number xs) (foldl (λ (e acc) (+ (* 10 acc) e)) 0 xs)) (define (calc n) (define rng (range 1 10)) (in-generator (for** [numer <- (permutations rng n)] [denom <- (permutations rng n #:lower numer)] (for* (#:when (not (equal? numer denom)) [crossed (in-list numer)] #:when (member crossed denom) [numer* (in-value (list->number (remove crossed numer)))] [denom* (in-value (list->number (remove crossed denom)))] [numer** (in-value (list->number numer))] [denom** (in-value (list->number denom))] #:when (= (* numer** denom*) (* numer* denom**))) (yield (list numer** denom** numer* denom* crossed)))))) (define (enumerate n) (for ([x (calc n)] [i (in-range 12)]) (apply printf "~a/~a = ~a/~a (~a crossed out)\n" x)) (newline)) (define (stats n) (define digits (make-hash)) (for ([x (calc n)]) (hash-update! digits (last x) add1 0)) (printf "There are ~a ~a-digit fractions of which:\n" (for/sum ([(k v) (in-hash digits)]) v) n) (for ([digit (in-list (sort (hash->list digits) < #:key car))]) (printf " The digit ~a was crossed out ~a times\n" (car digit) (cdr digit))) (newline)) (define (main) (enumerate 2) (enumerate 3) (enumerate 4) (enumerate 5) (stats 2) (stats 3) (stats 4) (stats 5)) (main)
Module Module1 Function IndexOf(n As Integer, s As Integer()) As Integer For ii = 1 To s.Length Dim i = ii - 1 If s(i) = n Then Return i End If Next Return -1 End Function Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean While n > 0 Dim r = n Mod 10 If r = 0 OrElse IndexOf(r, digits) >= 0 Then Return False End If le -= 1 digits(le) = r n \= 10 End While Return True End Function Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer Dim pows = {1, 10, 100, 1000, 10000} Dim sum = 0 Dim pow = pows(le - 2) For ii = 1 To le Dim i = ii - 1 If i = idx Then Continue For End If sum += digits(i) * pow pow \= 10 Next Return sum End Function Sub Main() Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}} Dim count(5) As Integer Dim omitted(5, 10) As Integer Dim upperBound = lims.GetLength(0) For ii = 1 To upperBound Dim i = ii - 1 Dim nDigits(i + 2 - 1) As Integer Dim dDigits(i + 2 - 1) As Integer Dim blank(i + 2 - 1) As Integer For n = lims(i, 0) To lims(i, 1) blank.CopyTo(nDigits, 0) Dim nOk = GetDigits(n, i + 2, nDigits) If Not nOk Then Continue For End If For d = n + 1 To lims(i, 1) + 1 blank.CopyTo(dDigits, 0) Dim dOk = GetDigits(d, i + 2, dDigits) If Not dOk Then Continue For End If For nixt = 1 To nDigits.Length Dim nix = nixt - 1 Dim digit = nDigits(nix) Dim dix = IndexOf(digit, dDigits) If dix >= 0 Then Dim rn = RemoveDigit(nDigits, i + 2, nix) Dim rd = RemoveDigit(dDigits, i + 2, dix) If (n / d) = (rn / rd) Then count(i) += 1 omitted(i, digit) += 1 If count(i) <= 12 Then Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4} End If End If End If Next Next Next Console.WriteLine() Next For i = 2 To 5 Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i) For j = 1 To 9 If omitted(i - 2, j) = 0 Then Continue For End If Console.WriteLine("{0,6} have {1} Next Console.WriteLine() Next End Sub End Module
Can you help me rewrite this code in Go instead of Racket, keeping it the same logically?
#lang racket (require racket/generator syntax/parse/define) (define-syntax-parser for** [(_ [x:id {~datum <-} (e ...)] rst ...) #'(e ... (λ (x) (for** rst ...)))] [(_ e ...) #'(begin e ...)]) (define (permutations xs n yield #:lower [lower #f]) (let loop ([xs xs] [n n] [acc '()] [lower lower]) (cond [(= n 0) (yield (reverse acc))] [else (for ([x (in-list xs)] #:when (or (not lower) (>= x (first lower)))) (loop (remove x xs) (sub1 n) (cons x acc) (and lower (= x (first lower)) (rest lower))))]))) (define (list->number xs) (foldl (λ (e acc) (+ (* 10 acc) e)) 0 xs)) (define (calc n) (define rng (range 1 10)) (in-generator (for** [numer <- (permutations rng n)] [denom <- (permutations rng n #:lower numer)] (for* (#:when (not (equal? numer denom)) [crossed (in-list numer)] #:when (member crossed denom) [numer* (in-value (list->number (remove crossed numer)))] [denom* (in-value (list->number (remove crossed denom)))] [numer** (in-value (list->number numer))] [denom** (in-value (list->number denom))] #:when (= (* numer** denom*) (* numer* denom**))) (yield (list numer** denom** numer* denom* crossed)))))) (define (enumerate n) (for ([x (calc n)] [i (in-range 12)]) (apply printf "~a/~a = ~a/~a (~a crossed out)\n" x)) (newline)) (define (stats n) (define digits (make-hash)) (for ([x (calc n)]) (hash-update! digits (last x) add1 0)) (printf "There are ~a ~a-digit fractions of which:\n" (for/sum ([(k v) (in-hash digits)]) v) n) (for ([digit (in-list (sort (hash->list digits) < #:key car))]) (printf " The digit ~a was crossed out ~a times\n" (car digit) (cdr digit))) (newline)) (define (main) (enumerate 2) (enumerate 3) (enumerate 4) (enumerate 5) (stats 2) (stats 3) (stats 4) (stats 5)) (main)
package main import ( "fmt" "time" ) func indexOf(n int, s []int) int { for i, j := range s { if n == j { return i } } return -1 } func getDigits(n, le int, digits []int) bool { for n > 0 { r := n % 10 if r == 0 || indexOf(r, digits) >= 0 { return false } le-- digits[le] = r n /= 10 } return true } var pows = [5]int{1, 10, 100, 1000, 10000} func removeDigit(digits []int, le, idx int) int { sum := 0 pow := pows[le-2] for i := 0; i < le; i++ { if i == idx { continue } sum += digits[i] * pow pow /= 10 } return sum } func main() { start := time.Now() lims := [5][2]int{ {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}, {123456, 987653}, } var count [5]int var omitted [5][10]int for i, lim := range lims { nDigits := make([]int, i+2) dDigits := make([]int, i+2) blank := make([]int, i+2) for n := lim[0]; n <= lim[1]; n++ { copy(nDigits, blank) nOk := getDigits(n, i+2, nDigits) if !nOk { continue } for d := n + 1; d <= lim[1]+1; d++ { copy(dDigits, blank) dOk := getDigits(d, i+2, dDigits) if !dOk { continue } for nix, digit := range nDigits { if dix := indexOf(digit, dDigits); dix >= 0 { rn := removeDigit(nDigits, i+2, nix) rd := removeDigit(dDigits, i+2, dix) if float64(n)/float64(d) == float64(rn)/float64(rd) { count[i]++ omitted[i][digit]++ if count[i] <= 12 { fmt.Printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit) } } } } } } fmt.Println() } for i := 2; i <= 6; i++ { fmt.Printf("There are %d %d-digit fractions of which:\n", count[i-2], i) for j := 1; j <= 9; j++ { if omitted[i-2][j] == 0 { continue } fmt.Printf("%6d have %d's omitted\n", omitted[i-2][j], j) } fmt.Println() } fmt.Printf("Took %s\n", time.Since(start)) }
Preserve the algorithm and functionality while converting the code from REXX to C.
parse arg high show . if high=='' | high=="," then high= 4 if show=='' | show=="," then show= 12 say center(' some samples of reduced fractions by crossing out digits ', 79, "═") $.=0 do L=2 to high; say lim= 10**L - 1 do n=10**(L-1) to lim if pos(0, n) \==0 then iterate if hasDup(n) then iterate do d=n+1 to lim if pos(0, d)\==0 then iterate if verify(d, n, 'M')==0 then iterate if hasDup(d) then iterate q= n/d do e=1 for L; xo= substr(n, e, 1) nn= space( translate(n, , xo), 0) dd= space( translate(d, , xo), 0) if nn/dd \== q then iterate $.L= $.L + 1 $.L.xo= $.L.xo + 1 if $.L>show then iterate say center(n'/'d " = " nn'/'dd " by crossing out the" xo"'s.", 79) end end end end say; @with= ' with crossed-out' do k=1 for 9 if $.k==0 then iterate say; say center('There are ' $.k " "k'-digit fractions.', 79, "═") @for= ' For ' do #=1 for 9; if $.k.#==0 then iterate say @for k"-digit fractions, there are " right($.k.#, k-1) @with #"'s." end end exit hasDup: parse arg x; do i=1 for L-1; if pos(substr(x,i,1), substr(x,i+1)) \== 0 then return 1 end
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }
Convert the following code from REXX to C#, ensuring the logic remains intact.
parse arg high show . if high=='' | high=="," then high= 4 if show=='' | show=="," then show= 12 say center(' some samples of reduced fractions by crossing out digits ', 79, "═") $.=0 do L=2 to high; say lim= 10**L - 1 do n=10**(L-1) to lim if pos(0, n) \==0 then iterate if hasDup(n) then iterate do d=n+1 to lim if pos(0, d)\==0 then iterate if verify(d, n, 'M')==0 then iterate if hasDup(d) then iterate q= n/d do e=1 for L; xo= substr(n, e, 1) nn= space( translate(n, , xo), 0) dd= space( translate(d, , xo), 0) if nn/dd \== q then iterate $.L= $.L + 1 $.L.xo= $.L.xo + 1 if $.L>show then iterate say center(n'/'d " = " nn'/'dd " by crossing out the" xo"'s.", 79) end end end end say; @with= ' with crossed-out' do k=1 for 9 if $.k==0 then iterate say; say center('There are ' $.k " "k'-digit fractions.', 79, "═") @for= ' For ' do #=1 for 9; if $.k.#==0 then iterate say @for k"-digit fractions, there are " right($.k.#, k-1) @with #"'s." end end exit hasDup: parse arg x; do i=1 for L-1; if pos(substr(x,i,1), substr(x,i+1)) \== 0 then return 1 end
using System; namespace FractionReduction { class Program { static int IndexOf(int n, int[] s) { for (int i = 0; i < s.Length; i++) { if (s[i] == n) { return i; } } return -1; } static bool GetDigits(int n, int le, int[] digits) { while (n > 0) { var r = n % 10; if (r == 0 || IndexOf(r, digits) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } static int RemoveDigit(int[] digits, int le, int idx) { int[] pows = { 1, 10, 100, 1000, 10000 }; var sum = 0; var pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } static void Main() { var lims = new int[,] { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; var count = new int[5]; var omitted = new int[5, 10]; var upperBound = lims.GetLength(0); for (int i = 0; i < upperBound; i++) { var nDigits = new int[i + 2]; var dDigits = new int[i + 2]; var blank = new int[i + 2]; for (int n = lims[i, 0]; n <= lims[i, 1]; n++) { blank.CopyTo(nDigits, 0); var nOk = GetDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i, 1] + 1; d++) { blank.CopyTo(dDigits, 0); var dOk = GetDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.Length; nix++) { var digit = nDigits[nix]; var dix = IndexOf(digit, dDigits); if (dix >= 0) { var rn = RemoveDigit(nDigits, i + 2, nix); var rd = RemoveDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i, digit]++; if (count[i] <= 12) { Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4}'s", n, d, rn, rd, digit); } } } } } } Console.WriteLine(); } for (int i = 2; i <= 5; i++) { Console.WriteLine("There are {0} {1}-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2, j] == 0) { continue; } Console.WriteLine("{0,6} have {1}'s omitted", omitted[i - 2, j], j); } Console.WriteLine(); } } } }
Port the provided REXX code into C++ while preserving the original functionality.
parse arg high show . if high=='' | high=="," then high= 4 if show=='' | show=="," then show= 12 say center(' some samples of reduced fractions by crossing out digits ', 79, "═") $.=0 do L=2 to high; say lim= 10**L - 1 do n=10**(L-1) to lim if pos(0, n) \==0 then iterate if hasDup(n) then iterate do d=n+1 to lim if pos(0, d)\==0 then iterate if verify(d, n, 'M')==0 then iterate if hasDup(d) then iterate q= n/d do e=1 for L; xo= substr(n, e, 1) nn= space( translate(n, , xo), 0) dd= space( translate(d, , xo), 0) if nn/dd \== q then iterate $.L= $.L + 1 $.L.xo= $.L.xo + 1 if $.L>show then iterate say center(n'/'d " = " nn'/'dd " by crossing out the" xo"'s.", 79) end end end end say; @with= ' with crossed-out' do k=1 for 9 if $.k==0 then iterate say; say center('There are ' $.k " "k'-digit fractions.', 79, "═") @for= ' For ' do #=1 for 9; if $.k.#==0 then iterate say @for k"-digit fractions, there are " right($.k.#, k-1) @with #"'s." end end exit hasDup: parse arg x; do i=1 for L-1; if pos(substr(x,i,1), substr(x,i+1)) \== 0 then return 1 end
#include <array> #include <iomanip> #include <iostream> #include <vector> int indexOf(const std::vector<int> &haystack, int needle) { auto it = haystack.cbegin(); auto end = haystack.cend(); int idx = 0; for (; it != end; it = std::next(it)) { if (*it == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, std::vector<int> &digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(const std::vector<int> &digits, int le, int idx) { static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 }; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } int main() { std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }; std::array<int, 5> count; std::array<std::array<int, 10>, 5> omitted; std::fill(count.begin(), count.end(), 0); std::for_each(omitted.begin(), omitted.end(), [](auto &a) { std::fill(a.begin(), a.end(), 0); } ); for (size_t i = 0; i < lims.size(); i++) { std::vector<int> nDigits(i + 2); std::vector<int> dDigits(i + 2); for (int n = lims[i].first; n <= lims[i].second; n++) { std::fill(nDigits.begin(), nDigits.end(), 0); bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i].second + 1; d++) { std::fill(dDigits.begin(), dDigits.end(), 0); bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (size_t nix = 0; nix < nDigits.size(); nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n"; } } } } } } std::cout << '\n'; } for (int i = 2; i <= 5; i++) { std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n"; for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n"; } std::cout << '\n'; } return 0; }
Transform the following REXX implementation into Java, maintaining the same output and logic.
parse arg high show . if high=='' | high=="," then high= 4 if show=='' | show=="," then show= 12 say center(' some samples of reduced fractions by crossing out digits ', 79, "═") $.=0 do L=2 to high; say lim= 10**L - 1 do n=10**(L-1) to lim if pos(0, n) \==0 then iterate if hasDup(n) then iterate do d=n+1 to lim if pos(0, d)\==0 then iterate if verify(d, n, 'M')==0 then iterate if hasDup(d) then iterate q= n/d do e=1 for L; xo= substr(n, e, 1) nn= space( translate(n, , xo), 0) dd= space( translate(d, , xo), 0) if nn/dd \== q then iterate $.L= $.L + 1 $.L.xo= $.L.xo + 1 if $.L>show then iterate say center(n'/'d " = " nn'/'dd " by crossing out the" xo"'s.", 79) end end end end say; @with= ' with crossed-out' do k=1 for 9 if $.k==0 then iterate say; say center('There are ' $.k " "k'-digit fractions.', 79, "═") @for= ' For ' do #=1 for 9; if $.k.#==0 then iterate say @for k"-digit fractions, there are " right($.k.#, k-1) @with #"'s." end end exit hasDup: parse arg x; do i=1 for L-1; if pos(substr(x,i,1), substr(x,i+1)) \== 0 then return 1 end
import java.util.ArrayList; import java.util.Collections; import java.util.HashMap; import java.util.List; import java.util.Map; public class FractionReduction { public static void main(String[] args) { for ( int size = 2 ; size <= 5 ; size++ ) { reduce(size); } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits); int min = (int) Math.pow(10, numDigits-1); int max = (int) Math.pow(10, numDigits) - 1; List<Integer> values = new ArrayList<>(); for ( int number = min ; number <= max ; number++ ) { if ( isValid(number) ) { values.add(number); } } Map<Integer,Integer> cancelCount = new HashMap<>(); int size = values.size(); int solutions = 0; for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) { int numerator = values.get(nIndex); for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) { int denominator = values.get(dIndex); for ( int commonDigit : digitsInCommon(numerator, denominator) ) { int numRemoved = removeDigit(numerator, commonDigit); int denRemoved = removeDigit(denominator, commonDigit); if ( numerator * denRemoved == denominator * numRemoved ) { solutions++; cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2); if ( solutions <= 12 ) { System.out.printf(" When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved); } } } } } System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions); List<Integer> sorted = new ArrayList<>(cancelCount.keySet()); Collections.sort(sorted); for ( int removed : sorted ) { System.out.printf(" The digit %d was removed %d times.%n", removed, cancelCount.get(removed)); } System.out.println(); } private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000}; private static int removeDigit(int n, int removed) { int m = 0; int pow = 0; while ( n > 0 ) { int r = n % 10; if ( r != removed ) { m = m + r*powers[pow]; pow++; } n /= 10; } return m; } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10]; List<Integer> common = new ArrayList<>(); while ( n1 > 0 ) { int r = n1 % 10; count[r] += 1; n1 /= 10; } while ( n2 > 0 ) { int r = n2 % 10; if ( count[r] > 0 ) { common.add(r); } n2 /= 10; } return common; } private static boolean isValid(int num) { int[] count = new int[10]; while ( num > 0 ) { int r = num % 10; if ( r == 0 || count[r] == 1 ) { return false; } count[r] = 1; num /= 10; } return true; } }
Maintain the same structure and functionality when rewriting this code in Python.
parse arg high show . if high=='' | high=="," then high= 4 if show=='' | show=="," then show= 12 say center(' some samples of reduced fractions by crossing out digits ', 79, "═") $.=0 do L=2 to high; say lim= 10**L - 1 do n=10**(L-1) to lim if pos(0, n) \==0 then iterate if hasDup(n) then iterate do d=n+1 to lim if pos(0, d)\==0 then iterate if verify(d, n, 'M')==0 then iterate if hasDup(d) then iterate q= n/d do e=1 for L; xo= substr(n, e, 1) nn= space( translate(n, , xo), 0) dd= space( translate(d, , xo), 0) if nn/dd \== q then iterate $.L= $.L + 1 $.L.xo= $.L.xo + 1 if $.L>show then iterate say center(n'/'d " = " nn'/'dd " by crossing out the" xo"'s.", 79) end end end end say; @with= ' with crossed-out' do k=1 for 9 if $.k==0 then iterate say; say center('There are ' $.k " "k'-digit fractions.', 79, "═") @for= ' For ' do #=1 for 9; if $.k.#==0 then iterate say @for k"-digit fractions, there are " right($.k.#, k-1) @with #"'s." end end exit hasDup: parse arg x; do i=1 for L-1; if pos(substr(x,i,1), substr(x,i+1)) \== 0 then return 1 end
def indexOf(haystack, needle): idx = 0 for straw in haystack: if straw == needle: return idx else: idx += 1 return -1 def getDigits(n, le, digits): while n > 0: r = n % 10 if r == 0 or indexOf(digits, r) >= 0: return False le -= 1 digits[le] = r n = int(n / 10) return True def removeDigit(digits, le, idx): pows = [1, 10, 100, 1000, 10000] sum = 0 pow = pows[le - 2] i = 0 while i < le: if i == idx: i += 1 continue sum = sum + digits[i] * pow pow = int(pow / 10) i += 1 return sum def main(): lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = [0 for i in range(5)] omitted = [[0 for i in range(10)] for j in range(5)] i = 0 while i < len(lims): n = lims[i][0] while n < lims[i][1]: nDigits = [0 for k in range(i + 2)] nOk = getDigits(n, i + 2, nDigits) if not nOk: n += 1 continue d = n + 1 while d <= lims[i][1] + 1: dDigits = [0 for k in range(i + 2)] dOk = getDigits(d, i + 2, dDigits) if not dOk: d += 1 continue nix = 0 while nix < len(nDigits): digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0: rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd): count[i] += 1 omitted[i][digit] += 1 if count[i] <= 12: print "%d/%d = %d/%d by omitting %d's" % (n, d, rn, rd, digit) nix += 1 d += 1 n += 1 print i += 1 i = 2 while i <= 5: print "There are %d %d-digit fractions of which:" % (count[i - 2], i) j = 1 while j <= 9: if omitted[i - 2][j] == 0: j += 1 continue print "%6s have %d's omitted" % (omitted[i - 2][j], j) j += 1 print i += 1 return None main()
Translate this program into VB but keep the logic exactly as in REXX.
parse arg high show . if high=='' | high=="," then high= 4 if show=='' | show=="," then show= 12 say center(' some samples of reduced fractions by crossing out digits ', 79, "═") $.=0 do L=2 to high; say lim= 10**L - 1 do n=10**(L-1) to lim if pos(0, n) \==0 then iterate if hasDup(n) then iterate do d=n+1 to lim if pos(0, d)\==0 then iterate if verify(d, n, 'M')==0 then iterate if hasDup(d) then iterate q= n/d do e=1 for L; xo= substr(n, e, 1) nn= space( translate(n, , xo), 0) dd= space( translate(d, , xo), 0) if nn/dd \== q then iterate $.L= $.L + 1 $.L.xo= $.L.xo + 1 if $.L>show then iterate say center(n'/'d " = " nn'/'dd " by crossing out the" xo"'s.", 79) end end end end say; @with= ' with crossed-out' do k=1 for 9 if $.k==0 then iterate say; say center('There are ' $.k " "k'-digit fractions.', 79, "═") @for= ' For ' do #=1 for 9; if $.k.#==0 then iterate say @for k"-digit fractions, there are " right($.k.#, k-1) @with #"'s." end end exit hasDup: parse arg x; do i=1 for L-1; if pos(substr(x,i,1), substr(x,i+1)) \== 0 then return 1 end
Module Module1 Function IndexOf(n As Integer, s As Integer()) As Integer For ii = 1 To s.Length Dim i = ii - 1 If s(i) = n Then Return i End If Next Return -1 End Function Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean While n > 0 Dim r = n Mod 10 If r = 0 OrElse IndexOf(r, digits) >= 0 Then Return False End If le -= 1 digits(le) = r n \= 10 End While Return True End Function Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer Dim pows = {1, 10, 100, 1000, 10000} Dim sum = 0 Dim pow = pows(le - 2) For ii = 1 To le Dim i = ii - 1 If i = idx Then Continue For End If sum += digits(i) * pow pow \= 10 Next Return sum End Function Sub Main() Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}} Dim count(5) As Integer Dim omitted(5, 10) As Integer Dim upperBound = lims.GetLength(0) For ii = 1 To upperBound Dim i = ii - 1 Dim nDigits(i + 2 - 1) As Integer Dim dDigits(i + 2 - 1) As Integer Dim blank(i + 2 - 1) As Integer For n = lims(i, 0) To lims(i, 1) blank.CopyTo(nDigits, 0) Dim nOk = GetDigits(n, i + 2, nDigits) If Not nOk Then Continue For End If For d = n + 1 To lims(i, 1) + 1 blank.CopyTo(dDigits, 0) Dim dOk = GetDigits(d, i + 2, dDigits) If Not dOk Then Continue For End If For nixt = 1 To nDigits.Length Dim nix = nixt - 1 Dim digit = nDigits(nix) Dim dix = IndexOf(digit, dDigits) If dix >= 0 Then Dim rn = RemoveDigit(nDigits, i + 2, nix) Dim rd = RemoveDigit(dDigits, i + 2, dix) If (n / d) = (rn / rd) Then count(i) += 1 omitted(i, digit) += 1 If count(i) <= 12 Then Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4} End If End If End If Next Next Next Console.WriteLine() Next For i = 2 To 5 Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i) For j = 1 To 9 If omitted(i - 2, j) = 0 Then Continue For End If Console.WriteLine("{0,6} have {1} Next Console.WriteLine() Next End Sub End Module
Convert the following code from REXX to Go, ensuring the logic remains intact.
parse arg high show . if high=='' | high=="," then high= 4 if show=='' | show=="," then show= 12 say center(' some samples of reduced fractions by crossing out digits ', 79, "═") $.=0 do L=2 to high; say lim= 10**L - 1 do n=10**(L-1) to lim if pos(0, n) \==0 then iterate if hasDup(n) then iterate do d=n+1 to lim if pos(0, d)\==0 then iterate if verify(d, n, 'M')==0 then iterate if hasDup(d) then iterate q= n/d do e=1 for L; xo= substr(n, e, 1) nn= space( translate(n, , xo), 0) dd= space( translate(d, , xo), 0) if nn/dd \== q then iterate $.L= $.L + 1 $.L.xo= $.L.xo + 1 if $.L>show then iterate say center(n'/'d " = " nn'/'dd " by crossing out the" xo"'s.", 79) end end end end say; @with= ' with crossed-out' do k=1 for 9 if $.k==0 then iterate say; say center('There are ' $.k " "k'-digit fractions.', 79, "═") @for= ' For ' do #=1 for 9; if $.k.#==0 then iterate say @for k"-digit fractions, there are " right($.k.#, k-1) @with #"'s." end end exit hasDup: parse arg x; do i=1 for L-1; if pos(substr(x,i,1), substr(x,i+1)) \== 0 then return 1 end
package main import ( "fmt" "time" ) func indexOf(n int, s []int) int { for i, j := range s { if n == j { return i } } return -1 } func getDigits(n, le int, digits []int) bool { for n > 0 { r := n % 10 if r == 0 || indexOf(r, digits) >= 0 { return false } le-- digits[le] = r n /= 10 } return true } var pows = [5]int{1, 10, 100, 1000, 10000} func removeDigit(digits []int, le, idx int) int { sum := 0 pow := pows[le-2] for i := 0; i < le; i++ { if i == idx { continue } sum += digits[i] * pow pow /= 10 } return sum } func main() { start := time.Now() lims := [5][2]int{ {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}, {123456, 987653}, } var count [5]int var omitted [5][10]int for i, lim := range lims { nDigits := make([]int, i+2) dDigits := make([]int, i+2) blank := make([]int, i+2) for n := lim[0]; n <= lim[1]; n++ { copy(nDigits, blank) nOk := getDigits(n, i+2, nDigits) if !nOk { continue } for d := n + 1; d <= lim[1]+1; d++ { copy(dDigits, blank) dOk := getDigits(d, i+2, dDigits) if !dOk { continue } for nix, digit := range nDigits { if dix := indexOf(digit, dDigits); dix >= 0 { rn := removeDigit(nDigits, i+2, nix) rd := removeDigit(dDigits, i+2, dix) if float64(n)/float64(d) == float64(rn)/float64(rd) { count[i]++ omitted[i][digit]++ if count[i] <= 12 { fmt.Printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit) } } } } } } fmt.Println() } for i := 2; i <= 6; i++ { fmt.Printf("There are %d %d-digit fractions of which:\n", count[i-2], i) for j := 1; j <= 9; j++ { if omitted[i-2][j] == 0 { continue } fmt.Printf("%6d have %d's omitted\n", omitted[i-2][j], j) } fmt.Println() } fmt.Printf("Took %s\n", time.Since(start)) }
Convert the following code from Ruby to C, ensuring the logic remains intact.
def indexOf(haystack, needle) idx = 0 for straw in haystack if straw == needle then return idx else idx = idx + 1 end end return -1 end def getDigits(n, le, digits) while n > 0 r = n % 10 if r == 0 or indexOf(digits, r) >= 0 then return false end le = le - 1 digits[le] = r n = (n / 10).floor end return true end POWS = [1, 10, 100, 1000, 10000] def removeDigit(digits, le, idx) sum = 0 pow = POWS[le - 2] i = 0 while i < le if i == idx then i = i + 1 next end sum = sum + digits[i] * pow pow = (pow / 10).floor i = i + 1 end return sum end def main lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = Array.new(5, 0) omitted = Array.new(5) { Array.new(10, 0) } i = 0 for lim in lims n = lim[0] while n < lim[1] nDigits = [0] * (i + 2) nOk = getDigits(n, i + 2, nDigits) if not nOk then n = n + 1 next end d = n + 1 while d <= lim[1] + 1 dDigits = [0] * (i + 2) dOk = getDigits(d, i + 2, dDigits) if not dOk then d = d + 1 next end nix = 0 while nix < nDigits.length digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0 then rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd) then count[i] = count[i] + 1 omitted[i][digit] = omitted[i][digit] + 1 if count[i] <= 12 then print "%d/%d = %d/%d by omitting %d's\n" % [n, d, rn, rd, digit] end end end nix = nix + 1 end d = d + 1 end n = n + 1 end print "\n" i = i + 1 end i = 2 while i <= 5 print "There are %d %d-digit fractions of which:\n" % [count[i - 2], i] j = 1 while j <= 9 if omitted[i - 2][j] == 0 then j = j + 1 next end print "%6s have %d's omitted\n" % [omitted[i - 2][j], j] j = j + 1 end print "\n" i = i + 1 end end main()
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }
Write a version of this Ruby function in C# with identical behavior.
def indexOf(haystack, needle) idx = 0 for straw in haystack if straw == needle then return idx else idx = idx + 1 end end return -1 end def getDigits(n, le, digits) while n > 0 r = n % 10 if r == 0 or indexOf(digits, r) >= 0 then return false end le = le - 1 digits[le] = r n = (n / 10).floor end return true end POWS = [1, 10, 100, 1000, 10000] def removeDigit(digits, le, idx) sum = 0 pow = POWS[le - 2] i = 0 while i < le if i == idx then i = i + 1 next end sum = sum + digits[i] * pow pow = (pow / 10).floor i = i + 1 end return sum end def main lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = Array.new(5, 0) omitted = Array.new(5) { Array.new(10, 0) } i = 0 for lim in lims n = lim[0] while n < lim[1] nDigits = [0] * (i + 2) nOk = getDigits(n, i + 2, nDigits) if not nOk then n = n + 1 next end d = n + 1 while d <= lim[1] + 1 dDigits = [0] * (i + 2) dOk = getDigits(d, i + 2, dDigits) if not dOk then d = d + 1 next end nix = 0 while nix < nDigits.length digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0 then rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd) then count[i] = count[i] + 1 omitted[i][digit] = omitted[i][digit] + 1 if count[i] <= 12 then print "%d/%d = %d/%d by omitting %d's\n" % [n, d, rn, rd, digit] end end end nix = nix + 1 end d = d + 1 end n = n + 1 end print "\n" i = i + 1 end i = 2 while i <= 5 print "There are %d %d-digit fractions of which:\n" % [count[i - 2], i] j = 1 while j <= 9 if omitted[i - 2][j] == 0 then j = j + 1 next end print "%6s have %d's omitted\n" % [omitted[i - 2][j], j] j = j + 1 end print "\n" i = i + 1 end end main()
using System; namespace FractionReduction { class Program { static int IndexOf(int n, int[] s) { for (int i = 0; i < s.Length; i++) { if (s[i] == n) { return i; } } return -1; } static bool GetDigits(int n, int le, int[] digits) { while (n > 0) { var r = n % 10; if (r == 0 || IndexOf(r, digits) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } static int RemoveDigit(int[] digits, int le, int idx) { int[] pows = { 1, 10, 100, 1000, 10000 }; var sum = 0; var pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } static void Main() { var lims = new int[,] { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; var count = new int[5]; var omitted = new int[5, 10]; var upperBound = lims.GetLength(0); for (int i = 0; i < upperBound; i++) { var nDigits = new int[i + 2]; var dDigits = new int[i + 2]; var blank = new int[i + 2]; for (int n = lims[i, 0]; n <= lims[i, 1]; n++) { blank.CopyTo(nDigits, 0); var nOk = GetDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i, 1] + 1; d++) { blank.CopyTo(dDigits, 0); var dOk = GetDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (int nix = 0; nix < nDigits.Length; nix++) { var digit = nDigits[nix]; var dix = IndexOf(digit, dDigits); if (dix >= 0) { var rn = RemoveDigit(nDigits, i + 2, nix); var rd = RemoveDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i, digit]++; if (count[i] <= 12) { Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4}'s", n, d, rn, rd, digit); } } } } } } Console.WriteLine(); } for (int i = 2; i <= 5; i++) { Console.WriteLine("There are {0} {1}-digit fractions of which:", count[i - 2], i); for (int j = 1; j <= 9; j++) { if (omitted[i - 2, j] == 0) { continue; } Console.WriteLine("{0,6} have {1}'s omitted", omitted[i - 2, j], j); } Console.WriteLine(); } } } }
Translate the given Ruby code snippet into C++ without altering its behavior.
def indexOf(haystack, needle) idx = 0 for straw in haystack if straw == needle then return idx else idx = idx + 1 end end return -1 end def getDigits(n, le, digits) while n > 0 r = n % 10 if r == 0 or indexOf(digits, r) >= 0 then return false end le = le - 1 digits[le] = r n = (n / 10).floor end return true end POWS = [1, 10, 100, 1000, 10000] def removeDigit(digits, le, idx) sum = 0 pow = POWS[le - 2] i = 0 while i < le if i == idx then i = i + 1 next end sum = sum + digits[i] * pow pow = (pow / 10).floor i = i + 1 end return sum end def main lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = Array.new(5, 0) omitted = Array.new(5) { Array.new(10, 0) } i = 0 for lim in lims n = lim[0] while n < lim[1] nDigits = [0] * (i + 2) nOk = getDigits(n, i + 2, nDigits) if not nOk then n = n + 1 next end d = n + 1 while d <= lim[1] + 1 dDigits = [0] * (i + 2) dOk = getDigits(d, i + 2, dDigits) if not dOk then d = d + 1 next end nix = 0 while nix < nDigits.length digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0 then rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd) then count[i] = count[i] + 1 omitted[i][digit] = omitted[i][digit] + 1 if count[i] <= 12 then print "%d/%d = %d/%d by omitting %d's\n" % [n, d, rn, rd, digit] end end end nix = nix + 1 end d = d + 1 end n = n + 1 end print "\n" i = i + 1 end i = 2 while i <= 5 print "There are %d %d-digit fractions of which:\n" % [count[i - 2], i] j = 1 while j <= 9 if omitted[i - 2][j] == 0 then j = j + 1 next end print "%6s have %d's omitted\n" % [omitted[i - 2][j], j] j = j + 1 end print "\n" i = i + 1 end end main()
#include <array> #include <iomanip> #include <iostream> #include <vector> int indexOf(const std::vector<int> &haystack, int needle) { auto it = haystack.cbegin(); auto end = haystack.cend(); int idx = 0; for (; it != end; it = std::next(it)) { if (*it == needle) { return idx; } idx++; } return -1; } bool getDigits(int n, int le, std::vector<int> &digits) { while (n > 0) { auto r = n % 10; if (r == 0 || indexOf(digits, r) >= 0) { return false; } le--; digits[le] = r; n /= 10; } return true; } int removeDigit(const std::vector<int> &digits, int le, int idx) { static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 }; int sum = 0; auto pow = pows[le - 2]; for (int i = 0; i < le; i++) { if (i == idx) continue; sum += digits[i] * pow; pow /= 10; } return sum; } int main() { std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }; std::array<int, 5> count; std::array<std::array<int, 10>, 5> omitted; std::fill(count.begin(), count.end(), 0); std::for_each(omitted.begin(), omitted.end(), [](auto &a) { std::fill(a.begin(), a.end(), 0); } ); for (size_t i = 0; i < lims.size(); i++) { std::vector<int> nDigits(i + 2); std::vector<int> dDigits(i + 2); for (int n = lims[i].first; n <= lims[i].second; n++) { std::fill(nDigits.begin(), nDigits.end(), 0); bool nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (int d = n + 1; d <= lims[i].second + 1; d++) { std::fill(dDigits.begin(), dDigits.end(), 0); bool dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (size_t nix = 0; nix < nDigits.size(); nix++) { auto digit = nDigits[nix]; auto dix = indexOf(dDigits, digit); if (dix >= 0) { auto rn = removeDigit(nDigits, i + 2, nix); auto rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n"; } } } } } } std::cout << '\n'; } for (int i = 2; i <= 5; i++) { std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n"; for (int j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n"; } std::cout << '\n'; } return 0; }
Port the following code from Ruby to Java with equivalent syntax and logic.
def indexOf(haystack, needle) idx = 0 for straw in haystack if straw == needle then return idx else idx = idx + 1 end end return -1 end def getDigits(n, le, digits) while n > 0 r = n % 10 if r == 0 or indexOf(digits, r) >= 0 then return false end le = le - 1 digits[le] = r n = (n / 10).floor end return true end POWS = [1, 10, 100, 1000, 10000] def removeDigit(digits, le, idx) sum = 0 pow = POWS[le - 2] i = 0 while i < le if i == idx then i = i + 1 next end sum = sum + digits[i] * pow pow = (pow / 10).floor i = i + 1 end return sum end def main lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = Array.new(5, 0) omitted = Array.new(5) { Array.new(10, 0) } i = 0 for lim in lims n = lim[0] while n < lim[1] nDigits = [0] * (i + 2) nOk = getDigits(n, i + 2, nDigits) if not nOk then n = n + 1 next end d = n + 1 while d <= lim[1] + 1 dDigits = [0] * (i + 2) dOk = getDigits(d, i + 2, dDigits) if not dOk then d = d + 1 next end nix = 0 while nix < nDigits.length digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0 then rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd) then count[i] = count[i] + 1 omitted[i][digit] = omitted[i][digit] + 1 if count[i] <= 12 then print "%d/%d = %d/%d by omitting %d's\n" % [n, d, rn, rd, digit] end end end nix = nix + 1 end d = d + 1 end n = n + 1 end print "\n" i = i + 1 end i = 2 while i <= 5 print "There are %d %d-digit fractions of which:\n" % [count[i - 2], i] j = 1 while j <= 9 if omitted[i - 2][j] == 0 then j = j + 1 next end print "%6s have %d's omitted\n" % [omitted[i - 2][j], j] j = j + 1 end print "\n" i = i + 1 end end main()
import java.util.ArrayList; import java.util.Collections; import java.util.HashMap; import java.util.List; import java.util.Map; public class FractionReduction { public static void main(String[] args) { for ( int size = 2 ; size <= 5 ; size++ ) { reduce(size); } } private static void reduce(int numDigits) { System.out.printf("Fractions with digits of length %d where cancellation is valid. Examples:%n", numDigits); int min = (int) Math.pow(10, numDigits-1); int max = (int) Math.pow(10, numDigits) - 1; List<Integer> values = new ArrayList<>(); for ( int number = min ; number <= max ; number++ ) { if ( isValid(number) ) { values.add(number); } } Map<Integer,Integer> cancelCount = new HashMap<>(); int size = values.size(); int solutions = 0; for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) { int numerator = values.get(nIndex); for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) { int denominator = values.get(dIndex); for ( int commonDigit : digitsInCommon(numerator, denominator) ) { int numRemoved = removeDigit(numerator, commonDigit); int denRemoved = removeDigit(denominator, commonDigit); if ( numerator * denRemoved == denominator * numRemoved ) { solutions++; cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2); if ( solutions <= 12 ) { System.out.printf(" When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved); } } } } } System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions); List<Integer> sorted = new ArrayList<>(cancelCount.keySet()); Collections.sort(sorted); for ( int removed : sorted ) { System.out.printf(" The digit %d was removed %d times.%n", removed, cancelCount.get(removed)); } System.out.println(); } private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000}; private static int removeDigit(int n, int removed) { int m = 0; int pow = 0; while ( n > 0 ) { int r = n % 10; if ( r != removed ) { m = m + r*powers[pow]; pow++; } n /= 10; } return m; } private static List<Integer> digitsInCommon(int n1, int n2) { int[] count = new int[10]; List<Integer> common = new ArrayList<>(); while ( n1 > 0 ) { int r = n1 % 10; count[r] += 1; n1 /= 10; } while ( n2 > 0 ) { int r = n2 % 10; if ( count[r] > 0 ) { common.add(r); } n2 /= 10; } return common; } private static boolean isValid(int num) { int[] count = new int[10]; while ( num > 0 ) { int r = num % 10; if ( r == 0 || count[r] == 1 ) { return false; } count[r] = 1; num /= 10; } return true; } }
Translate the given Ruby code snippet into Python without altering its behavior.
def indexOf(haystack, needle) idx = 0 for straw in haystack if straw == needle then return idx else idx = idx + 1 end end return -1 end def getDigits(n, le, digits) while n > 0 r = n % 10 if r == 0 or indexOf(digits, r) >= 0 then return false end le = le - 1 digits[le] = r n = (n / 10).floor end return true end POWS = [1, 10, 100, 1000, 10000] def removeDigit(digits, le, idx) sum = 0 pow = POWS[le - 2] i = 0 while i < le if i == idx then i = i + 1 next end sum = sum + digits[i] * pow pow = (pow / 10).floor i = i + 1 end return sum end def main lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = Array.new(5, 0) omitted = Array.new(5) { Array.new(10, 0) } i = 0 for lim in lims n = lim[0] while n < lim[1] nDigits = [0] * (i + 2) nOk = getDigits(n, i + 2, nDigits) if not nOk then n = n + 1 next end d = n + 1 while d <= lim[1] + 1 dDigits = [0] * (i + 2) dOk = getDigits(d, i + 2, dDigits) if not dOk then d = d + 1 next end nix = 0 while nix < nDigits.length digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0 then rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd) then count[i] = count[i] + 1 omitted[i][digit] = omitted[i][digit] + 1 if count[i] <= 12 then print "%d/%d = %d/%d by omitting %d's\n" % [n, d, rn, rd, digit] end end end nix = nix + 1 end d = d + 1 end n = n + 1 end print "\n" i = i + 1 end i = 2 while i <= 5 print "There are %d %d-digit fractions of which:\n" % [count[i - 2], i] j = 1 while j <= 9 if omitted[i - 2][j] == 0 then j = j + 1 next end print "%6s have %d's omitted\n" % [omitted[i - 2][j], j] j = j + 1 end print "\n" i = i + 1 end end main()
def indexOf(haystack, needle): idx = 0 for straw in haystack: if straw == needle: return idx else: idx += 1 return -1 def getDigits(n, le, digits): while n > 0: r = n % 10 if r == 0 or indexOf(digits, r) >= 0: return False le -= 1 digits[le] = r n = int(n / 10) return True def removeDigit(digits, le, idx): pows = [1, 10, 100, 1000, 10000] sum = 0 pow = pows[le - 2] i = 0 while i < le: if i == idx: i += 1 continue sum = sum + digits[i] * pow pow = int(pow / 10) i += 1 return sum def main(): lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = [0 for i in range(5)] omitted = [[0 for i in range(10)] for j in range(5)] i = 0 while i < len(lims): n = lims[i][0] while n < lims[i][1]: nDigits = [0 for k in range(i + 2)] nOk = getDigits(n, i + 2, nDigits) if not nOk: n += 1 continue d = n + 1 while d <= lims[i][1] + 1: dDigits = [0 for k in range(i + 2)] dOk = getDigits(d, i + 2, dDigits) if not dOk: d += 1 continue nix = 0 while nix < len(nDigits): digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0: rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd): count[i] += 1 omitted[i][digit] += 1 if count[i] <= 12: print "%d/%d = %d/%d by omitting %d's" % (n, d, rn, rd, digit) nix += 1 d += 1 n += 1 print i += 1 i = 2 while i <= 5: print "There are %d %d-digit fractions of which:" % (count[i - 2], i) j = 1 while j <= 9: if omitted[i - 2][j] == 0: j += 1 continue print "%6s have %d's omitted" % (omitted[i - 2][j], j) j += 1 print i += 1 return None main()
Rewrite this program in VB while keeping its functionality equivalent to the Ruby version.
def indexOf(haystack, needle) idx = 0 for straw in haystack if straw == needle then return idx else idx = idx + 1 end end return -1 end def getDigits(n, le, digits) while n > 0 r = n % 10 if r == 0 or indexOf(digits, r) >= 0 then return false end le = le - 1 digits[le] = r n = (n / 10).floor end return true end POWS = [1, 10, 100, 1000, 10000] def removeDigit(digits, le, idx) sum = 0 pow = POWS[le - 2] i = 0 while i < le if i == idx then i = i + 1 next end sum = sum + digits[i] * pow pow = (pow / 10).floor i = i + 1 end return sum end def main lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = Array.new(5, 0) omitted = Array.new(5) { Array.new(10, 0) } i = 0 for lim in lims n = lim[0] while n < lim[1] nDigits = [0] * (i + 2) nOk = getDigits(n, i + 2, nDigits) if not nOk then n = n + 1 next end d = n + 1 while d <= lim[1] + 1 dDigits = [0] * (i + 2) dOk = getDigits(d, i + 2, dDigits) if not dOk then d = d + 1 next end nix = 0 while nix < nDigits.length digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0 then rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd) then count[i] = count[i] + 1 omitted[i][digit] = omitted[i][digit] + 1 if count[i] <= 12 then print "%d/%d = %d/%d by omitting %d's\n" % [n, d, rn, rd, digit] end end end nix = nix + 1 end d = d + 1 end n = n + 1 end print "\n" i = i + 1 end i = 2 while i <= 5 print "There are %d %d-digit fractions of which:\n" % [count[i - 2], i] j = 1 while j <= 9 if omitted[i - 2][j] == 0 then j = j + 1 next end print "%6s have %d's omitted\n" % [omitted[i - 2][j], j] j = j + 1 end print "\n" i = i + 1 end end main()
Module Module1 Function IndexOf(n As Integer, s As Integer()) As Integer For ii = 1 To s.Length Dim i = ii - 1 If s(i) = n Then Return i End If Next Return -1 End Function Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean While n > 0 Dim r = n Mod 10 If r = 0 OrElse IndexOf(r, digits) >= 0 Then Return False End If le -= 1 digits(le) = r n \= 10 End While Return True End Function Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer Dim pows = {1, 10, 100, 1000, 10000} Dim sum = 0 Dim pow = pows(le - 2) For ii = 1 To le Dim i = ii - 1 If i = idx Then Continue For End If sum += digits(i) * pow pow \= 10 Next Return sum End Function Sub Main() Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}} Dim count(5) As Integer Dim omitted(5, 10) As Integer Dim upperBound = lims.GetLength(0) For ii = 1 To upperBound Dim i = ii - 1 Dim nDigits(i + 2 - 1) As Integer Dim dDigits(i + 2 - 1) As Integer Dim blank(i + 2 - 1) As Integer For n = lims(i, 0) To lims(i, 1) blank.CopyTo(nDigits, 0) Dim nOk = GetDigits(n, i + 2, nDigits) If Not nOk Then Continue For End If For d = n + 1 To lims(i, 1) + 1 blank.CopyTo(dDigits, 0) Dim dOk = GetDigits(d, i + 2, dDigits) If Not dOk Then Continue For End If For nixt = 1 To nDigits.Length Dim nix = nixt - 1 Dim digit = nDigits(nix) Dim dix = IndexOf(digit, dDigits) If dix >= 0 Then Dim rn = RemoveDigit(nDigits, i + 2, nix) Dim rd = RemoveDigit(dDigits, i + 2, dix) If (n / d) = (rn / rd) Then count(i) += 1 omitted(i, digit) += 1 If count(i) <= 12 Then Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4} End If End If End If Next Next Next Console.WriteLine() Next For i = 2 To 5 Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i) For j = 1 To 9 If omitted(i - 2, j) = 0 Then Continue For End If Console.WriteLine("{0,6} have {1} Next Console.WriteLine() Next End Sub End Module
Port the following code from Ruby to Go with equivalent syntax and logic.
def indexOf(haystack, needle) idx = 0 for straw in haystack if straw == needle then return idx else idx = idx + 1 end end return -1 end def getDigits(n, le, digits) while n > 0 r = n % 10 if r == 0 or indexOf(digits, r) >= 0 then return false end le = le - 1 digits[le] = r n = (n / 10).floor end return true end POWS = [1, 10, 100, 1000, 10000] def removeDigit(digits, le, idx) sum = 0 pow = POWS[le - 2] i = 0 while i < le if i == idx then i = i + 1 next end sum = sum + digits[i] * pow pow = (pow / 10).floor i = i + 1 end return sum end def main lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] count = Array.new(5, 0) omitted = Array.new(5) { Array.new(10, 0) } i = 0 for lim in lims n = lim[0] while n < lim[1] nDigits = [0] * (i + 2) nOk = getDigits(n, i + 2, nDigits) if not nOk then n = n + 1 next end d = n + 1 while d <= lim[1] + 1 dDigits = [0] * (i + 2) dOk = getDigits(d, i + 2, dDigits) if not dOk then d = d + 1 next end nix = 0 while nix < nDigits.length digit = nDigits[nix] dix = indexOf(dDigits, digit) if dix >= 0 then rn = removeDigit(nDigits, i + 2, nix) rd = removeDigit(dDigits, i + 2, dix) if (1.0 * n / d) == (1.0 * rn / rd) then count[i] = count[i] + 1 omitted[i][digit] = omitted[i][digit] + 1 if count[i] <= 12 then print "%d/%d = %d/%d by omitting %d's\n" % [n, d, rn, rd, digit] end end end nix = nix + 1 end d = d + 1 end n = n + 1 end print "\n" i = i + 1 end i = 2 while i <= 5 print "There are %d %d-digit fractions of which:\n" % [count[i - 2], i] j = 1 while j <= 9 if omitted[i - 2][j] == 0 then j = j + 1 next end print "%6s have %d's omitted\n" % [omitted[i - 2][j], j] j = j + 1 end print "\n" i = i + 1 end end main()
package main import ( "fmt" "time" ) func indexOf(n int, s []int) int { for i, j := range s { if n == j { return i } } return -1 } func getDigits(n, le int, digits []int) bool { for n > 0 { r := n % 10 if r == 0 || indexOf(r, digits) >= 0 { return false } le-- digits[le] = r n /= 10 } return true } var pows = [5]int{1, 10, 100, 1000, 10000} func removeDigit(digits []int, le, idx int) int { sum := 0 pow := pows[le-2] for i := 0; i < le; i++ { if i == idx { continue } sum += digits[i] * pow pow /= 10 } return sum } func main() { start := time.Now() lims := [5][2]int{ {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}, {123456, 987653}, } var count [5]int var omitted [5][10]int for i, lim := range lims { nDigits := make([]int, i+2) dDigits := make([]int, i+2) blank := make([]int, i+2) for n := lim[0]; n <= lim[1]; n++ { copy(nDigits, blank) nOk := getDigits(n, i+2, nDigits) if !nOk { continue } for d := n + 1; d <= lim[1]+1; d++ { copy(dDigits, blank) dOk := getDigits(d, i+2, dDigits) if !dOk { continue } for nix, digit := range nDigits { if dix := indexOf(digit, dDigits); dix >= 0 { rn := removeDigit(nDigits, i+2, nix) rd := removeDigit(dDigits, i+2, dix) if float64(n)/float64(d) == float64(rn)/float64(rd) { count[i]++ omitted[i][digit]++ if count[i] <= 12 { fmt.Printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit) } } } } } } fmt.Println() } for i := 2; i <= 6; i++ { fmt.Printf("There are %d %d-digit fractions of which:\n", count[i-2], i) for j := 1; j <= 9; j++ { if omitted[i-2][j] == 0 { continue } fmt.Printf("%6d have %d's omitted\n", omitted[i-2][j], j) } fmt.Println() } fmt.Printf("Took %s\n", time.Since(start)) }
Port the following code from Scala to C with equivalent syntax and logic.
fun indexOf(n: Int, s: IntArray): Int { for (i_j in s.withIndex()) { if (n == i_j.value) { return i_j.index } } return -1 } fun getDigits(n: Int, le: Int, digits: IntArray): Boolean { var mn = n var mle = le while (mn > 0) { val r = mn % 10 if (r == 0 || indexOf(r, digits) >= 0) { return false } mle-- digits[mle] = r mn /= 10 } return true } val pows = intArrayOf(1, 10, 100, 1_000, 10_000) fun removeDigit(digits: IntArray, le: Int, idx: Int): Int { var sum = 0 var pow = pows[le - 2] for (i in 0 until le) { if (i == idx) { continue } sum += digits[i] * pow pow /= 10 } return sum } fun main() { val lims = listOf( Pair(12, 97), Pair(123, 986), Pair(1234, 9875), Pair(12345, 98764) ) val count = IntArray(5) var omitted = arrayOf<Array<Int>>() for (i in 0 until 5) { var array = arrayOf<Int>() for (j in 0 until 10) { array += 0 } omitted += array } for (i_lim in lims.withIndex()) { val i = i_lim.index val lim = i_lim.value val nDigits = IntArray(i + 2) val dDigits = IntArray(i + 2) val blank = IntArray(i + 2) { 0 } for (n in lim.first..lim.second) { blank.copyInto(nDigits) val nOk = getDigits(n, i + 2, nDigits) if (!nOk) { continue } for (d in n + 1..lim.second + 1) { blank.copyInto(dDigits) val dOk = getDigits(d, i + 2, dDigits) if (!dOk) { continue } for (nix_digit in nDigits.withIndex()) { val dix = indexOf(nix_digit.value, dDigits) if (dix >= 0) { val rn = removeDigit(nDigits, i + 2, nix_digit.index) val rd = removeDigit(dDigits, i + 2, dix) if (n.toDouble() / d.toDouble() == rn.toDouble() / rd.toDouble()) { count[i]++ omitted[i][nix_digit.value]++ if (count[i] <= 12) { println("$n/$d = $rn/$rd by omitting ${nix_digit.value}'s") } } } } } } println() } for (i in 2..5) { println("There are ${count[i - 2]} $i-digit fractions of which:") for (j in 1..9) { if (omitted[i - 2][j] == 0) { continue } println("%6d have %d's omitted".format(omitted[i - 2][j], j)) } println() } }
#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct IntArray_t { int *ptr; size_t length; } IntArray; IntArray make(size_t size) { IntArray temp; temp.ptr = calloc(size, sizeof(int)); temp.length = size; return temp; } void destroy(IntArray *ia) { if (ia->ptr != NULL) { free(ia->ptr); ia->ptr = NULL; ia->length = 0; } } void zeroFill(IntArray dst) { memset(dst.ptr, 0, dst.length * sizeof(int)); } int indexOf(const int n, const IntArray ia) { size_t i; for (i = 0; i < ia.length; i++) { if (ia.ptr[i] == n) { return i; } } return -1; } bool getDigits(int n, int le, IntArray digits) { while (n > 0) { int r = n % 10; if (r == 0 || indexOf(r, digits) >= 0) { return false; } le--; digits.ptr[le] = r; n /= 10; } return true; } int removeDigit(IntArray digits, size_t le, size_t idx) { static const int POWS[] = { 1, 10, 100, 1000, 10000 }; int sum = 0; int pow = POWS[le - 2]; size_t i; for (i = 0; i < le; i++) { if (i == idx) continue; sum += digits.ptr[i] * pow; pow /= 10; } return sum; } int main() { int lims[4][2] = { { 12, 97 }, { 123, 986 }, { 1234, 9875 }, { 12345, 98764 } }; int count[5] = { 0 }; int omitted[5][10] = { {0} }; size_t upperBound = sizeof(lims) / sizeof(lims[0]); size_t i; for (i = 0; i < upperBound; i++) { IntArray nDigits = make(i + 2); IntArray dDigits = make(i + 2); int n; for (n = lims[i][0]; n <= lims[i][1]; n++) { int d; bool nOk; zeroFill(nDigits); nOk = getDigits(n, i + 2, nDigits); if (!nOk) { continue; } for (d = n + 1; d <= lims[i][1] + 1; d++) { size_t nix; bool dOk; zeroFill(dDigits); dOk = getDigits(d, i + 2, dDigits); if (!dOk) { continue; } for (nix = 0; nix < nDigits.length; nix++) { int digit = nDigits.ptr[nix]; int dix = indexOf(digit, dDigits); if (dix >= 0) { int rn = removeDigit(nDigits, i + 2, nix); int rd = removeDigit(dDigits, i + 2, dix); if ((double)n / d == (double)rn / rd) { count[i]++; omitted[i][digit]++; if (count[i] <= 12) { printf("%d/%d = %d/%d by omitting %d's\n", n, d, rn, rd, digit); } } } } } } printf("\n"); destroy(&nDigits); destroy(&dDigits); } for (i = 2; i <= 5; i++) { int j; printf("There are %d %d-digit fractions of which:\n", count[i - 2], i); for (j = 1; j <= 9; j++) { if (omitted[i - 2][j] == 0) { continue; } printf("%6d have %d's omitted\n", omitted[i - 2][j], j); } printf("\n"); } return 0; }