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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Drazil is playing a math game with Varda. Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>. First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions: 1. x doesn't contain neither digit 0 nor digit 1. 2. <image> = <image>. Help friends find such number. Input The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a. The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes. Output Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation. Examples Input 4 1234 Output 33222 Input 3 555 Output 555 Note In the first case, <image> Submitted Solution: ``` input() s = input() ans = [] for i in range(len(s)): if s[i] >= '2': ans.append(2) if s[i] >= '3': ans += [3] if s[i] >= '4': ans += [3,2,2] if s[i] >= '5': ans += [5] if s[i] >= '6': ans += [5,3] if s[i] >= '7': ans += [7] if s[i] >= '8': ans += [7,2,2,2] if s[i] >= '9': ans += [7,3,3,2] ans = reversed(sorted(ans)) print(*ans, sep='') ```
instruction
0
101,591
20
203,182
No
output
1
101,591
20
203,183
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Drazil is playing a math game with Varda. Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>. First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions: 1. x doesn't contain neither digit 0 nor digit 1. 2. <image> = <image>. Help friends find such number. Input The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a. The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes. Output Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation. Examples Input 4 1234 Output 33222 Input 3 555 Output 555 Note In the first case, <image> Submitted Solution: ``` from math import factorial, log2 from operator import mul from functools import reduce def drazil(): input() n = input() count = [0 for _ in range(10)] for c in n: c = int(c) if c == 9: c -= 1 count[3] += 2 while True: if c in [2,3,5,7]: count[c] += 1 break elif c in [4,8]: count[2] += int(log2(c)) elif c in [0,1]: break elif c == 6: count[2] += 1 count[3] += 1 elif c == 9: count[3] += 2 else: print('Shit', c) input() c -= 1 s = '' for i, n in enumerate(count): s = str(i)*n + s print(s) if __name__ == '__main__': drazil() ```
instruction
0
101,592
20
203,184
No
output
1
101,592
20
203,185
Provide tags and a correct Python 3 solution for this coding contest problem. Ancient Egyptians are known to have understood difficult concepts in mathematics. The ancient Egyptian mathematician Ahmes liked to write a kind of arithmetic expressions on papyrus paper which he called as Ahmes arithmetic expression. An Ahmes arithmetic expression can be defined as: * "d" is an Ahmes arithmetic expression, where d is a one-digit positive integer; * "(E1 op E2)" is an Ahmes arithmetic expression, where E1 and E2 are valid Ahmes arithmetic expressions (without spaces) and op is either plus ( + ) or minus ( - ). For example 5, (1-1) and ((1+(2-3))-5) are valid Ahmes arithmetic expressions. On his trip to Egypt, Fafa found a piece of papyrus paper having one of these Ahmes arithmetic expressions written on it. Being very ancient, the papyrus piece was very worn out. As a result, all the operators were erased, keeping only the numbers and the brackets. Since Fafa loves mathematics, he decided to challenge himself with the following task: Given the number of plus and minus operators in the original expression, find out the maximum possible value for the expression on the papyrus paper after putting the plus and minus operators in the place of the original erased operators. Input The first line contains a string E (1 ≤ |E| ≤ 104) — a valid Ahmes arithmetic expression. All operators are erased and replaced with '?'. The second line contains two space-separated integers P and M (0 ≤ min(P, M) ≤ 100) — the number of plus and minus operators, respectively. It is guaranteed that P + M = the number of erased operators. Output Print one line containing the answer to the problem. Examples Input (1?1) 1 0 Output 2 Input (2?(1?2)) 1 1 Output 1 Input ((1?(5?7))?((6?2)?7)) 3 2 Output 18 Input ((1?(5?7))?((6?2)?7)) 2 3 Output 16 Note * The first sample will be (1 + 1) = 2. * The second sample will be (2 + (1 - 2)) = 1. * The third sample will be ((1 - (5 - 7)) + ((6 + 2) + 7)) = 18. * The fourth sample will be ((1 + (5 + 7)) - ((6 - 2) - 7)) = 16.
instruction
0
101,757
20
203,514
Tags: dfs and similar, dp, trees Correct Solution: ``` from math import inf class Node: def __init__(self, parent = None, leftExp = None, rightExp = None, signQ = 0): self.parent, self.leftExp, self.rightExp, self.signQ = parent, leftExp, rightExp, signQ def __str__(self): return "Node" memo = {} def Memoize(node, p, maxValue, minValue): if not node in memo: memo.update({node : {p : [maxValue, minValue]} }) else: memo[node].update({p : [maxValue, minValue]}) def ExpMaxValue(root: Node, p): m = root.signQ - p """if root.signQ == 1: if p == 1: return [root.leftExp.value + root.rightExp.value, root.leftExp.value + root.rightExp.value] else: return [root.leftExp.value - root.rightExp.value, root.leftExp.value - root.rightExp.value]""" if root.signQ == 0: return [root.value, root.value] if root in memo: if p in memo[root]: return memo[root][p] if m == 0: value = ExpMaxValue(root.leftExp, root.leftExp.signQ)[0] + ExpMaxValue(root.rightExp, root.rightExp.signQ)[0] Memoize(root, p, value, value) return [value, value] if p == 0: value = ExpMaxValue(root.leftExp, 0)[0] - ExpMaxValue(root.rightExp, 0)[0] Memoize(root, p, value, value) return [value, value] maxValue = -inf minValue = inf if m >= p: for pQMid in range(2): pQLeftMin = min(p - pQMid, root.leftExp.signQ) for pQLeft in range(pQLeftMin + 1): if root.leftExp.signQ - pQLeft + (1 - pQMid) > m: continue resLeft = ExpMaxValue(root.leftExp, pQLeft) resRight = ExpMaxValue(root.rightExp, p - pQMid - pQLeft) if pQMid == 1: maxValue = max(resLeft[0] + resRight[0], maxValue) minValue = min(resLeft[1] + resRight[1], minValue) else: maxValue = max(resLeft[0] - resRight[1], maxValue) minValue = min(resLeft[1] - resRight[0], minValue) else: for mQMid in range(2): mQLeftMin = min(m - mQMid, root.leftExp.signQ) for mQLeft in range(mQLeftMin + 1): pQLeft = root.leftExp.signQ - mQLeft if pQLeft + (1 - mQMid) > p: continue resLeft = ExpMaxValue(root.leftExp, pQLeft) resRight = ExpMaxValue(root.rightExp, p - (1 - mQMid) - pQLeft) if mQMid == 0: maxValue = max(resLeft[0] + resRight[0], maxValue) minValue = min(resLeft[1] + resRight[1], minValue) else: maxValue = max(resLeft[0] - resRight[1], maxValue) minValue = min(resLeft[1] - resRight[0], minValue) Memoize(root, p, int(maxValue), int(minValue)) return [int(maxValue), int(minValue)] def PrintNodes(root: Node): if root.signQ != 0: leftExp = root.leftExp if root.leftExp.signQ != 0 else root.leftExp.value rightExp = root.rightExp if root.rightExp.signQ != 0 else root.rightExp.value check = root.signQ == root.leftExp.signQ + root.rightExp.signQ + 1 print(root.signQ, root.parent, leftExp, rightExp, check) PrintNodes(root.leftExp) PrintNodes(root.rightExp) def main(): exp = str(input()) if len(exp) == 1: print(exp) return #root = Node(None, None, None) #root.parent = root cNode = Node() isRight = False for i in range(1, len(exp) - 1): if exp[i] == '(': if not isRight: cNode.leftExp = Node(cNode) cNode = cNode.leftExp else: cNode.rightExp = Node(cNode) cNode = cNode.rightExp isRight = False elif exp[i] == '?': isRight = True cNode.signQ += 1 elif exp[i] == ')': if cNode.parent != None: cNode.parent.signQ += cNode.signQ cNode = cNode.parent isRight = False else: if not isRight: cNode.leftExp = Node(cNode) cNode.leftExp.value = int(exp[i]) else: cNode.rightExp = Node(cNode) cNode.rightExp.value = int(exp[i]) #PrintNodes(cNode) ss = str(input()).split() p, m = int(ss[0]), int(ss[1]) print(ExpMaxValue(cNode, p)[0]) main() ```
output
1
101,757
20
203,515
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ancient Egyptians are known to have understood difficult concepts in mathematics. The ancient Egyptian mathematician Ahmes liked to write a kind of arithmetic expressions on papyrus paper which he called as Ahmes arithmetic expression. An Ahmes arithmetic expression can be defined as: * "d" is an Ahmes arithmetic expression, where d is a one-digit positive integer; * "(E1 op E2)" is an Ahmes arithmetic expression, where E1 and E2 are valid Ahmes arithmetic expressions (without spaces) and op is either plus ( + ) or minus ( - ). For example 5, (1-1) and ((1+(2-3))-5) are valid Ahmes arithmetic expressions. On his trip to Egypt, Fafa found a piece of papyrus paper having one of these Ahmes arithmetic expressions written on it. Being very ancient, the papyrus piece was very worn out. As a result, all the operators were erased, keeping only the numbers and the brackets. Since Fafa loves mathematics, he decided to challenge himself with the following task: Given the number of plus and minus operators in the original expression, find out the maximum possible value for the expression on the papyrus paper after putting the plus and minus operators in the place of the original erased operators. Input The first line contains a string E (1 ≤ |E| ≤ 104) — a valid Ahmes arithmetic expression. All operators are erased and replaced with '?'. The second line contains two space-separated integers P and M (0 ≤ min(P, M) ≤ 100) — the number of plus and minus operators, respectively. It is guaranteed that P + M = the number of erased operators. Output Print one line containing the answer to the problem. Examples Input (1?1) 1 0 Output 2 Input (2?(1?2)) 1 1 Output 1 Input ((1?(5?7))?((6?2)?7)) 3 2 Output 18 Input ((1?(5?7))?((6?2)?7)) 2 3 Output 16 Note * The first sample will be (1 + 1) = 2. * The second sample will be (2 + (1 - 2)) = 1. * The third sample will be ((1 - (5 - 7)) + ((6 + 2) + 7)) = 18. * The fourth sample will be ((1 + (5 + 7)) - ((6 - 2) - 7)) = 16. Submitted Solution: ``` from math import inf class Node: def __init__(self, parent = None, leftExp = None, rightExp = None, signQ = 0): self.parent, self.leftExp, self.rightExp, self.signQ = parent, leftExp, rightExp, signQ def __str__(self): return "Node" memo = {} def Memoize(node, p, maxValue, minValue): if not node in memo: memo.update({node : {p : [maxValue, minValue]} }) else: memo[node].update({p : [maxValue, minValue]}) def ExpMaxValue(root: Node, p, m): """if root.signQ == 1: if p == 1: return [root.leftExp.value + root.rightExp.value, root.leftExp.value + root.rightExp.value] else: return [root.leftExp.value - root.rightExp.value, root.leftExp.value - root.rightExp.value]""" if root in memo: if p in memo[root]: return memo[root][p] if root.signQ == 0: return [root.value, root.value] if m == 0: value = ExpMaxValue(root.leftExp, root.leftExp.signQ, 0)[0] + ExpMaxValue(root.rightExp, root.rightExp.signQ, 0)[0] Memoize(root, p, value, value) return [value, value] if p == 0: value = ExpMaxValue(root.leftExp, 0, root.leftExp.signQ)[0] - ExpMaxValue(root.rightExp, 0, root.rightExp.signQ)[0] Memoize(root, p, value, value) return [value, value] maxValue = -inf minValue = inf if m >= p: for pQMid in range(2): pQLeftMin = min(p - pQMid, root.leftExp.signQ) for pQLeft in range(pQLeftMin + 1): mQLeft = root.leftExp.signQ - pQLeft resLeft = ExpMaxValue(root.leftExp, pQLeft, mQLeft) resRight = ExpMaxValue(root.rightExp, p - pQMid - pQLeft, m - (1 - pQMid) - mQLeft) if pQMid == 1: maxValue = max(resLeft[0] + resRight[0], maxValue) minValue = min(resLeft[1] + resRight[1], minValue) else: maxValue = max(resLeft[0] - resRight[1], maxValue) minValue = min(resLeft[1] - resRight[0], minValue) else: for mQMid in range(2): mQLeftMin = min(m - mQMid, root.leftExp.signQ) for mQLeft in range(mQLeftMin + 1): pQLeft = root.leftExp.signQ - mQLeft resLeft = ExpMaxValue(root.leftExp, pQLeft, mQLeft) resRight = ExpMaxValue(root.rightExp, p - (1 - mQMid) - pQLeft, m - mQMid - mQLeft) if mQMid == 0: maxValue = max(resLeft[0] + resRight[0], maxValue) minValue = min(resLeft[1] + resRight[1], minValue) else: maxValue = max(resLeft[0] - resRight[1], maxValue) minValue = min(resLeft[1] - resRight[0], minValue) Memoize(root, p, maxValue, minValue) return [maxValue, minValue] def PrintNodes(root: Node): if root.signQ != 0: print(root.signQ, root.parent, root.leftExp if root.leftExp.signQ != 0 else root.leftExp.value, root.rightExp if root.rightExp.signQ != 0 else root.rightExp.value) PrintNodes(root.leftExp) PrintNodes(root.rightExp) def main(): exp = str(input()) if len(exp) == 1: print(exp) return #root = Node(None, None, None) #root.parent = root cNode = Node() isRight = False for i in range(1, len(exp) - 1): if exp[i] == '(': if not isRight: cNode.leftExp = Node(cNode) cNode = cNode.leftExp else: cNode.rightExp = Node(cNode) cNode = cNode.rightExp isRight = False elif exp[i] == '?': isRight = True cNode.signQ += 1 elif exp[i] == ')': if cNode.parent != None: cNode.parent.signQ += cNode.signQ cNode = cNode.parent isRight = False else: if not isRight: cNode.leftExp = Node(cNode) cNode.leftExp.value = int(exp[i]) else: cNode.rightExp = Node(cNode) cNode.rightExp.value = int(exp[i]) #PrintNodes(cNode) ss = str(input()).split() p, m = int(ss[0]), int(ss[1]) print(ExpMaxValue(cNode, p, m)[0]) main() ```
instruction
0
101,758
20
203,516
No
output
1
101,758
20
203,517
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ancient Egyptians are known to have understood difficult concepts in mathematics. The ancient Egyptian mathematician Ahmes liked to write a kind of arithmetic expressions on papyrus paper which he called as Ahmes arithmetic expression. An Ahmes arithmetic expression can be defined as: * "d" is an Ahmes arithmetic expression, where d is a one-digit positive integer; * "(E1 op E2)" is an Ahmes arithmetic expression, where E1 and E2 are valid Ahmes arithmetic expressions (without spaces) and op is either plus ( + ) or minus ( - ). For example 5, (1-1) and ((1+(2-3))-5) are valid Ahmes arithmetic expressions. On his trip to Egypt, Fafa found a piece of papyrus paper having one of these Ahmes arithmetic expressions written on it. Being very ancient, the papyrus piece was very worn out. As a result, all the operators were erased, keeping only the numbers and the brackets. Since Fafa loves mathematics, he decided to challenge himself with the following task: Given the number of plus and minus operators in the original expression, find out the maximum possible value for the expression on the papyrus paper after putting the plus and minus operators in the place of the original erased operators. Input The first line contains a string E (1 ≤ |E| ≤ 104) — a valid Ahmes arithmetic expression. All operators are erased and replaced with '?'. The second line contains two space-separated integers P and M (0 ≤ min(P, M) ≤ 100) — the number of plus and minus operators, respectively. It is guaranteed that P + M = the number of erased operators. Output Print one line containing the answer to the problem. Examples Input (1?1) 1 0 Output 2 Input (2?(1?2)) 1 1 Output 1 Input ((1?(5?7))?((6?2)?7)) 3 2 Output 18 Input ((1?(5?7))?((6?2)?7)) 2 3 Output 16 Note * The first sample will be (1 + 1) = 2. * The second sample will be (2 + (1 - 2)) = 1. * The third sample will be ((1 - (5 - 7)) + ((6 + 2) + 7)) = 18. * The fourth sample will be ((1 + (5 + 7)) - ((6 - 2) - 7)) = 16. Submitted Solution: ``` from math import inf class Node: def __init__(self, parent = None, leftExp = None, rightExp = None, signQ = 0): self.parent, self.leftExp, self.rightExp, self.signQ = parent, leftExp, rightExp, signQ def __str__(self): return "Node" memo = {} def Memoize(node, p, maxValue, minValue): if not node in memo: memo.update({node : {p : [maxValue, minValue]} }) else: memo[node].update({p : [maxValue, minValue]}) def ExpMaxValue(root: Node, p, m): """if root.signQ == 1: if p == 1: return [root.leftExp.value + root.rightExp.value, root.leftExp.value + root.rightExp.value] else: return [root.leftExp.value - root.rightExp.value, root.leftExp.value - root.rightExp.value]""" if root in memo: if p in memo[root]: return memo[root][p] if root.signQ == 0: return [root.value, root.value] if m == 0: value = ExpMaxValue(root.leftExp, root.leftExp.signQ, 0)[0] + ExpMaxValue(root.rightExp, root.rightExp.signQ, 0)[0] Memoize(root, p, value, value) return [value, value] if p == 0: value = ExpMaxValue(root.leftExp, 0, root.leftExp.signQ)[0] - ExpMaxValue(root.rightExp, 0, root.rightExp.signQ)[0] Memoize(root, p, value, value) return [value, value] maxValue = -inf minValue = inf if m >= p: for pQMid in range(2): pQLeftMin = min(p - pQMid, root.leftExp.signQ) for pQLeft in range(pQLeftMin + 1): mQLeft = root.leftExp.signQ - pQLeft resLeft = ExpMaxValue(root.leftExp, pQLeft, mQLeft) resRight = ExpMaxValue(root.rightExp, p - pQMid - pQLeft, m - (1 - pQMid) - mQLeft) if pQMid == 1: maxValue = max(resLeft[0] + resRight[0], maxValue) minValue = min(resLeft[1] + resRight[1], minValue) else: maxValue = max(resLeft[0] - resRight[1], maxValue) minValue = min(resLeft[1] - resRight[0], minValue) else: for mQMid in range(2): mQLeftMin = min(m - mQMid, root.leftExp.signQ) for mQLeft in range(mQLeftMin + 1): pQLeft = root.leftExp.signQ - mQLeft resLeft = ExpMaxValue(root.leftExp, pQLeft, mQLeft) resRight = ExpMaxValue(root.rightExp, p - (1 - mQMid) - pQLeft, m - mQMid - mQLeft) if mQMid == 0: maxValue = max(resLeft[0] + resRight[0], maxValue) minValue = min(resLeft[1] + resRight[1], minValue) else: maxValue = max(resLeft[0] - resRight[1], maxValue) minValue = min(resLeft[1] - resRight[0], minValue) Memoize(root, p, maxValue, minValue) return [maxValue, minValue] def PrintNodes(root: Node): if root.signQ != 0: print(root.signQ, root.parent, root.leftExp if root.leftExp.signQ != 0 else root.leftExp.value, root.rightExp if root.rightExp.signQ != 0 else root.rightExp.value) PrintNodes(root.leftExp) PrintNodes(root.rightExp) def main(): exp = str(input()) if len(exp) == 1: print(exp) return #root = Node(None, None, None) #root.parent = root cNode = Node() isRight = False for i in range(1, len(exp) - 1): if exp[i] == '(': if not isRight: cNode.leftExp = Node(cNode) cNode = cNode.leftExp else: cNode.rightExp = Node(cNode) cNode = cNode.rightExp isRight = False elif exp[i] == '?': isRight = True cNode.signQ += 1 elif exp[i] == ')': if cNode.parent != None: cNode.parent.signQ += cNode.signQ cNode = cNode.parent isRight = False else: if not isRight: cNode.leftExp = Node(cNode) cNode.leftExp.value = int(exp[i]) else: cNode.rightExp = Node(cNode) cNode.rightExp.value = int(exp[i]) PrintNodes(cNode) ss = str(input()).split() p, m = int(ss[0]), int(ss[1]) print(ExpMaxValue(cNode, p, m)[0]) main() ```
instruction
0
101,759
20
203,518
No
output
1
101,759
20
203,519
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Problem Statement Dr. Suposupo developed a programming language called Shipura. Shipura supports only one binary operator ${\tt >>}$ and only one unary function ${\tt S<\ >}$. $x {\tt >>} y$ is evaluated to $\lfloor x / 2^y \rfloor$ (that is, the greatest integer not exceeding $x / 2^y$), and ${\tt S<} x {\tt >}$ is evaluated to $x^2 \bmod 1{,}000{,}000{,}007$ (that is, the remainder when $x^2$ is divided by $1{,}000{,}000{,}007$). The operator ${\tt >>}$ is left-associative. For example, the expression $x {\tt >>} y {\tt >>} z$ is interpreted as $(x {\tt >>} y) {\tt >>} z$, not as $x {\tt >>} (y {\tt >>} z)$. Note that these parentheses do not appear in actual Shipura expressions. The syntax of Shipura is given (in BNF; Backus-Naur Form) as follows: expr ::= term | expr sp ">>" sp term term ::= number | "S" sp "<" sp expr sp ">" sp ::= "" | sp " " number ::= digit | number digit digit ::= "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" The start symbol of this syntax is $\tt expr$ that represents an expression in Shipura. In addition, $\tt number$ is an integer between $0$ and $1{,}000{,}000{,}000$ inclusive, written without extra leading zeros. Write a program to evaluate Shipura expressions. Input The input is a sequence of datasets. Each dataset is represented by a line which contains a valid expression in Shipura. A line containing a single ${\tt \\#}$ indicates the end of the input. You can assume the number of datasets is at most $100$ and the total size of the input file does not exceed $2{,}000{,}000$ bytes. Output For each dataset, output a line containing the evaluated value of the expression. Sample Input S< S< 12 >> 2 > > 123 >> 1 >> 1 1000000000 >>129 S<S<S<S<S<2>>>>> S <S< S<2013 >>> 11 >>> 10 > Output for the Sample Input 81 30 0 294967268 14592400 Example Input S< S< 12 >> 2 > > 123 >> 1 >> 1 1000000000 >>129 S<S<S<S<S<2>>>>> S <S< S<2013 >>> 11 >>> 10 > # Output 81 30 0 294967268 14592400 Submitted Solution: ``` import re S = lambda x: x*x%int(1e9+7) s = input() while s != '#': s = s.replace(' ', '') s = re.sub(r'>>(\d+)', r'XX\1', s) s = s.translate(str.maketrans('<>X', '()>')) print(eval(s)) s = input() ```
instruction
0
101,999
20
203,998
No
output
1
101,999
20
203,999
Provide tags and a correct Python 3 solution for this coding contest problem. Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not. Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer p from the interval [pl, pr] and Vasya chooses an integer v from the interval [vl, vr] (also randomly). Both players choose their integers equiprobably. Find the probability that the interval [min(v, p), max(v, p)] contains exactly k lucky numbers. Input The single line contains five integers pl, pr, vl, vr and k (1 ≤ pl ≤ pr ≤ 109, 1 ≤ vl ≤ vr ≤ 109, 1 ≤ k ≤ 1000). Output On the single line print the result with an absolute error of no more than 10 - 9. Examples Input 1 10 1 10 2 Output 0.320000000000 Input 5 6 8 10 1 Output 1.000000000000 Note Consider that [a, b] denotes an interval of integers; this interval includes the boundaries. That is, <image> In first case there are 32 suitable pairs: (1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 8), (2, 9), (2, 10), (3, 7), (3, 8), (3, 9), (3, 10), (4, 7), (4, 8), (4, 9), (4, 10), (7, 1), (7, 2), (7, 3), (7, 4), (8, 1), (8, 2), (8, 3), (8, 4), (9, 1), (9, 2), (9, 3), (9, 4), (10, 1), (10, 2), (10, 3), (10, 4). Total number of possible pairs is 10·10 = 100, so answer is 32 / 100. In second case Petya always get number less than Vasya and the only lucky 7 is between this numbers, so there will be always 1 lucky number.
instruction
0
102,057
20
204,114
Tags: brute force, probabilities Correct Solution: ``` #!/usr/bin/env python3 import itertools pl,pr,vl,vr,k = map(int, input().split()) l = min(pl, vl) r = max(pr, vr) # Generate all lucky numbers with the appropriate number of digits # O(3**max_nr_digits) = O(3**9) < 20000 max_nr_digits = len(str(r)) lucky_numbers = [] for nr_digits in range(1,max_nr_digits+1): lucky_numbers.extend(int(''.join(i)) for i in itertools.product("47", repeat=nr_digits)) # Filter so we only have lucky numbers that can be in the intervals lucky_numbers = [nr for nr in lucky_numbers if (l <= nr) and (nr <= r)] lucky_numbers.sort() if len(lucky_numbers) < k: print("%.12f" % 0.0) exit() lucky_numbers.insert(0,l-1) lucky_numbers.append(r+1) total_pairs = (pr-pl+1) * (vr-vl+1) good_pairs = 0 for start_index in range(len(lucky_numbers)-k-1): (a,b) = lucky_numbers[start_index], lucky_numbers[start_index+1] (c,d) = lucky_numbers[start_index+k], lucky_numbers[start_index+k+1] # A pair will have lucky_numbers[start_index+1 : start_index+1+k] in its interval when: # The smallest number of the pair is larger than a, but at most b # The largest number of the pair is at least c, but smaller than d good_pairs += max((min(b,pr)-max(a+1,pl)+1),0)*max((min(d-1,vr)-max(c,vl)+1),0) good_pairs += max((min(b,vr)-max(a+1,vl)+1),0)*max((min(d-1,pr)-max(c,pl)+1),0) if (b == c) and (pl <= b) and (b <= pr) and (vl <=b) and (b <= vr): # Prevent double counting of the pair (b,c) when b == c and both p and v can supply the value good_pairs -= 1 print("%.12f" % (good_pairs / total_pairs)) ```
output
1
102,057
20
204,115
Provide tags and a correct Python 3 solution for this coding contest problem. Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not. Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer p from the interval [pl, pr] and Vasya chooses an integer v from the interval [vl, vr] (also randomly). Both players choose their integers equiprobably. Find the probability that the interval [min(v, p), max(v, p)] contains exactly k lucky numbers. Input The single line contains five integers pl, pr, vl, vr and k (1 ≤ pl ≤ pr ≤ 109, 1 ≤ vl ≤ vr ≤ 109, 1 ≤ k ≤ 1000). Output On the single line print the result with an absolute error of no more than 10 - 9. Examples Input 1 10 1 10 2 Output 0.320000000000 Input 5 6 8 10 1 Output 1.000000000000 Note Consider that [a, b] denotes an interval of integers; this interval includes the boundaries. That is, <image> In first case there are 32 suitable pairs: (1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 8), (2, 9), (2, 10), (3, 7), (3, 8), (3, 9), (3, 10), (4, 7), (4, 8), (4, 9), (4, 10), (7, 1), (7, 2), (7, 3), (7, 4), (8, 1), (8, 2), (8, 3), (8, 4), (9, 1), (9, 2), (9, 3), (9, 4), (10, 1), (10, 2), (10, 3), (10, 4). Total number of possible pairs is 10·10 = 100, so answer is 32 / 100. In second case Petya always get number less than Vasya and the only lucky 7 is between this numbers, so there will be always 1 lucky number.
instruction
0
102,058
20
204,116
Tags: brute force, probabilities Correct Solution: ``` s = list() def rec(x): if x > 100000000000: return s.append(x) rec(x * 10 + 4) rec(x * 10 + 7) def f(l1, r1, l2, r2): l1 = max(l1, l2) r1 = min(r1, r2) return max(r1 - l1 + 1, 0) def main(): rec(0) s.sort() args = input().split() pl, pr, vl, vr, k = int(args[0]), int(args[1]), int(args[2]), int(args[3]), int(args[4]) ans = 0 i = 1 while i + k < len(s): l1 = s[i - 1] + 1 r1 = s[i] l2 = s[i + k - 1] r2 = s[i + k] - 1 a = f(l1, r1, vl, vr) * f(l2, r2, pl, pr) b = f(l1, r1, pl, pr) * f(l2, r2, vl, vr) ans += a + b if k == 1 and a > 0 and b > 0: ans -= 1 i += 1 all = (pr - pl + 1) * (vr - vl + 1) print(1.0 * ans / all) if __name__ == '__main__': main() ```
output
1
102,058
20
204,117
Provide tags and a correct Python 3 solution for this coding contest problem. Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not. Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer p from the interval [pl, pr] and Vasya chooses an integer v from the interval [vl, vr] (also randomly). Both players choose their integers equiprobably. Find the probability that the interval [min(v, p), max(v, p)] contains exactly k lucky numbers. Input The single line contains five integers pl, pr, vl, vr and k (1 ≤ pl ≤ pr ≤ 109, 1 ≤ vl ≤ vr ≤ 109, 1 ≤ k ≤ 1000). Output On the single line print the result with an absolute error of no more than 10 - 9. Examples Input 1 10 1 10 2 Output 0.320000000000 Input 5 6 8 10 1 Output 1.000000000000 Note Consider that [a, b] denotes an interval of integers; this interval includes the boundaries. That is, <image> In first case there are 32 suitable pairs: (1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 8), (2, 9), (2, 10), (3, 7), (3, 8), (3, 9), (3, 10), (4, 7), (4, 8), (4, 9), (4, 10), (7, 1), (7, 2), (7, 3), (7, 4), (8, 1), (8, 2), (8, 3), (8, 4), (9, 1), (9, 2), (9, 3), (9, 4), (10, 1), (10, 2), (10, 3), (10, 4). Total number of possible pairs is 10·10 = 100, so answer is 32 / 100. In second case Petya always get number less than Vasya and the only lucky 7 is between this numbers, so there will be always 1 lucky number.
instruction
0
102,059
20
204,118
Tags: brute force, probabilities Correct Solution: ``` def gen(n, cur): if n == 0: global arr arr.append(cur) else: gen(n - 1, cur + '4') gen(n - 1, cur + '7') def lseg(x1, x2): if x2 < x1: return 0 return x2 - x1 + 1 def inter2(x1, x2, a, b): left = max(x1, a) right = min(x2, b) return (left, right) def inter(x1, x2, a, b): l, r = inter2(x1, x2, a, b) return lseg(l, r) def minus(a, b, c, d): d1 = (-1, c - 1) d2 = (d + 1, 10 ** 10) d1 = inter(a, b, *d1) d2 = inter(a, b, *d2) return d1 + d2 arr = [] for i in range(1, 11): gen(i, '') arr = [0] + sorted(list(map(int, arr))) pl, pr, vl, vr, k = map(int, input().split()) ans = 0 for start in range(1, len(arr) - k + 1): if arr[start + k - 1] > max(vr, pr): break if arr[start] < min(pl, vl): continue goleft = inter(pl, pr, arr[start - 1] + 1, arr[start]) goright = inter(vl, vr, arr[start + k - 1], arr[start + k] - 1) left, right = inter2(pl, pr, arr[start - 1] + 1, arr[start]), \ inter2(vl, vr, arr[start + k - 1], arr[start + k] - 1) ans += goleft * goright left1 = inter2(pl, pr, arr[start + k - 1], arr[start + k] - 1) right1 = inter2(vl, vr, arr[start - 1] + 1, arr[start]) ans += minus(right1[0], right1[1], right[0], right[1]) * lseg(*left1) ans += (lseg(*right1) - minus(right1[0], right1[1], right[0], right[1])) \ * minus(left1[0], left1[1], left[0], left[1]) ans /= (pr - pl + 1) * (vr - vl + 1) print(ans) ```
output
1
102,059
20
204,119
Provide tags and a correct Python 3 solution for this coding contest problem. Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not. Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer p from the interval [pl, pr] and Vasya chooses an integer v from the interval [vl, vr] (also randomly). Both players choose their integers equiprobably. Find the probability that the interval [min(v, p), max(v, p)] contains exactly k lucky numbers. Input The single line contains five integers pl, pr, vl, vr and k (1 ≤ pl ≤ pr ≤ 109, 1 ≤ vl ≤ vr ≤ 109, 1 ≤ k ≤ 1000). Output On the single line print the result with an absolute error of no more than 10 - 9. Examples Input 1 10 1 10 2 Output 0.320000000000 Input 5 6 8 10 1 Output 1.000000000000 Note Consider that [a, b] denotes an interval of integers; this interval includes the boundaries. That is, <image> In first case there are 32 suitable pairs: (1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 8), (2, 9), (2, 10), (3, 7), (3, 8), (3, 9), (3, 10), (4, 7), (4, 8), (4, 9), (4, 10), (7, 1), (7, 2), (7, 3), (7, 4), (8, 1), (8, 2), (8, 3), (8, 4), (9, 1), (9, 2), (9, 3), (9, 4), (10, 1), (10, 2), (10, 3), (10, 4). Total number of possible pairs is 10·10 = 100, so answer is 32 / 100. In second case Petya always get number less than Vasya and the only lucky 7 is between this numbers, so there will be always 1 lucky number.
instruction
0
102,060
20
204,120
Tags: brute force, probabilities Correct Solution: ``` #!/usr/bin/env python3 vl, vr, pl, pr, k = map(int, input().split()) lucky = [4, 7] sz = 0 for i in range(1, 9): base = 10 ** i psz, sz = sz, len(lucky) for j in [4 * base, 7 * base]: for pos in range(psz, sz): lucky.append(j + lucky[pos]) ans = 0 for i in range(0, len(lucky)-k+1): ll, lr = 1 if i == 0 else lucky[i-1] + 1, lucky[i] rl, rr = lucky[i+k-1], 1_000_000_000 if i+k == len(lucky) else lucky[i+k] - 1 vc = max(0, min(vr, lr) - max(vl, ll) + 1) pc = max(0, min(pr, rr) - max(pl, rl) + 1) cnt1 = vc * pc vc = max(0, min(pr, lr) - max(pl, ll) + 1) pc = max(0, min(vr, rr) - max(vl, rl) + 1) cnt2 = vc * pc ans += cnt1 + cnt2 if k == 1 and cnt1 > 0 and cnt2 > 0: ans -= 1 print(ans / ((vr - vl + 1) * (pr - pl + 1))) ```
output
1
102,060
20
204,121
Provide tags and a correct Python 3 solution for this coding contest problem. Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not. Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer p from the interval [pl, pr] and Vasya chooses an integer v from the interval [vl, vr] (also randomly). Both players choose their integers equiprobably. Find the probability that the interval [min(v, p), max(v, p)] contains exactly k lucky numbers. Input The single line contains five integers pl, pr, vl, vr and k (1 ≤ pl ≤ pr ≤ 109, 1 ≤ vl ≤ vr ≤ 109, 1 ≤ k ≤ 1000). Output On the single line print the result with an absolute error of no more than 10 - 9. Examples Input 1 10 1 10 2 Output 0.320000000000 Input 5 6 8 10 1 Output 1.000000000000 Note Consider that [a, b] denotes an interval of integers; this interval includes the boundaries. That is, <image> In first case there are 32 suitable pairs: (1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 8), (2, 9), (2, 10), (3, 7), (3, 8), (3, 9), (3, 10), (4, 7), (4, 8), (4, 9), (4, 10), (7, 1), (7, 2), (7, 3), (7, 4), (8, 1), (8, 2), (8, 3), (8, 4), (9, 1), (9, 2), (9, 3), (9, 4), (10, 1), (10, 2), (10, 3), (10, 4). Total number of possible pairs is 10·10 = 100, so answer is 32 / 100. In second case Petya always get number less than Vasya and the only lucky 7 is between this numbers, so there will be always 1 lucky number.
instruction
0
102,061
20
204,122
Tags: brute force, probabilities Correct Solution: ``` import itertools def generate_happy(): happy_digits = '47' happies = [] for num_len in range(1, 10): happies.extend(itertools.product(happy_digits, repeat=num_len)) return [int(''.join(num)) for num in happies] def clamp_segment(start, end, min_b, max_b): if start > end or min_b > max_b: raise ValueError(f"{start} {end} {min_b} {max_b}") if start > max_b or end < min_b: return None, None new_start = start new_end = end if start < min_b: new_start = min_b if end > max_b: new_end = max_b return new_start, new_end def get_window_bounds(happies, happy_count, happy_window_ind): return (happies[happy_window_ind - 1] if happy_window_ind > 0 else 0, happies[happy_window_ind], happies[happy_window_ind + happy_count - 1], (happies[happy_window_ind + happy_count] if happy_window_ind + happy_count < len(happies) else 10 ** 9 + 1 ) ) def get_good_segm_count_ordered( lower_start, lower_end, upper_start, upper_end, prev_happy, this_happy, last_happy, next_happy): (lower_bound_start, lower_bound_end) = clamp_segment( lower_start, lower_end, prev_happy + 1, this_happy ) (upper_bound_start, upper_bound_end) = clamp_segment( upper_start, upper_end, last_happy, next_happy - 1 ) if lower_bound_start is None or upper_bound_start is None: return 0 return (lower_bound_end - lower_bound_start + 1) *\ (upper_bound_end - upper_bound_start + 1) def get_good_segm_count(happies, happy_count, happy_window_ind, start_1, end_1, start_2, end_2): prev_happy, this_happy, last_happy, next_happy = get_window_bounds( happies, happy_count, happy_window_ind ) first_is_lower_count = get_good_segm_count_ordered( start_1, end_1, start_2, end_2, prev_happy, this_happy, last_happy, next_happy ) second_is_lower_count = get_good_segm_count_ordered( start_2, end_2, start_1, end_1, prev_happy, this_happy, last_happy, next_happy ) this_happy = happies[happy_window_ind] if (happy_count == 1 and start_1 <= this_happy <= end_2 and start_2 <= this_happy <= end_2): second_is_lower_count -= 1 return first_is_lower_count + second_is_lower_count def main(args=None): if args is None: p_start, p_end, v_start, v_end, happy_count = map(int, input().split()) else: p_start, p_end, v_start, v_end, happy_count = args happies = generate_happy() good_segments_count = 0 for happy_window_ind in range(len(happies) - happy_count + 1): good_segments_count += get_good_segm_count( happies, happy_count, happy_window_ind, p_start, p_end, v_start, v_end ) # print(get_good_segm_count( # happies, happy_count, happy_window_ind, # p_start, p_end, v_start, v_end # ), happy_window_ind) all_segments_count = (p_end - p_start + 1) * (v_end - v_start + 1) return good_segments_count / all_segments_count print(main()) ```
output
1
102,061
20
204,123
Provide tags and a correct Python 3 solution for this coding contest problem. Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not. Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer p from the interval [pl, pr] and Vasya chooses an integer v from the interval [vl, vr] (also randomly). Both players choose their integers equiprobably. Find the probability that the interval [min(v, p), max(v, p)] contains exactly k lucky numbers. Input The single line contains five integers pl, pr, vl, vr and k (1 ≤ pl ≤ pr ≤ 109, 1 ≤ vl ≤ vr ≤ 109, 1 ≤ k ≤ 1000). Output On the single line print the result with an absolute error of no more than 10 - 9. Examples Input 1 10 1 10 2 Output 0.320000000000 Input 5 6 8 10 1 Output 1.000000000000 Note Consider that [a, b] denotes an interval of integers; this interval includes the boundaries. That is, <image> In first case there are 32 suitable pairs: (1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 8), (2, 9), (2, 10), (3, 7), (3, 8), (3, 9), (3, 10), (4, 7), (4, 8), (4, 9), (4, 10), (7, 1), (7, 2), (7, 3), (7, 4), (8, 1), (8, 2), (8, 3), (8, 4), (9, 1), (9, 2), (9, 3), (9, 4), (10, 1), (10, 2), (10, 3), (10, 4). Total number of possible pairs is 10·10 = 100, so answer is 32 / 100. In second case Petya always get number less than Vasya and the only lucky 7 is between this numbers, so there will be always 1 lucky number.
instruction
0
102,062
20
204,124
Tags: brute force, probabilities Correct Solution: ``` import itertools as it all_lucky = [] for length in range(1, 10): for comb in it.product(['7', '4'], repeat=length): all_lucky += [int(''.join(comb))] all_lucky.sort() # print(len(all_lucky)) pl, pr, vl, vr, k = map(int, input().split()) result = 0 def inters_len(a, b, c, d): a, b = sorted([a, b]) c, d = sorted([c, d]) return (max([a, c]), min([b, d])) def check_for_intervals(pl, pr, vl, vr): global result for i in range(1, len(all_lucky) - k): le, re = i, i + k - 1 a, b = inters_len(all_lucky[le - 1] + 1, all_lucky[le], pl, pr) left_len = max([0, b - a + 1]) c, d = inters_len(all_lucky[re], all_lucky[re + 1] - 1, vl, vr) right_len = max([0, d - c + 1]) result += (left_len / (pr - pl + 1)) * (right_len / (vr - vl + 1)) if b == c and left_len * right_len > 1e-6: result -= (1 / (pr - pl + 1) / (vr - vl + 1)) / 2 a, b = inters_len(0, all_lucky[0], pl, pr) left_len = max([0, b - a + 1]) c, d = inters_len(all_lucky[k - 1], all_lucky[k] - 1, vl, vr) right_len = max([0, d - c + 1]) #print((left_len / (pr - pl + 1)) * (right_len / (vr - vl + 1))) #print(left_len, right_len) result += (left_len / (pr - pl + 1)) * (right_len / (vr - vl + 1)) if b == c and left_len * right_len > 1e-6: result -= (1 / (pr - pl + 1) / (vr - vl + 1)) / 2 a, b = inters_len(all_lucky[-(k + 1)] + 1, all_lucky[-k], pl, pr) left_len = max([0, b - a + 1]) c, d = inters_len(all_lucky[-1], 10**9, vl, vr) right_len = max([0, d - c + 1]) #print((left_len / (pr - pl + 1)) * (right_len / (vr - vl + 1))) result += (left_len / (pr - pl + 1)) * (right_len / (vr - vl + 1)) if b == c and left_len * right_len > 1e-6: result -= (1 / (pr - pl + 1) / (vr - vl + 1)) / 2 #print(all_lucky[:5]) if k != len(all_lucky): check_for_intervals(pl, pr, vl, vr) check_for_intervals(vl, vr, pl, pr) else: a, b = inters_len(0, all_lucky[0], pl, pr) left_len = max([0, b - a + 1]) c, d = inters_len(all_lucky[-1], 10**9, vl, vr) right_len = max([0, d - c + 1]) result += (left_len / (pr - pl + 1)) * (right_len / (vr - vl + 1)) if b == c and left_len * right_len > 1e-6: result -= (1 / (pr - pl + 1) / (vr - vl + 1)) / 2 a, b = inters_len(0, all_lucky[0], vl, vr) left_len = max([0, b - a + 1]) c, d = inters_len(all_lucky[-1], 10**9, pl, pr) right_len = max([0, d - c + 1]) result += (left_len / (vr - vl + 1)) * (right_len / (pr - pl + 1)) if b == c and left_len * right_len > 1e-6: result -= (1 / (pr - pl + 1) / (vr - vl + 1)) / 2 print(result) # Made By Mostafa_Khaled ```
output
1
102,062
20
204,125
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not. Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer p from the interval [pl, pr] and Vasya chooses an integer v from the interval [vl, vr] (also randomly). Both players choose their integers equiprobably. Find the probability that the interval [min(v, p), max(v, p)] contains exactly k lucky numbers. Input The single line contains five integers pl, pr, vl, vr and k (1 ≤ pl ≤ pr ≤ 109, 1 ≤ vl ≤ vr ≤ 109, 1 ≤ k ≤ 1000). Output On the single line print the result with an absolute error of no more than 10 - 9. Examples Input 1 10 1 10 2 Output 0.320000000000 Input 5 6 8 10 1 Output 1.000000000000 Note Consider that [a, b] denotes an interval of integers; this interval includes the boundaries. That is, <image> In first case there are 32 suitable pairs: (1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 8), (2, 9), (2, 10), (3, 7), (3, 8), (3, 9), (3, 10), (4, 7), (4, 8), (4, 9), (4, 10), (7, 1), (7, 2), (7, 3), (7, 4), (8, 1), (8, 2), (8, 3), (8, 4), (9, 1), (9, 2), (9, 3), (9, 4), (10, 1), (10, 2), (10, 3), (10, 4). Total number of possible pairs is 10·10 = 100, so answer is 32 / 100. In second case Petya always get number less than Vasya and the only lucky 7 is between this numbers, so there will be always 1 lucky number. Submitted Solution: ``` import itertools def generate_happy(): happy_digits = '47' happies = [] for num_len in range(1, 10): happies.extend(itertools.product(happy_digits, repeat=num_len)) return [int(''.join(num)) for num in happies] def clamp_segment(start, end, min_b, max_b): if start > end or min_b > max_b: raise ValueError(f"{start} {end} {min_b} {max_b}") if start > max_b or end < min_b: return None, None new_start = start new_end = end if start < min_b: new_start = min_b if end > max_b: new_end = max_b return new_start, new_end def get_window_bounds(happies, happy_count, happy_window_ind): return (happies[happy_window_ind - 1] if happy_window_ind > 0 else 1, happies[happy_window_ind], happies[happy_window_ind + happy_count - 1], (happies[happy_window_ind + happy_count] if happy_window_ind + happy_count < len(happies) else 10 ** 9 ) ) def get_good_segm_count_ordered( lower_start, lower_end, upper_start, upper_end, prev_happy, this_happy, last_happy, next_happy): (lower_bound_start, lower_bound_end) = clamp_segment( lower_start, lower_end, prev_happy, this_happy ) (upper_bound_start, upper_bound_end) = clamp_segment( upper_start, upper_end, last_happy, next_happy ) if lower_bound_start is None or upper_bound_start is None: return 0 return (lower_bound_end - lower_bound_start + 1) *\ (upper_bound_end - upper_bound_start + 1) def get_good_segm_count(happies, happy_count, happy_window_ind, start_1, end_1, start_2, end_2): prev_happy, this_happy, last_happy, next_happy = get_window_bounds( happies, happy_count, happy_window_ind ) first_is_lower_count = get_good_segm_count_ordered( start_1, end_1, start_2, end_2, prev_happy, this_happy, last_happy, next_happy ) second_is_lower_count = get_good_segm_count_ordered( start_2, end_2, start_1, end_2, prev_happy, this_happy, last_happy, next_happy ) return first_is_lower_count + second_is_lower_count def main(args=None): if args is None: p_start, p_end, v_start, v_end, happy_count = map(int, input().split()) else: p_start, p_end, v_start, v_end, happy_count = args happies = generate_happy() good_segments_count = 0 for happy_window_ind in range(len(happies) - happy_count + 1): good_segments_count += get_good_segm_count( happies, happy_count, happy_window_ind, p_start, p_end, v_start, v_end ) all_segments_count = (p_end - p_start + 1) * (v_end - v_start + 1) return good_segments_count / all_segments_count main() ```
instruction
0
102,063
20
204,126
No
output
1
102,063
20
204,127
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not. Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer p from the interval [pl, pr] and Vasya chooses an integer v from the interval [vl, vr] (also randomly). Both players choose their integers equiprobably. Find the probability that the interval [min(v, p), max(v, p)] contains exactly k lucky numbers. Input The single line contains five integers pl, pr, vl, vr and k (1 ≤ pl ≤ pr ≤ 109, 1 ≤ vl ≤ vr ≤ 109, 1 ≤ k ≤ 1000). Output On the single line print the result with an absolute error of no more than 10 - 9. Examples Input 1 10 1 10 2 Output 0.320000000000 Input 5 6 8 10 1 Output 1.000000000000 Note Consider that [a, b] denotes an interval of integers; this interval includes the boundaries. That is, <image> In first case there are 32 suitable pairs: (1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 8), (2, 9), (2, 10), (3, 7), (3, 8), (3, 9), (3, 10), (4, 7), (4, 8), (4, 9), (4, 10), (7, 1), (7, 2), (7, 3), (7, 4), (8, 1), (8, 2), (8, 3), (8, 4), (9, 1), (9, 2), (9, 3), (9, 4), (10, 1), (10, 2), (10, 3), (10, 4). Total number of possible pairs is 10·10 = 100, so answer is 32 / 100. In second case Petya always get number less than Vasya and the only lucky 7 is between this numbers, so there will be always 1 lucky number. Submitted Solution: ``` import itertools def generate_happy(): happy_digits = '47' happies = [] for num_len in range(1, 10): happies.extend(itertools.product(happy_digits, repeat=num_len)) return [int(''.join(num)) for num in happies] def clamp_segment(start, end, min_b, max_b): if start > end or min_b > max_b: raise ValueError(f"{start} {end} {min_b} {max_b}") if start > max_b or end < min_b: return None, None new_start = start new_end = end if start < min_b: new_start = min_b if end > max_b: new_end = max_b return new_start, new_end def get_window_bounds(happies, happy_count, happy_window_ind): return (happies[happy_window_ind - 1] if happy_window_ind > 0 else 0, happies[happy_window_ind], happies[happy_window_ind + happy_count - 1], (happies[happy_window_ind + happy_count] if happy_window_ind + happy_count < len(happies) else 10 ** 9 + 1 ) ) def get_good_segm_count_ordered( lower_start, lower_end, upper_start, upper_end, prev_happy, this_happy, last_happy, next_happy): (lower_bound_start, lower_bound_end) = clamp_segment( lower_start, lower_end, prev_happy + 1, this_happy ) (upper_bound_start, upper_bound_end) = clamp_segment( upper_start, upper_end, last_happy, next_happy - 1 ) if lower_bound_start is None or upper_bound_start is None: return 0 return (lower_bound_end - lower_bound_start + 1) *\ (upper_bound_end - upper_bound_start + 1) def get_good_segm_count(happies, happy_count, happy_window_ind, start_1, end_1, start_2, end_2): prev_happy, this_happy, last_happy, next_happy = get_window_bounds( happies, happy_count, happy_window_ind ) first_is_lower_count = get_good_segm_count_ordered( start_1, end_1, start_2, end_2, prev_happy, this_happy, last_happy, next_happy ) second_is_lower_count = get_good_segm_count_ordered( start_2, end_2, start_1, end_1, prev_happy, this_happy, last_happy, next_happy ) return first_is_lower_count + second_is_lower_count def main(args=None): if args is None: p_start, p_end, v_start, v_end, happy_count = map(int, input().split()) else: p_start, p_end, v_start, v_end, happy_count = args happies = generate_happy() good_segments_count = 0 for happy_window_ind in range(len(happies) - happy_count + 1): good_segments_count += get_good_segm_count( happies, happy_count, happy_window_ind, p_start, p_end, v_start, v_end ) # print(get_good_segm_count( # happies, happy_count, happy_window_ind, # p_start, p_end, v_start, v_end # ), happy_window_ind) all_segments_count = (p_end - p_start + 1) * (v_end - v_start + 1) return good_segments_count / all_segments_count main() ```
instruction
0
102,064
20
204,128
No
output
1
102,064
20
204,129
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not. Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer p from the interval [pl, pr] and Vasya chooses an integer v from the interval [vl, vr] (also randomly). Both players choose their integers equiprobably. Find the probability that the interval [min(v, p), max(v, p)] contains exactly k lucky numbers. Input The single line contains five integers pl, pr, vl, vr and k (1 ≤ pl ≤ pr ≤ 109, 1 ≤ vl ≤ vr ≤ 109, 1 ≤ k ≤ 1000). Output On the single line print the result with an absolute error of no more than 10 - 9. Examples Input 1 10 1 10 2 Output 0.320000000000 Input 5 6 8 10 1 Output 1.000000000000 Note Consider that [a, b] denotes an interval of integers; this interval includes the boundaries. That is, <image> In first case there are 32 suitable pairs: (1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 8), (2, 9), (2, 10), (3, 7), (3, 8), (3, 9), (3, 10), (4, 7), (4, 8), (4, 9), (4, 10), (7, 1), (7, 2), (7, 3), (7, 4), (8, 1), (8, 2), (8, 3), (8, 4), (9, 1), (9, 2), (9, 3), (9, 4), (10, 1), (10, 2), (10, 3), (10, 4). Total number of possible pairs is 10·10 = 100, so answer is 32 / 100. In second case Petya always get number less than Vasya and the only lucky 7 is between this numbers, so there will be always 1 lucky number. Submitted Solution: ``` def gen(n, cur): if n == 0: global arr arr.append(cur) else: gen(n - 1, cur + '4') gen(n - 1, cur + '7') def inter(x1, x2, a, b): left = max(x1, a) right = min(x2, b) if right < left: return 0 return right - left + 1 arr = [] for i in range(1, 11): gen(i, '') arr = [0] + sorted(list(map(int, arr))) pl, pr, vl, vr, k = map(int, input().split()) ans = 0 for start in range(1, len(arr) - k + 1): if arr[start + k - 1] > max(vr, pr): break if arr[start] < min(pl, vl): continue goleft = inter(pl, pr, arr[start - 1] + 1, arr[start]) goright = inter(vl, vr, arr[start + k - 1], arr[start + k] - 1) ans += goleft * goright goright = inter(vl, vr, arr[start - 1] + 1, arr[start]) goleft = inter(pl, pr, arr[start + k - 1], arr[start + k] - 1) ans += goleft * goright ans /= (pr - pl + 1) * (vr - vl + 1) print(ans) ```
instruction
0
102,065
20
204,130
No
output
1
102,065
20
204,131
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not. Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer p from the interval [pl, pr] and Vasya chooses an integer v from the interval [vl, vr] (also randomly). Both players choose their integers equiprobably. Find the probability that the interval [min(v, p), max(v, p)] contains exactly k lucky numbers. Input The single line contains five integers pl, pr, vl, vr and k (1 ≤ pl ≤ pr ≤ 109, 1 ≤ vl ≤ vr ≤ 109, 1 ≤ k ≤ 1000). Output On the single line print the result with an absolute error of no more than 10 - 9. Examples Input 1 10 1 10 2 Output 0.320000000000 Input 5 6 8 10 1 Output 1.000000000000 Note Consider that [a, b] denotes an interval of integers; this interval includes the boundaries. That is, <image> In first case there are 32 suitable pairs: (1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 8), (2, 9), (2, 10), (3, 7), (3, 8), (3, 9), (3, 10), (4, 7), (4, 8), (4, 9), (4, 10), (7, 1), (7, 2), (7, 3), (7, 4), (8, 1), (8, 2), (8, 3), (8, 4), (9, 1), (9, 2), (9, 3), (9, 4), (10, 1), (10, 2), (10, 3), (10, 4). Total number of possible pairs is 10·10 = 100, so answer is 32 / 100. In second case Petya always get number less than Vasya and the only lucky 7 is between this numbers, so there will be always 1 lucky number. Submitted Solution: ``` #!/usr/bin/env python3 vl, vr, pl, pr, k = map(int, input().split()) lucky = [4, 7] sz = 0 for i in range(1, 9): base = 10 ** i psz, sz = sz, len(lucky) for j in [4 * base, 7 * base]: for pos in range(psz, sz): lucky.append(j + lucky[pos]) ans = 0 for i in range(0, len(lucky)-k+1): ll, lr = 1 if i == 0 else lucky[i-1] + 1, lucky[i] rl, rr = lucky[i+k-1], 1_000_000_000 if i+k == len(lucky) else lucky[i+k] vc = max(0, min(vr, lr) - max(vl, ll) + 1) pc = max(0, min(pr, rr) - max(pl, rl) + 1) ans += vc * pc vc = max(0, min(pr, lr) - max(pl, ll) + 1) pc = max(0, min(vr, rr) - max(vl, rl) + 1) ans += vc * pc print(ans / ((vr-vl+1) * (pr - pl + 1))) ```
instruction
0
102,066
20
204,132
No
output
1
102,066
20
204,133
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1
instruction
0
102,253
20
204,506
Tags: brute force, greedy, math Correct Solution: ``` resList = [] testCount = int(input()) for test in range(testCount): num = int(input()) sum = 0 numStr="" if(num>45): resList.append(str(-1)) elif(len(str(num)) == 1): resList.append(str(num)) else: for i in reversed(range(1,10)): if(num == 0): break elif(num < i): sum = sum + num numStr += str(num) break sum = sum + i num = num - i numStr += str(i) resList.append(numStr[::-1]) for res in resList: print(res) ```
output
1
102,253
20
204,507
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1
instruction
0
102,254
20
204,508
Tags: brute force, greedy, math Correct Solution: ``` def suma(n): s=0 while n!=0 : s=s+n%10 n=n//10 return s te=int(input()) for i in range(te): num=int(input()) res="987654321" if num>45: print("-1") else: for i in range(100): if res[-1]=="0": res=res[:-1] if suma(int(res))==num: print(res[::-1]) break res=str(int(res)-1) ```
output
1
102,254
20
204,509
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1
instruction
0
102,255
20
204,510
Tags: brute force, greedy, math Correct Solution: ``` for _ in range (int(input())): n=int(input()) if n==43: print("13456789") continue elif n==44: print("23456789") continue elif n==45: print("123456789") continue s=set() curr=9 num=0 copy=n ch=1 while n>9: if curr<1: ch=0 break num=num*10+curr s.add(curr) n-=curr curr-=1 if ch==0: print(-1) elif n in s: num=num*10+curr s.add(curr) n-=curr curr-=1 if n in s: print(-1) else: num=num*10+n num=str(num) num=num[::-1] print(num) else: num=num*10+n num=str(num) num=num[::-1] print(num) ```
output
1
102,255
20
204,511
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1
instruction
0
102,256
20
204,512
Tags: brute force, greedy, math Correct Solution: ``` t = int(input()) for _ in range(t): x = int(input()) if x > 45: print(-1) else: l = 0 while l*(l+1)//2+((9-l)*l) < x: l += 1 s = [] for i in range(10-l, 10): s += [i] while sum(s)>x: s[0] -= 1 for i in s: print(i, end='') print() ```
output
1
102,256
20
204,513
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1
instruction
0
102,257
20
204,514
Tags: brute force, greedy, math Correct Solution: ``` # cook your dish here from sys import stdin, stdout import math from itertools import permutations, combinations from collections import defaultdict from collections import Counter from bisect import bisect_left import sys from queue import PriorityQueue import operator as op from functools import reduce import re mod = 1000000007 input = sys.stdin.readline def L(): return list(map(int, stdin.readline().split())) def In(): return map(int, stdin.readline().split()) def I(): return int(stdin.readline()) def printIn(ob): return stdout.write(str(ob) + '\n') def powerLL(n, p): result = 1 while (p): if (p & 1): result = result * n % mod p = int(p / 2) n = n * n % mod return result def ncr(n, r): r = min(r, n - r) numer = reduce(op.mul, range(n, n - r, -1), 1) denom = reduce(op.mul, range(1, r + 1), 1) return numer // denom def SieveOfEratosthenes(n): # Create a boolean array "prime[0..n]" and initialize # all entries it as true. A value in prime[i] will # finally be false if i is Not a prime, else true. prime_list = [] prime = [True for i in range(n+1)] p = 2 while (p * p <= n): # If prime[p] is not changed, then it is a prime if (prime[p] == True): prime_list.append(p) # Update all multiples of p for i in range(p * p, n+1, p): prime[i] = False p += 1 return prime_list def get_divisors(n): for i in range(1, int(n / 2) + 1): if n % i == 0: yield i yield n # ------------------------------------- def myCode(): n = I() if n<=9: print(n) elif n>=10 and n<=17: for i in ("12345678"): if int(i)+9 == n: print(i+str(9)) break elif n>=18 and n<=24: for i in ("1234567"): if int(i)+8+9 == n: print(i+str(89)) break elif n>=25 and n<=30: for i in ("123456"): if int(i)+7+8+9 == n: print(i+str(789)) break elif n>=31 and n<=35: for i in ("12345"): if int(i)+6+7+8+9 == n: print(i+str(6789)) break elif n>=36 and n<=39: for i in ("1234"): if int(i)+5+6+7+8+9 == n: print(i+str(56789)) break elif n>=40 and n<=42: for i in ("123"): if int(i)+4+5+6+7+8+9 == n: print(i+str(456789)) break elif n>=43 and n<=44: for i in ("12"): if int(i)+3+4+5+6+7+8+9 == n: print(i+str(3456789)) break elif n==45: print(123456789) else: print(-1) def main(): for t in range(I()): myCode() if __name__ == '__main__': # print(int(math.log2(10))) main() ```
output
1
102,257
20
204,515
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1
instruction
0
102,258
20
204,516
Tags: brute force, greedy, math Correct Solution: ``` import collections from collections import defaultdict for _ in range(int(input())): n=int(input()) #s=input() #n,q=[int(x) for x in input().split()] if n>45: print(-1) continue if n<10: print(n) continue z = list(range(9,0,-1)) s = 0 ans=[] for x in z: if s+x<=n: ans.append(x) s+=x ans=[str(x) for x in ans] ans.sort() print("".join(ans)) ```
output
1
102,258
20
204,517
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1
instruction
0
102,259
20
204,518
Tags: brute force, greedy, math Correct Solution: ``` '''input 1 46 ''' T = int(input()) while T: dig = 9 ans = '' x = int(input()) dig = list(range(9,0,-1)) if(x > 45): print(-1) T -= 1 continue for i in dig: if(x >= i): ans += str(i) x -= i print(ans[::-1]) T -= 1 ```
output
1
102,259
20
204,519
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1
instruction
0
102,260
20
204,520
Tags: brute force, greedy, math Correct Solution: ``` """ pppppppppppppppppppp ppppp ppppppppppppppppppp ppppppp ppppppppppppppppppppp pppppppp pppppppppppppppppppppp pppppppppppppppppppppppppppppppp pppppppppppppppppppppppp ppppppppppppppppppppppppppppppppppppppppppppppp pppppppppppppppppppp pppppppppppppppppppppppppppppppppppppppppppppppp ppppppppppppppppppppp ppppppppppppppppppppppppppppppppppppppppppppppppp pppppppppppppppppppppp ppppppppppppppppppppppppppppppppppppppppppppppp pppppppppppppppppppppppp pppppppppppppppppppppppppppppppppppppppppppppp pppppppppppppppppppppppppp ppppppppppppppppppppppppppppppppppppppppppppp pppppppppppppppppppppppppppp pppppppppppppppppppppppppppppppp pppppppppppppppppppppppppppppppp pppppppppppppppppppppppppppp pppppppppppppppppppppppppppppppppppppppppppppp ppppppppppppppppppppppppppp pppppppppppppppppppppppppppppppppppppppppppppppp pppppppppppppppppppppppp pppppppppppppppppppppppppppppppppppppppppppppppppp ppppppppppppppppppppppp ppppppppppppppppppppppppppppppppppppppppppppppppp pppppppppppppppppppppp ppppppppppppppppppppppppppppppppppppppppppppppp ppppppppppppppppppppp ppppppppppppppppppppppppppppppppppppppppppppp pppppppppppppppppppppppp pppppppppppppppppppppppppppppppp pppppppppppppppppppppp pppppppp ppppppppppppppppppppp ppppppp ppppppppppppppppppp ppppp pppppppppppppppppppp """ import sys from functools import lru_cache, cmp_to_key from heapq import merge, heapify, heappop, heappush, nsmallest from math import ceil, floor, gcd, fabs, factorial, fmod, sqrt, inf from collections import defaultdict as dd, deque, Counter as C from itertools import combinations as comb, permutations as perm from bisect import bisect_left as bl, bisect_right as br, bisect from time import perf_counter from fractions import Fraction from decimal import Decimal # sys.setrecursionlimit(pow(10, 6)) # sys.stdin = open("input.txt", "r") # sys.stdout = open("output.txt", "w") mod = pow(10, 9) + 7 # mod2 = 998244353 def data(): return sys.stdin.readline().strip() def out(var): sys.stdout.write(str(var)+"\n") def outa(*var, end="\n"): sys.stdout.write(' '.join(map(str, var)) + end) def l(): return list(sp()) def sl(): return list(ssp()) def sp(): return map(int, data().split()) def ssp(): return map(str, data().split()) def l1d(n, val=0): return [val for i in range(n)] def l2d(n, m, val=0): return [l1d(n, val) for j in range(m)] for _ in range(int(data())): x = int(data()) if x > 45: out(-1) continue answer = [] temp = 9 while x: if x >= temp: answer.append(str(temp)) x -= temp temp -= 1 else: answer.append(str(x)) break out(''.join(answer[::-1])) ```
output
1
102,260
20
204,521
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1 Submitted Solution: ``` import copy import math t = int(input()) for case in range(t): n = int(input()) s ="" k = 9 if(n>45): print(-1) continue while(n>0): if n>=k: n-=k s+=str(k) k-=1 else: s+=str(n) break print(s[::-1]) ```
instruction
0
102,261
20
204,522
Yes
output
1
102,261
20
204,523
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1 Submitted Solution: ``` t = int(input()) while t: t -= 1; n = int(input()) if n>45: print(-1) continue x = 0 i = 9 j = 0 while n: z = min(n, i) i-=1 x = x + z*(10**j) n -= z j += 1 print(x) ```
instruction
0
102,262
20
204,524
Yes
output
1
102,262
20
204,525
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1 Submitted Solution: ``` def main(): n = int(input()) output = [] for i in range(n): x = int(input()) y = x for i in range(9, 0, -1): if x - i >= 0: output.append(i) x -= i if sum(output) != y: print(-1) else: print("".join(sorted([str(x) for x in output]))) output = [] if __name__ == "__main__": main() ```
instruction
0
102,263
20
204,526
Yes
output
1
102,263
20
204,527
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1 Submitted Solution: ``` def f(x): s=0 for i in range(10): if x>=sum(range(i,10)): s = sum(range(i,10)) break if x == s: return "".join(map(str,range(i,10))) return "".join(map(str, sorted([x-s]+list(range(i,10))))) t = int(input()) for _ in range(t): x = int(input()) if x>45: print(-1) elif x==45: print(123456789) elif x<10: print(x) else: print(f(x)) ```
instruction
0
102,264
20
204,528
Yes
output
1
102,264
20
204,529
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1 Submitted Solution: ``` t = int(input()) for i in range(t): n = int(input()) e = [46,47,48,49,50] if int(n/10)==0: print(n) elif n in e: print(-1) elif n>9 and n<18: s=n%9 print(s*(10**1)+9) elif n>17 and n<25: s=n%17 print(s*(10**2)+89) elif n>24 and n<31: s=n%24 print(s*(10**3)+789) elif n>30 and n<36: s=n%30 print(s*(10**4)+6789) elif n>35 and n<40: s=n%35 print(s*(10**5)+56789) elif n>39 and n<43: s=n%39 print(s*(10**6)+456789) elif n==44: print(23456789) else: print(123456789) ```
instruction
0
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204,530
No
output
1
102,265
20
204,531
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1 Submitted Solution: ``` class var: list = 50 * [-1] def sod(n): s = 0 for j in range(len(n)): s += ord(n[j]) - 48 return s def f(s): val = sod(s) if val <= 50: if var.list[val - 1] == -1 or int(s) < var.list[val - 1]: var.list[val - 1] = int(s) for j in range(10): if chr(j + 48) not in s: f(s + chr(j + 48)) #for j in range(10): #f(chr(j + 48)) #print(var.list) List = [1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 29, 39, 49, 59, 69, 79, 89, 189, 289, 389, 489, 589, 689, 789, 1789, 2789, 3789, 4789, 5789, 6789, 16789, 26789, 36789, 46789, 56789, 156789, 256789, 356789, 456789, 1456789, 2456789, 3456789, 13456789, 23456789, 123456789, -1, -1, -1, -1, 0] for _ in range(int(input())): print(List[int(input()) - 1]) ```
instruction
0
102,266
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204,532
No
output
1
102,266
20
204,533
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1 Submitted Solution: ``` from math import * sInt = lambda: int(input()) mInt = lambda: map(int, input().split()) lInt = lambda: list(map(int, input().split())) t = sInt() for _ in range(t): n = sInt() if n>17: print(-1) elif n==1: print(n) else: a = n//2-1 print(a,end='') print(n-a) ```
instruction
0
102,267
20
204,534
No
output
1
102,267
20
204,535
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique). Input The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow. Each test case consists of a single integer number x (1 ≤ x ≤ 50). Output Output t answers to the test cases: * if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number; * otherwise print -1. Example Input 4 1 5 15 50 Output 1 5 69 -1 Submitted Solution: ``` t = int(input()) for test in range(0,t): n = int(input()) if n>45: print(-1) elif len(str(n))==1: print(n) else: s = '' big = 9 while(len(str(n))>1): n = n-big s = s+str(big) big = big-1 if n<=big: s = s+str(n) s = s[::-1] print(int(s)) else: k = n-big s = s+str(big)+str(k) s = s[::-1] print(int(s)) ```
instruction
0
102,268
20
204,536
No
output
1
102,268
20
204,537
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110
instruction
0
102,301
20
204,602
Tags: binary search, dp, math, number theory Correct Solution: ``` t = int(input()) while(t > 0): t -= 1 l, r = [int(x) for x in input().split()] num1 = str(l) num2 = str(r) ans = 0 while(len(num1) != len(num2)): num1 = '0' + num1 for i in range(len(num1)): k1 = int(num1[:i+1]) k2 = int(num2[:i+1]) ans += k2 - k1 print(ans) ```
output
1
102,301
20
204,603
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110
instruction
0
102,302
20
204,604
Tags: binary search, dp, math, number theory Correct Solution: ``` for _ in range(int(input())): l,r=map(int,input().split()) ansl=0 ansr=0 ansl+=l-1 ansr+=r-1 # print(ansl,ansr) while(l): ansl+=l//10 l//=10 while(r): ansr+=r//10 r//=10 print(ansr-ansl) ```
output
1
102,302
20
204,605
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110
instruction
0
102,303
20
204,606
Tags: binary search, dp, math, number theory Correct Solution: ``` import sys input = sys.stdin.readline def main(): t = int(input()) for _ in range(t): L, R = [int(x) for x in input().split()] ans = R - L cnt_r = 0 cnt_l = 0 for i in range(1, 20): cnt_r += R // pow(10, i) cnt_l += L // pow(10, i) ans += cnt_r - cnt_l print(ans) if __name__ == '__main__': main() ```
output
1
102,303
20
204,607
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110
instruction
0
102,304
20
204,608
Tags: binary search, dp, math, number theory Correct Solution: ``` for s in[*open(0)][1:]: x,y=map(int,s.split());r=0 while y:r+=y-x;x//=10;y//=10 print(r) ```
output
1
102,304
20
204,609
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110
instruction
0
102,305
20
204,610
Tags: binary search, dp, math, number theory Correct Solution: ``` def main(): ans = [] #Respuestas for _ in range(int(input())): l, t = map(int, input().split()) #Numeros iniciales cha = 0 #Cantidad de cambios while t > 0: cha += t - l l //= 10 t //= 10 ans.append(cha) for i in ans: print(i) if __name__ == "__main__": main() ```
output
1
102,305
20
204,611
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110
instruction
0
102,306
20
204,612
Tags: binary search, dp, math, number theory Correct Solution: ``` t=int(input()) for _ in range(t): l,r=map(int,input().split()) c1=r-l for i in range(1,10): c1+=r//(10**i) c2=0 for i in range(1,10): c2+=l//(10**i) print(c1-c2) ```
output
1
102,306
20
204,613
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110
instruction
0
102,307
20
204,614
Tags: binary search, dp, math, number theory Correct Solution: ``` for _ in range(int(input())): l,r = map(int,input().split()) ans = 0 while r: ans += r-l r //= 10 l //= 10 print(ans) ```
output
1
102,307
20
204,615
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110
instruction
0
102,308
20
204,616
Tags: binary search, dp, math, number theory Correct Solution: ``` import sys input=sys.stdin.readline t=int(input()) c=[1,11,111,1111,11111,111111,1111111,11111111,111111111,1111111111] for _ in range(t): l,r=map(int,input().split()) aa=0 a=len(str(r)) r=str(r) for i in range(a): aa+=int(r[i])*c[a-i-1] bb=0 b=len(str(l)) l=str(l) for i in range(b): bb+=int(l[i])*c[b-i-1] print(aa-bb) ```
output
1
102,308
20
204,617
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110 Submitted Solution: ``` def func(r): if r==1: return 0 total_digits = len(str(r)) nums_divisible_by_ten = [0 for i in range(total_digits+1)] starting = total_digits-1 count = 0 while starting>0: divisor = 10**(starting) nums_divisible_by_ten[starting] = (r//divisor)-count count = (r//divisor) starting-=1 total_sum = 0 for j in range(1, total_digits+1): total_sum += nums_divisible_by_ten[j]*(j+1) total_sum += r-sum(nums_divisible_by_ten)-1 return total_sum t = int(input()) for i in range(t): l, r = map(int, input().split()) print(func(r)-func(l)) ```
instruction
0
102,309
20
204,618
Yes
output
1
102,309
20
204,619
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110 Submitted Solution: ``` T=int(input()) for t in range(T): l,r=map(int,input().split()) ans=0 for i in range(10): div=10**i ans+=r//div-l//div print(ans) ```
instruction
0
102,310
20
204,620
Yes
output
1
102,310
20
204,621
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110 Submitted Solution: ``` for s in[*open(0)][1:]: r=0;k=-1 for x in map(int,s.split()): while x:r+=k*x;x//=10 k=1 print(r) ```
instruction
0
102,311
20
204,622
Yes
output
1
102,311
20
204,623
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110 Submitted Solution: ``` import time,math as mt,bisect as bs,sys from sys import stdin,stdout from collections import deque from fractions import Fraction from collections import Counter from collections import OrderedDict from collections import defaultdict pi=3.14159265358979323846264338327950 def II(): # to take integer input return int(stdin.readline()) def IP(): # to take tuple as input return map(int,stdin.readline().split()) def L(): # to take list as input return list(map(int,stdin.readline().split())) def P(x): # to print integer,list,string etc.. return stdout.write(str(x)+"\n") def PI(x,y): # to print tuple separatedly return stdout.write(str(x)+" "+str(y)+"\n") def lcm(a,b): # to calculate lcm return (a*b)//gcd(a,b) def gcd(a,b): # to calculate gcd if a==0: return b elif b==0: return a if a>b: return gcd(a%b,b) else: return gcd(a,b%a) def bfs(adj,v): # a schema of bfs visited=[False]*(v+1) q=deque() while q: pass def setBit(n): count=0 while n!=0: n=n&(n-1) count+=1 return count def readTree(n,e): # to read tree adj=[set() for i in range(n+1)] for i in range(e): u1,u2=IP() adj[u1].add(u2) return adj def sieve(): li=[True]*(10**3+5) li[0],li[1]=False,False for i in range(2,len(li),1): if li[i]==True: for j in range(i*i,len(li),i): li[j]=False prime,cur=[0]*200,0 for i in range(10**3+5): if li[i]==True: prime[cur]=i cur+=1 return prime def SPF(): mx=(10**7+1) spf=[mx]*(mx) spf[1]=1 for i in range(2,mx): if spf[i]==mx: spf[i]=i for j in range(i*i,mx,i): if i<spf[j]: spf[j]=i return spf def prime(n,d): while n!=1: d[spf[n]]=d.get(spf[n],0)+1 n=n//spf[n] return ##################################################################################### mod = 1000000007 inf = 1e18 def solve(): l,r=IP() strt = 1 ans=0 while r: ans+=(r-l) r//=10 l//=10 print(ans) return t = II() for i in range(t): solve() ####### # # ####### # # # #### # # # # # # # # # # # # # # # #### # # #### #### # # ###### # # #### # # # # # # ``````¶0````1¶1_``````````````````````````````````````` # ```````¶¶¶0_`_¶¶¶0011100¶¶¶¶¶¶¶001_```````````````````` # ````````¶¶¶¶¶00¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶0_```````````````` # `````1_``¶¶00¶0000000000000000000000¶¶¶¶0_````````````` # `````_¶¶_`0¶000000000000000000000000000¶¶¶¶¶1`````````` # ```````¶¶¶00¶00000000000000000000000000000¶¶¶_````````` # ````````_¶¶00000000000000000000¶¶00000000000¶¶````````` # `````_0011¶¶¶¶¶000000000000¶¶00¶¶0¶¶00000000¶¶_```````` # ```````_¶¶¶¶¶¶¶00000000000¶¶¶¶0¶¶¶¶¶00000000¶¶1```````` # ``````````1¶¶¶¶¶000000¶¶0¶¶¶¶¶¶¶¶¶¶¶¶0000000¶¶¶```````` # ```````````¶¶¶0¶000¶00¶0¶¶`_____`__1¶0¶¶00¶00¶¶```````` # ```````````¶¶¶¶¶00¶00¶10¶0``_1111_`_¶¶0000¶0¶¶¶```````` # ``````````1¶¶¶¶¶00¶0¶¶_¶¶1`_¶_1_0_`1¶¶_0¶0¶¶0¶¶```````` # ````````1¶¶¶¶¶¶¶0¶¶0¶0_0¶``100111``_¶1_0¶0¶¶_1¶```````` # ```````1¶¶¶¶00¶¶¶¶¶¶¶010¶``1111111_0¶11¶¶¶¶¶_10```````` # ```````0¶¶¶¶__10¶¶¶¶¶100¶¶¶0111110¶¶¶1__¶¶¶¶`__```````` # ```````¶¶¶¶0`__0¶¶0¶¶_¶¶¶_11````_0¶¶0`_1¶¶¶¶``````````` # ```````¶¶¶00`__0¶¶_00`_0_``````````1_``¶0¶¶_``````````` # ``````1¶1``¶¶``1¶¶_11``````````````````¶`¶¶```````````` # ``````1_``¶0_¶1`0¶_`_``````````_``````1_`¶1```````````` # 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```¶¶¶00000¶¶¶¶¶¶¶¶¶01___1___00_1¶¶¶`_``1¶¶10¶¶0``````` # ```1010000¶000¶¶0100_11__1011000¶¶0¶1_10¶¶¶_0¶¶00`````` # 10¶000000000¶0________0¶000000¶¶0000¶¶¶¶000_0¶0¶00````` # ¶¶¶¶¶¶0000¶¶¶¶_`___`_0¶¶¶¶¶¶¶00000000000000_0¶00¶01```` # ¶¶¶¶¶0¶¶¶¶¶¶¶¶¶_``_1¶¶¶00000000000000000000_0¶000¶01``` # 1__```1¶¶¶¶¶¶¶¶¶00¶¶¶¶00000000000000000000¶_0¶0000¶0_`` # ```````¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶00000000000000000000010¶00000¶¶_` # ```````0¶¶¶¶¶¶¶¶¶¶¶¶¶¶00000000000000000000¶10¶¶0¶¶¶¶¶0` # ````````¶¶¶¶¶¶¶¶¶¶0¶¶¶00000000000000000000010¶¶¶0011``` # ````````1¶¶¶¶¶¶¶¶¶¶0¶¶¶0000000000000000000¶100__1_````` # `````````¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶000000000000000000¶11``_1`````` # `````````1¶¶¶¶¶¶¶¶¶¶¶0¶¶¶00000000000000000¶11___1_````` # ``````````¶¶¶¶¶¶0¶0¶¶¶¶¶¶¶0000000000000000¶11__``1_```` # ``````````¶¶¶¶¶¶¶0¶¶¶0¶¶¶¶¶000000000000000¶1__````__``` # ``````````¶¶¶¶¶¶¶¶0¶¶¶¶¶¶¶¶¶0000000000000000__`````11`` # `````````_¶¶¶¶¶¶¶¶¶000¶¶¶¶¶¶¶¶000000000000011_``_1¶¶¶0` # `````````_¶¶¶¶¶¶0¶¶000000¶¶¶¶¶¶¶000000000000100¶¶¶¶0_`_ # `````````1¶¶¶¶¶0¶¶¶000000000¶¶¶¶¶¶000000000¶00¶¶01````` # `````````¶¶¶¶¶0¶0¶¶¶0000000000000¶0¶00000000011_``````_ # ````````1¶¶0¶¶¶0¶¶¶¶¶¶¶000000000000000000000¶11___11111 # ````````¶¶¶¶0¶¶¶¶¶00¶¶¶¶¶¶000000000000000000¶011111111_ # ```````_¶¶¶¶¶¶¶¶¶0000000¶0¶00000000000000000¶01_1111111 # ```````0¶¶¶¶¶¶¶¶¶000000000000000000000000000¶01___````` # ```````¶¶¶¶¶¶0¶¶¶000000000000000000000000000¶01___1```` # ``````_¶¶¶¶¶¶¶¶¶00000000000000000000000000000011_111``` # ``````0¶¶0¶¶¶0¶¶0000000000000000000000000000¶01`1_11_`` # ``````¶¶¶¶¶¶0¶¶¶0000000000000000000000000000001`_0_11_` # ``````¶¶¶¶¶¶¶¶¶00000000000000000000000000000¶01``_0_11` # ``````¶¶¶¶0¶¶¶¶00000000000000000000000000000001```_1_11 ```
instruction
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102,312
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Yes
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1
102,312
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204,625
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110 Submitted Solution: ``` for _ in range(int(input())): l,r=map(int,input().split()) tmp=1 count=0 a=1 while tmp//a>0: count += tmp//a a*=10 tmp=r count1=0 a=1 while tmp//a>0: count1 += tmp//a a*=10 print(count1-count) ```
instruction
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102,313
20
204,626
No
output
1
102,313
20
204,627
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110 Submitted Solution: ``` # by the authority of GOD author: Kritarth Sharma # import math,copy from collections import defaultdict,Counter #from itertools import permutations def fact(n): return 1 if (n == 1 or n == 0) else n * fact(n - 1) def prime(n) : if (n <= 1) : return False if (n <= 3) : return True if (n % 2 == 0 or n % 3 == 0) : return False i = 5 while(i * i <= n) : if (n % i == 0 or n % (i + 2) == 0) : return False i = i + 6 return True def inp(): l=list(map(int,input().split())) return l ## code starts here ################################################################################################################# def ll(s): s=str(s) k=1 for i in range(len(s)-1,-1,-1): if s[i]=='9': k+=1 else: break return k def main(): for _ in range(int(input())): l,r=inp() k=0 while l<r: if l+1000000000<r: k+=1111111111 l+=1000000000 elif l+100000000<r: k+=111111111 l+=100000000 elif l+10000000<r: k+=11111111 l+=10000000 elif l+1000000<r: k+=1111111 l+=1000000 elif l+100000<r: k+=111111 l+=100000 elif l+10000<r: k+=11111 l+=10000 elif l+1000<r: k+=1111 l+=1000 elif l+100<r: k+=111 l+=100 elif l+10<r: k+=11 l+=10 else: k+=ll(l) l+=1 print(k) import os,sys from io import BytesIO,IOBase #Fast IO Region BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") if __name__ == "__main__": main() def random(): """My code gets caught in plagiarism check for no reason due to the fast IO template, . Due to this reason, I am making useless functions""" rating=100 rating=rating*100 rating=rating*100 print(rating) def random(): """My code gets caught in plagiarism check for no reason due to the fast IO template, . Due to this reason, I am making useless functions""" rating=100 rating=rating*100 rating=rating*100 print(rating) def random(): """My code gets caught in plagiarism check for no reason due to the fast IO template, . Due to this reason, I am making useless functions""" rating=100 rating=rating*100 rating=rating*100 print(rating) def random(): """My code gets caught in plagiarism check for no reason due to the fast IO template, . Due to this reason, I am making useless functions""" rating=100 rating=rating*100 rating=rating*100 print(rating) ```
instruction
0
102,314
20
204,628
No
output
1
102,314
20
204,629
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110 Submitted Solution: ``` t = int(input()) for _ in range(t): l,r = map(int,input().split()) res = r-l nin = res//9 res+= (nin) if(l%9==0 and r%10==2): res+=1 print(res) ```
instruction
0
102,315
20
204,630
No
output
1
102,315
20
204,631
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers l and r, where l < r. We will add 1 to l until the result is equal to r. Thus, there will be exactly r-l additions performed. For each such addition, let's look at the number of digits that will be changed after it. For example: * if l=909, then adding one will result in 910 and 2 digits will be changed; * if you add one to l=9, the result will be 10 and 2 digits will also be changed; * if you add one to l=489999, the result will be 490000 and 5 digits will be changed. Changed digits always form a suffix of the result written in the decimal system. Output the total number of changed digits, if you want to get r from l, adding 1 each time. Input The first line contains an integer t (1 ≤ t ≤ 10^4). Then t test cases follow. Each test case is characterized by two integers l and r (1 ≤ l < r ≤ 10^9). Output For each test case, calculate the total number of changed digits if you want to get r from l, adding one each time. Example Input 4 1 9 9 10 10 20 1 1000000000 Output 8 2 11 1111111110 Submitted Solution: ``` t = int(input()) for _ in range(t): # n = int(input()) l,r = map(int, input().split()) q = str(l) w = str(r) cnt = -len(q)+len(w) x = r-l while x>0: cnt+=x x=x//10 print(cnt) ```
instruction
0
102,316
20
204,632
No
output
1
102,316
20
204,633
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There have recently been elections in the zoo. Overall there were 7 main political parties: one of them is the Little Elephant Political Party, 6 other parties have less catchy names. Political parties find their number in the ballot highly important. Overall there are m possible numbers: 1, 2, ..., m. Each of these 7 parties is going to be assigned in some way to exactly one number, at that, two distinct parties cannot receive the same number. The Little Elephant Political Party members believe in the lucky digits 4 and 7. They want to evaluate their chances in the elections. For that, they need to find out, how many correct assignments are there, such that the number of lucky digits in the Little Elephant Political Party ballot number is strictly larger than the total number of lucky digits in the ballot numbers of 6 other parties. Help the Little Elephant Political Party, calculate this number. As the answer can be rather large, print the remainder from dividing it by 1000000007 (109 + 7). Input A single line contains a single positive integer m (7 ≤ m ≤ 109) — the number of possible numbers in the ballot. Output In a single line print a single integer — the answer to the problem modulo 1000000007 (109 + 7). Examples Input 7 Output 0 Input 8 Output 1440 Submitted Solution: ``` def fact(n): if n==0:return 1 return n*fact(n-1) n = int(input()) print((2*fact(n-2))%1000000007 if n>7 else 0) ```
instruction
0
102,350
20
204,700
No
output
1
102,350
20
204,701
Provide tags and a correct Python 3 solution for this coding contest problem. Little X used to play a card game called "24 Game", but recently he has found it too easy. So he invented a new game. Initially you have a sequence of n integers: 1, 2, ..., n. In a single step, you can pick two of them, let's denote them a and b, erase them from the sequence, and append to the sequence either a + b, or a - b, or a × b. After n - 1 steps there is only one number left. Can you make this number equal to 24? Input The first line contains a single integer n (1 ≤ n ≤ 105). Output If it's possible, print "YES" in the first line. Otherwise, print "NO" (without the quotes). If there is a way to obtain 24 as the result number, in the following n - 1 lines print the required operations an operation per line. Each operation should be in form: "a op b = c". Where a and b are the numbers you've picked at this operation; op is either "+", or "-", or "*"; c is the result of corresponding operation. Note, that the absolute value of c mustn't be greater than 1018. The result of the last operation must be equal to 24. Separate operator sign and equality sign from numbers with spaces. If there are multiple valid answers, you may print any of them. Examples Input 1 Output NO Input 8 Output YES 8 * 7 = 56 6 * 5 = 30 3 - 4 = -1 1 - 2 = -1 30 - -1 = 31 56 - 31 = 25 25 + -1 = 24
instruction
0
102,441
20
204,882
Tags: constructive algorithms, greedy, math Correct Solution: ``` n = int(input()) if n < 4: print("NO") else: print("YES") while n > 5: a = str(n) b = str(n-1) print(a + " - " + b + " = 1 ") print("1 * 1 = 1") n -= 2 if n == 4: print("4 * 3 = 12\n12 * 2 = 24\n24 * 1 = 24") else: print("5 - 2 = 3\n3 - 1 = 2\n2 * 3 = 6\n6 * 4 = 24") # Made By Mostafa_Khaled ```
output
1
102,441
20
204,883