text stringlengths 198 433k | conversation_id int64 0 109k |
|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yaroslav, Andrey and Roman can play cubes for hours and hours. But the game is for three, so when Roman doesn't show up, Yaroslav and Andrey play another game.
Roman leaves a word for each of them. Each word consists of 2Β·n binary characters "0" or "1". After that the players start moving in turns. Yaroslav moves first. During a move, a player must choose an integer from 1 to 2Β·n, which hasn't been chosen by anybody up to that moment. Then the player takes a piece of paper and writes out the corresponding character from his string.
Let's represent Yaroslav's word as s = s1s2... s2n. Similarly, let's represent Andrey's word as t = t1t2... t2n. Then, if Yaroslav choose number k during his move, then he is going to write out character sk on the piece of paper. Similarly, if Andrey choose number r during his move, then he is going to write out character tr on the piece of paper.
The game finishes when no player can make a move. After the game is over, Yaroslav makes some integer from the characters written on his piece of paper (Yaroslav can arrange these characters as he wants). Andrey does the same. The resulting numbers can contain leading zeroes. The person with the largest number wins. If the numbers are equal, the game ends with a draw.
You are given two strings s and t. Determine the outcome of the game provided that Yaroslav and Andrey play optimally well.
Input
The first line contains integer n (1 β€ n β€ 106). The second line contains string s β Yaroslav's word. The third line contains string t β Andrey's word.
It is guaranteed that both words consist of 2Β·n characters "0" and "1".
Output
Print "First", if both players play optimally well and Yaroslav wins. If Andrey wins, print "Second" and if the game ends with a draw, print "Draw". Print the words without the quotes.
Examples
Input
2
0111
0001
Output
First
Input
3
110110
001001
Output
First
Input
3
111000
000111
Output
Draw
Input
4
01010110
00101101
Output
First
Input
4
01100000
10010011
Output
Second
Submitted Solution:
```
import sys
import math
n = int(input())
st1 = input()
st2 = input()
res1 = 0
res2 = 0
k = 0
for i in range(2 * n):
if(st1[i] == '1' and st2[i] == '1'):
k += 1
elif(st1[i] == '1'):
res1 += 1
elif(st2[i] == '1'):
res2 += 1
if(k % 2 != 0):
res1 += 1
if(res1 > res2):
print("First")
elif(res1 < res2):
print("Second")
else:
print("Draw")
```
No
| 95,600 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yaroslav, Andrey and Roman can play cubes for hours and hours. But the game is for three, so when Roman doesn't show up, Yaroslav and Andrey play another game.
Roman leaves a word for each of them. Each word consists of 2Β·n binary characters "0" or "1". After that the players start moving in turns. Yaroslav moves first. During a move, a player must choose an integer from 1 to 2Β·n, which hasn't been chosen by anybody up to that moment. Then the player takes a piece of paper and writes out the corresponding character from his string.
Let's represent Yaroslav's word as s = s1s2... s2n. Similarly, let's represent Andrey's word as t = t1t2... t2n. Then, if Yaroslav choose number k during his move, then he is going to write out character sk on the piece of paper. Similarly, if Andrey choose number r during his move, then he is going to write out character tr on the piece of paper.
The game finishes when no player can make a move. After the game is over, Yaroslav makes some integer from the characters written on his piece of paper (Yaroslav can arrange these characters as he wants). Andrey does the same. The resulting numbers can contain leading zeroes. The person with the largest number wins. If the numbers are equal, the game ends with a draw.
You are given two strings s and t. Determine the outcome of the game provided that Yaroslav and Andrey play optimally well.
Input
The first line contains integer n (1 β€ n β€ 106). The second line contains string s β Yaroslav's word. The third line contains string t β Andrey's word.
It is guaranteed that both words consist of 2Β·n characters "0" and "1".
Output
Print "First", if both players play optimally well and Yaroslav wins. If Andrey wins, print "Second" and if the game ends with a draw, print "Draw". Print the words without the quotes.
Examples
Input
2
0111
0001
Output
First
Input
3
110110
001001
Output
First
Input
3
111000
000111
Output
Draw
Input
4
01010110
00101101
Output
First
Input
4
01100000
10010011
Output
Second
Submitted Solution:
```
import sys
import math
n = int(input())
st1 = input()
st2 = input()
k = 0
res = 0
for i in range(2 * n):
if(st1[i] == '1' and st2[i] == '1'):
k += 1
elif(st1[i] == '1'):
res -= 1
elif(st2[i] == '1'):
res += 1
res1 = int(k / 2) + k % 2
res2 = int(k / 2)
if(res < 0):
b = math.fabs(res)
res1 += int(b / 2)
elif(res > 0):
res2 += int(res / 2)
if(res1 > res2):
print("First")
elif(res1 < res2):
print("Second")
else:
print("Draw")
```
No
| 95,601 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yaroslav, Andrey and Roman can play cubes for hours and hours. But the game is for three, so when Roman doesn't show up, Yaroslav and Andrey play another game.
Roman leaves a word for each of them. Each word consists of 2Β·n binary characters "0" or "1". After that the players start moving in turns. Yaroslav moves first. During a move, a player must choose an integer from 1 to 2Β·n, which hasn't been chosen by anybody up to that moment. Then the player takes a piece of paper and writes out the corresponding character from his string.
Let's represent Yaroslav's word as s = s1s2... s2n. Similarly, let's represent Andrey's word as t = t1t2... t2n. Then, if Yaroslav choose number k during his move, then he is going to write out character sk on the piece of paper. Similarly, if Andrey choose number r during his move, then he is going to write out character tr on the piece of paper.
The game finishes when no player can make a move. After the game is over, Yaroslav makes some integer from the characters written on his piece of paper (Yaroslav can arrange these characters as he wants). Andrey does the same. The resulting numbers can contain leading zeroes. The person with the largest number wins. If the numbers are equal, the game ends with a draw.
You are given two strings s and t. Determine the outcome of the game provided that Yaroslav and Andrey play optimally well.
Input
The first line contains integer n (1 β€ n β€ 106). The second line contains string s β Yaroslav's word. The third line contains string t β Andrey's word.
It is guaranteed that both words consist of 2Β·n characters "0" and "1".
Output
Print "First", if both players play optimally well and Yaroslav wins. If Andrey wins, print "Second" and if the game ends with a draw, print "Draw". Print the words without the quotes.
Examples
Input
2
0111
0001
Output
First
Input
3
110110
001001
Output
First
Input
3
111000
000111
Output
Draw
Input
4
01010110
00101101
Output
First
Input
4
01100000
10010011
Output
Second
Submitted Solution:
```
import sys
n = input()
x = input()
y = input()
k = 0
s = 0
for i in range(len(list(x))):
if x[i] == "1":
k += 1
for i in range(len(list(y))):
if y[i] == "1":
s += 1
if int(x)>int(y) and s != k:
print("First")
if int(x)<int(y) and s != k:
print("Second")
if s == k:
print("Draw")
```
No
| 95,602 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Tags: binary search, data structures, dp
Correct Solution:
```
import sys
input = sys.stdin.readline
I = lambda : list(map(int,input().split()))
def CeilIndex(A, l, r, key):
while (r - l > 1):
m = l + (r - l)//2
if (A[m] >= key):
r = m
else:
l = m
return r
def lis(A, size):
tailTable = [0 for i in range(size + 1)]
len = 0 # always points empty slot
tailTable[0] = A[0]
len = 1
for i in range(1, size):
if (A[i] < tailTable[0]):
tailTable[0] = A[i]
elif (A[i] > tailTable[len-1]):
tailTable[len] = A[i]
len+= 1
else:
tailTable[CeilIndex(tailTable, -1, len-1, A[i])] = A[i]
return len
n,=I()
p=I()
an=1
print(lis(p,n))
```
| 95,603 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Tags: binary search, data structures, dp
Correct Solution:
```
from sys import stdin
input = stdin.readline
class BIT():
def __init__(self, n):
self.n = n
self.tree = [0] * (n + 1)
def sum(self, i):
ans = 0
i += 1
while i > 0:
ans =max(ans, self.tree[i])
i -= (i & (-i))
return ans
def update(self, i, value):
i += 1
while i <= self.n:
self.tree[i] = max(value,self.tree[i])
i += (i & (-i))
def f(a):
newind=0
maxs=0
ans=0
ft=BIT(2*(10**5)+5)
for i in a:
maxs=ft.sum(i-1)
# print(maxs,i)
ft.update(i,maxs+1)
ans=max(ans,maxs+1)
# print(ft.tree)
return ans
a=input()
l=list(map(int,input().strip().split()))
print(f(l))
```
| 95,604 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Tags: binary search, data structures, dp
Correct Solution:
```
import math
import sys
from bisect import bisect_right, bisect_left, insort_right
from collections import Counter, defaultdict
from heapq import heappop, heappush
from itertools import accumulate, permutations, combinations
from sys import stdout
R = lambda: map(int, input().split())
n = int(input())
arr = list(R())
tps = [(0, 0)]
for x in arr:
i = bisect_left(tps, (x, -1)) - 1
tps.insert(i + 1, (x, tps[i][1] + 1))
if i + 2 < len(tps) and tps[i + 1][1] >= tps[i + 2][1]:
del tps[i + 2]
print(max(x[1] for x in tps))
```
| 95,605 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Tags: binary search, data structures, dp
Correct Solution:
```
from bisect import *
s, n = [0], input()
for i in map(int, input().split()):
if i > s[-1]: s.append(i)
else: s[bisect_right(s, i)] = i
print(len(s) - 1)
```
| 95,606 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Tags: binary search, data structures, dp
Correct Solution:
```
from bisect import bisect_left, bisect_right, insort
R = lambda: map(int, input().split())
n, arr = int(input()), list(R())
dp = []
for i in range(n):
idx = bisect_left(dp, arr[i])
if idx >= len(dp):
dp.append(arr[i])
else:
dp[idx] = arr[i]
print(len(dp))
```
| 95,607 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Tags: binary search, data structures, dp
Correct Solution:
```
def CeilIndex(A, l, r, key):
while (r - l > 1):
m = l + (r - l)//2
if (A[m] >= key):
r = m
else:
l = m
return r
def LongestIncreasingSubsequenceLength(A, size):
# Add boundary case,
# when array size is one
tailTable = [0 for i in range(size + 1)]
len = 0 # always points empty slot
tailTable[0] = A[0]
len = 1
for i in range(1, size):
if (A[i] < tailTable[0]):
# new smallest value
tailTable[0] = A[i]
elif (A[i] > tailTable[len-1]):
# A[i] wants to extend
# largest subsequence
tailTable[len] = A[i]
len+= 1
else:
# A[i] wants to be current
# end candidate of an existing
# subsequence. It will replace
# ceil value in tailTable
tailTable[CeilIndex(tailTable, -1, len-1, A[i])] = A[i]
return len
N = int(input())
List = [int(x) for x in input().split()]
print(LongestIncreasingSubsequenceLength(List,N))
```
| 95,608 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Tags: binary search, data structures, dp
Correct Solution:
```
n = int(input())
num_list = list(map(int, input().split()))
# def lower_bound(min_lis, x):
# #goal return the position of the first element >= x
# left = 0
# right = len(min_lis) - 1
# res = -1
# while left <= right:
# mid = (left + right) // 2
# if min_lis[mid] < x:
# left = mid + 1
# else:
# res = mid
# right = mid - 1
# return res
import bisect
def LongestIncreasingSubsequence(a, n):
min_lis = []
#lis = [0 for i in range(n)]
for i in range(n):
pos = bisect.bisect_left(min_lis, a[i])
if pos == len(min_lis):
#lis[i] = len(min_lis) + 1
min_lis.append(a[i])
else:
#lis[i] = pos + 1
min_lis[pos] = a[i]
#print(*min_lis)
return (len(min_lis))
print(LongestIncreasingSubsequence(num_list, n))
```
| 95,609 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Tags: binary search, data structures, dp
Correct Solution:
```
def CeilIndex(A, l, r, key):
while (r - l > 1):
m = l + (r - l)//2
if (A[m] >= key):
r = m
else:
l = m
return r
def LIS(A, size):
tailTable = [0 for i in range(size + 1)]
len = 0
tailTable[0] = A[0]
len = 1
for i in range(1, size):
if (A[i] < tailTable[0]):
tailTable[0] = A[i]
elif (A[i] > tailTable[len-1]):
tailTable[len] = A[i]
len+= 1
else:
tailTable[CeilIndex(tailTable, -1, len-1, A[i])] = A[i]
return len
def main():
n = int(input())
arr = list(map(int,input().split()))
print(LIS(arr,n))
main()
```
| 95,610 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Submitted Solution:
```
# Python program to find
# length of longest
# increasing subsequence
# in O(n Log n) time
# Binary search (note
# boundaries in the caller)
# A[] is ceilIndex
# in the caller
def CeilIndex(A, l, r, key):
while (r - l > 1):
m = l + (r - l)//2
if (A[m] >= key):
r = m
else:
l = m
return r
def Lis(A, size):
# Add boundary case,
# when array size is one
tailTable = [0 for i in range(size + 1)]
len = 0 # always points empty slot
tailTable[0] = A[0]
len = 1
for i in range(1, size):
if (A[i] < tailTable[0]):
# new smallest value
tailTable[0] = A[i]
elif (A[i] > tailTable[len-1]):
# A[i] wants to extend
# largest subsequence
tailTable[len] = A[i]
len+= 1
else:
# A[i] wants to be current
# end candidate of an existing
# subsequence. It will replace
# ceil value in tailTable
tailTable[CeilIndex(tailTable, -1, len-1, A[i])] = A[i]
return len
# Driver program to
# test above function
a=int(input())
z=list(map(int,input().split()))
print(Lis(z,a))
```
Yes
| 95,611 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Submitted Solution:
```
def lis(a):
b = []
for c in a:
# if len(b) == 0 or c > b[-1]
if len(b) == 0 or c > b[-1]:
b.append(c)
else:
l = 0
r = len(b)
while l < r-1:
m = l+r>>1
# if b[m] <= c: l = m
if b[m] < c: l = m
else: r = m
# if b[l] <= c: l += 1
if b[l] < c: l += 1
b[l] = c
return len(b)
n = int(input())
a = list(map(int, input().split()))
print(lis(a))
```
Yes
| 95,612 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Submitted Solution:
```
import sys,math as mt
import heapq as hp
import collections as cc
import math as mt
import itertools as it
input=sys.stdin.readline
I=lambda:list(map(int,input().split()))
def CeilIndex(A, l, r, key):
while (r - l > 1):
m = l + (r - l)//2
if (A[m] >= key):
r = m
else:
l = m
return r
def lis(A, size):
tailTable = [0 for i in range(size + 1)]
len = 0
tailTable[0] = A[0]
len = 1
for i in range(1, size):
if (A[i] < tailTable[0]):
tailTable[0] = A[i]
elif (A[i] > tailTable[len-1]):
tailTable[len] = A[i]
len+= 1
else:
tailTable[CeilIndex(tailTable, -1, len-1, A[i])] = A[i]
return len
n,=I()
l=I()
print(lis(l,n))
```
Yes
| 95,613 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Submitted Solution:
```
n=int(input())
a=list(map(lambda x: int(x), input().split()))
def CeilIndex(A, l, r, key):
while (r - l > 1):
m = l + (r - l) // 2
if (A[m] >= key):
r = m
else:
l = m
return r
def LongestIncreasingSubsequenceLength(A, size):
# Add boundary case,
# when array size is one
tailTable = [0 for i in range(size + 1)]
len = 0 # always points empty slot
tailTable[0] = A[0]
len = 1
for i in range(1, size):
if (A[i] < tailTable[0]):
# new smallest value
tailTable[0] = A[i]
elif (A[i] > tailTable[len - 1]):
# A[i] wants to extend
# largest subsequence
tailTable[len] = A[i]
len += 1
else:
# A[i] wants to be current
# end candidate of an existing
# subsequence. It will replace
# ceil value in tailTable
tailTable[CeilIndex(tailTable, -1, len - 1, A[i])] = A[i]
return len
print(LongestIncreasingSubsequenceLength(a,len(a)))
```
Yes
| 95,614 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Submitted Solution:
```
s, n = [0], input()
for i in map(int, input().split()):
if i > s[-1]: s.append(i)
else: s[-1] = i
print(len(s) - 1)
```
No
| 95,615 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Submitted Solution:
```
from collections import defaultdict
class UnionFind():
def __init__(self, n):
self.n = n
self.parents = [-1] * n
def find(self, x):
if self.parents[x] < 0:
return x
else:
self.parents[x] = self.find(self.parents[x])
return self.parents[x]
def union(self, x, y):
x = self.find(x)
y = self.find(y)
if x == y:
return
if self.parents[x] > self.parents[y]:
x, y = y, x
self.parents[x] += self.parents[y]
self.parents[y] = x
def size(self, x):
return -self.parents[self.find(x)]
def same(self, x, y):
return self.find(x) == self.find(y)
def members(self, x):
root = self.find(x)
return [i for i in range(self.n) if self.find(i) == root]
def roots(self):
return [i for i, x in enumerate(self.parents) if x < 0]
def group_count(self):
return len(self.roots())
def all_group_members(self):
group_members = defaultdict(list)
for member in range(self.n):
group_members[self.find(member)].append(member)
return group_members
n=int(input())
a=list(map(int,input().split()))
uf=UnionFind(n)
for i in range(n-1):
if a[i]>a[i+1]:
uf.union(a[i]-1,a[i+1]-1)
ans=0
for p in uf.roots():
ans=max(ans,uf.size(p))
print(ans)
```
No
| 95,616 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Submitted Solution:
```
n = int(input())
num_list = list(map(int, input().split()))
def lower_bound(min_lis, x):
#goal return the position of the first element >= x
left = 0
right = len(min_lis) - 1
res = -1
while left <= right:
mid = (left + right) // 2
if min_lis[mid] < x:
left = mid + 1
else:
res = mid
right = mid - 1
return res
def LongestIncreasingSubsequence(a, n):
min_lis = []
#lis = [0 for i in range(n)]
for i in range(n-1, -1, -1):
pos = lower_bound(min_lis, a[i])
if pos == -1:
#lis[i] = len(min_lis) + 1
min_lis.append(a[i])
else:
#lis[i] = pos + 1
min_lis[pos] = a[i]
return (len(min_lis))
print(LongestIncreasingSubsequence(num_list, n))
```
No
| 95,617 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).
procedure bubbleSortGraph()
build a graph G with n vertices and 0 edges
repeat
swapped = false
for i = 1 to n - 1 inclusive do:
if a[i] > a[i + 1] then
add an undirected edge in G between a[i] and a[i + 1]
swap( a[i], a[i + 1] )
swapped = true
end if
end for
until not swapped
/* repeat the algorithm as long as swapped value is true. */
end procedure
For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.
Input
The first line of the input contains an integer n (2 β€ n β€ 105). The next line contains n distinct integers a1, a2, ..., an (1 β€ ai β€ n).
Output
Output a single integer β the answer to the problem.
Examples
Input
3
3 1 2
Output
2
Note
Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
Submitted Solution:
```
N = int(input())
List = [int(x) for x in input().split()]
MinPre = [0] * N
Min = List[0]
index = 0
for i in range(1,N):
if(Min>List[i]):
index = i
Min = List[i]
MinPre[i] = index
Ans = [1] * N
for i in range(N):
if(MinPre[i] == i):
continue
else:
Ans[i] = Ans[MinPre[i]] + 1
print(max(Ans))
```
No
| 95,618 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Tags: combinatorics, data structures, implementation
Correct Solution:
```
import sys
from math import log2,floor,ceil,sqrt
# import bisect
# from collections import deque
Ri = lambda : [int(x) for x in sys.stdin.readline().split()]
ri = lambda : sys.stdin.readline().strip()
def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
INF = 10 ** 18
MOD = 10**9+7
a = int(ri())
st= ri()
arr = [int(i) for i in st]
dic = {}
cnt = 0
nz = 0
for i in range(len(st)):
summ = 0
for j in range(i,len(st)):
summ+=arr[j]
if summ != 0:
nz+=1
if summ in dic:
dic[summ]+=1
else:
dic[summ] = 1
if a!= 0:
for i in dic:
if i != 0:
val = a/i
if val in dic:
cnt = cnt + dic[val]*dic[i]
print(cnt)
else:
n = len(st)
print(n**2*(n+1)**2//4 - nz*nz)
```
| 95,619 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Tags: combinatorics, data structures, implementation
Correct Solution:
```
from math import *
#from bisect import *
#from collections import *
#from random import *
#from decimal import *"""
#from heapq import *
#from random import *
import sys
input=sys.stdin.readline
#sys.setrecursionlimit(3*(10**5))
global flag
def inp():
return int(input())
def st():
return input().rstrip('\n')
def lis():
return list(map(int,input().split()))
def ma():
return map(int,input().split())
t=1
def pos(su,le):
if(su>=0 and su<=(9*le)):
return 1
return 0
while(t):
t-=1
a=inp()
s=st()
di={}
for i in range(len(s)):
su=0
for j in range(i,len(s)):
su+=int(s[j])
try:
di[su]+=1
except:
di[su]=1
co=0
for i in di.keys():
if(a==0 and i==0):
co+=di[0]*(len(s)*(len(s)+1))
co-=(di[0]*di[0])
if(i and a%i==0 and (a//i) in di and a):
co+=di[i]*di[a//i]
print(co)
```
| 95,620 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Tags: combinatorics, data structures, implementation
Correct 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
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 sieve():
li=[True]*(2*(10**5)+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=[]
for i in range((2*(10**5)+5)):
if li[i]==True:
prime.append(i)
return prime
def setBit(n):
count=0
while n!=0:
n=n&(n-1)
count+=1
return count
mx=10**7
spf=[mx]*(mx+1)
def SPF():
spf[1]=1
for i in range(2,mx+1):
if spf[i]==mx:
spf[i]=i
for j in range(i*i,mx+1,i):
if i<spf[j]:
spf[j]=i
return
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
#####################################################################################
mod=10**9+7
def solve():
a=II()
s=input()
li=[int(i) for i in s]
n=len(li)
pref=[li[0]]+[0]*(n-1)
for i in range(1,n):
pref[i]=pref[i-1]+li[i]
pref.insert(0,0)
d={}
for i in range(1,n+1):
for j in range(i,n+1):
val=pref[j]-pref[i-1]
d[val]=d.get(val,0)+1
ans=0
if a!=0:
for ele in d:
if ele!=0:
if a%ele==0 and a//ele in d:
ans+=d[ele]*d[a//ele]
else:
cnt=d.get(0,0)
ans=2*cnt*((n*(n+1))//2)-cnt**2
P(ans)
return
t=1
for i in range(t):
solve()
#######
#
#
####### # # # #### # # #
# # # # # # # # # # #
# #### # # #### #### # #
###### # # #### # # # # #
```
| 95,621 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Tags: combinatorics, data structures, implementation
Correct Solution:
```
import sys,collections as cc
input = sys.stdin.readline
I = lambda : list(map(int,input().split()))
a,=I()
s=list(map(int,[i for i in input().strip()]))
d=cc.Counter([])
n=len(s)
for i in range(1,n+1):
su=sum(s[:i])
for j in range(i,n):
d[su]+=1
su=su-s[j-i]+s[j]
d[su]+=1
an=0
if a==0:
an=(n*(n+1)//2)**2
del d[0]
xx=sum(d.values())
for i in d:
an-=d[i]*(xx)
else:
for i in d.keys():
if i!=0 and a%i==0:
an=an+(d[i]*d[a//i])
print(an)
```
| 95,622 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Tags: combinatorics, data structures, implementation
Correct Solution:
```
import sys
from math import gcd,sqrt,ceil,log2
from collections import defaultdict,Counter,deque
from bisect import bisect_left,bisect_right
import math
sys.setrecursionlimit(2*10**5+10)
import heapq
from itertools import permutations
# input=sys.stdin.readline
# def print(x):
# sys.stdout.write(str(x)+"\n")
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
aa='abcdefghijklmnopqrstuvwxyz'
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")
# import sys
# import io, os
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def get_sum(bit,i):
s = 0
i+=1
while i>0:
s+=bit[i]
i-=i&(-i)
return s
def update(bit,n,i,v):
i+=1
while i<=n:
bit[i]+=v
i+=i&(-i)
def modInverse(b,m):
g = math.gcd(b, m)
if (g != 1):
return -1
else:
return pow(b, m - 2, m)
def primeFactors(n):
sa = []
# sa.add(n)
while n % 2 == 0:
sa.append(2)
n = n // 2
for i in range(3,int(math.sqrt(n))+1,2):
while n % i== 0:
sa.append(i)
n = n // i
# sa.add(n)
if n > 2:
sa.append(n)
return sa
def seive(n):
pri = [True]*(n+1)
p = 2
while p*p<=n:
if pri[p] == True:
for i in range(p*p,n+1,p):
pri[i] = False
p+=1
return pri
def check_prim(n):
if n<0:
return False
for i in range(2,int(sqrt(n))+1):
if n%i == 0:
return False
return True
def getZarr(string, z):
n = len(string)
# [L,R] make a window which matches
# with prefix of s
l, r, k = 0, 0, 0
for i in range(1, n):
# if i>R nothing matches so we will calculate.
# Z[i] using naive way.
if i > r:
l, r = i, i
# R-L = 0 in starting, so it will start
# checking from 0'th index. For example,
# for "ababab" and i = 1, the value of R
# remains 0 and Z[i] becomes 0. For string
# "aaaaaa" and i = 1, Z[i] and R become 5
while r < n and string[r - l] == string[r]:
r += 1
z[i] = r - l
r -= 1
else:
# k = i-L so k corresponds to number which
# matches in [L,R] interval.
k = i - l
# if Z[k] is less than remaining interval
# then Z[i] will be equal to Z[k].
# For example, str = "ababab", i = 3, R = 5
# and L = 2
if z[k] < r - i + 1:
z[i] = z[k]
# For example str = "aaaaaa" and i = 2,
# R is 5, L is 0
else:
# else start from R and check manually
l = i
while r < n and string[r - l] == string[r]:
r += 1
z[i] = r - l
r -= 1
def search(text, pattern):
# Create concatenated string "P$T"
concat = pattern + "$" + text
l = len(concat)
z = [0] * l
getZarr(concat, z)
ha = []
for i in range(l):
if z[i] == len(pattern):
ha.append(i - len(pattern) - 1)
return ha
# n,k = map(int,input().split())
# l = list(map(int,input().split()))
#
# n = int(input())
# l = list(map(int,input().split()))
#
# hash = defaultdict(list)
# la = []
#
# for i in range(n):
# la.append([l[i],i+1])
#
# la.sort(key = lambda x: (x[0],-x[1]))
# ans = []
# r = n
# flag = 0
# lo = []
# ha = [i for i in range(n,0,-1)]
# yo = []
# for a,b in la:
#
# if a == 1:
# ans.append([r,b])
# # hash[(1,1)].append([b,r])
# lo.append((r,b))
# ha.pop(0)
# yo.append([r,b])
# r-=1
#
# elif a == 2:
# # print(yo,lo)
# # print(hash[1,1])
# if lo == []:
# flag = 1
# break
# c,d = lo.pop(0)
# yo.pop(0)
# if b>=d:
# flag = 1
# break
# ans.append([c,b])
# yo.append([c,b])
#
#
#
# elif a == 3:
#
# if yo == []:
# flag = 1
# break
# c,d = yo.pop(0)
# if b>=d:
# flag = 1
# break
# if ha == []:
# flag = 1
# break
#
# ka = ha.pop(0)
#
# ans.append([ka,b])
# ans.append([ka,d])
# yo.append([ka,b])
#
# if flag:
# print(-1)
# else:
# print(len(ans))
# for a,b in ans:
# print(a,b)
def mergeIntervals(arr):
# Sorting based on the increasing order
# of the start intervals
arr.sort(key = lambda x: x[0])
# array to hold the merged intervals
m = []
s = -10000
max = -100000
for i in range(len(arr)):
a = arr[i]
if a[0] > max:
if i != 0:
m.append([s,max])
max = a[1]
s = a[0]
else:
if a[1] >= max:
max = a[1]
#'max' value gives the last point of
# that particular interval
# 's' gives the starting point of that interval
# 'm' array contains the list of all merged intervals
if max != -100000 and [s, max] not in m:
m.append([s, max])
return m
class SortedList:
def __init__(self, iterable=[], _load=200):
"""Initialize sorted list instance."""
values = sorted(iterable)
self._len = _len = len(values)
self._load = _load
self._lists = _lists = [values[i:i + _load] for i in range(0, _len, _load)]
self._list_lens = [len(_list) for _list in _lists]
self._mins = [_list[0] for _list in _lists]
self._fen_tree = []
self._rebuild = True
def _fen_build(self):
"""Build a fenwick tree instance."""
self._fen_tree[:] = self._list_lens
_fen_tree = self._fen_tree
for i in range(len(_fen_tree)):
if i | i + 1 < len(_fen_tree):
_fen_tree[i | i + 1] += _fen_tree[i]
self._rebuild = False
def _fen_update(self, index, value):
"""Update `fen_tree[index] += value`."""
if not self._rebuild:
_fen_tree = self._fen_tree
while index < len(_fen_tree):
_fen_tree[index] += value
index |= index + 1
def _fen_query(self, end):
"""Return `sum(_fen_tree[:end])`."""
if self._rebuild:
self._fen_build()
_fen_tree = self._fen_tree
x = 0
while end:
x += _fen_tree[end - 1]
end &= end - 1
return x
def _fen_findkth(self, k):
"""Return a pair of (the largest `idx` such that `sum(_fen_tree[:idx]) <= k`, `k - sum(_fen_tree[:idx])`)."""
_list_lens = self._list_lens
if k < _list_lens[0]:
return 0, k
if k >= self._len - _list_lens[-1]:
return len(_list_lens) - 1, k + _list_lens[-1] - self._len
if self._rebuild:
self._fen_build()
_fen_tree = self._fen_tree
idx = -1
for d in reversed(range(len(_fen_tree).bit_length())):
right_idx = idx + (1 << d)
if right_idx < len(_fen_tree) and k >= _fen_tree[right_idx]:
idx = right_idx
k -= _fen_tree[idx]
return idx + 1, k
def _delete(self, pos, idx):
"""Delete value at the given `(pos, idx)`."""
_lists = self._lists
_mins = self._mins
_list_lens = self._list_lens
self._len -= 1
self._fen_update(pos, -1)
del _lists[pos][idx]
_list_lens[pos] -= 1
if _list_lens[pos]:
_mins[pos] = _lists[pos][0]
else:
del _lists[pos]
del _list_lens[pos]
del _mins[pos]
self._rebuild = True
def _loc_left(self, value):
"""Return an index pair that corresponds to the first position of `value` in the sorted list."""
if not self._len:
return 0, 0
_lists = self._lists
_mins = self._mins
lo, pos = -1, len(_lists) - 1
while lo + 1 < pos:
mi = (lo + pos) >> 1
if value <= _mins[mi]:
pos = mi
else:
lo = mi
if pos and value <= _lists[pos - 1][-1]:
pos -= 1
_list = _lists[pos]
lo, idx = -1, len(_list)
while lo + 1 < idx:
mi = (lo + idx) >> 1
if value <= _list[mi]:
idx = mi
else:
lo = mi
return pos, idx
def _loc_right(self, value):
"""Return an index pair that corresponds to the last position of `value` in the sorted list."""
if not self._len:
return 0, 0
_lists = self._lists
_mins = self._mins
pos, hi = 0, len(_lists)
while pos + 1 < hi:
mi = (pos + hi) >> 1
if value < _mins[mi]:
hi = mi
else:
pos = mi
_list = _lists[pos]
lo, idx = -1, len(_list)
while lo + 1 < idx:
mi = (lo + idx) >> 1
if value < _list[mi]:
idx = mi
else:
lo = mi
return pos, idx
def add(self, value):
"""Add `value` to sorted list."""
_load = self._load
_lists = self._lists
_mins = self._mins
_list_lens = self._list_lens
self._len += 1
if _lists:
pos, idx = self._loc_right(value)
self._fen_update(pos, 1)
_list = _lists[pos]
_list.insert(idx, value)
_list_lens[pos] += 1
_mins[pos] = _list[0]
if _load + _load < len(_list):
_lists.insert(pos + 1, _list[_load:])
_list_lens.insert(pos + 1, len(_list) - _load)
_mins.insert(pos + 1, _list[_load])
_list_lens[pos] = _load
del _list[_load:]
self._rebuild = True
else:
_lists.append([value])
_mins.append(value)
_list_lens.append(1)
self._rebuild = True
def discard(self, value):
"""Remove `value` from sorted list if it is a member."""
_lists = self._lists
if _lists:
pos, idx = self._loc_right(value)
if idx and _lists[pos][idx - 1] == value:
self._delete(pos, idx - 1)
def remove(self, value):
"""Remove `value` from sorted list; `value` must be a member."""
_len = self._len
self.discard(value)
if _len == self._len:
raise ValueError('{0!r} not in list'.format(value))
def pop(self, index=-1):
"""Remove and return value at `index` in sorted list."""
pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
value = self._lists[pos][idx]
self._delete(pos, idx)
return value
def bisect_left(self, value):
"""Return the first index to insert `value` in the sorted list."""
pos, idx = self._loc_left(value)
return self._fen_query(pos) + idx
def bisect_right(self, value):
"""Return the last index to insert `value` in the sorted list."""
pos, idx = self._loc_right(value)
return self._fen_query(pos) + idx
def count(self, value):
"""Return number of occurrences of `value` in the sorted list."""
return self.bisect_right(value) - self.bisect_left(value)
def __len__(self):
"""Return the size of the sorted list."""
return self._len
def __getitem__(self, index):
"""Lookup value at `index` in sorted list."""
pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
return self._lists[pos][idx]
def __delitem__(self, index):
"""Remove value at `index` from sorted list."""
pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
self._delete(pos, idx)
def __contains__(self, value):
"""Return true if `value` is an element of the sorted list."""
_lists = self._lists
if _lists:
pos, idx = self._loc_left(value)
return idx < len(_lists[pos]) and _lists[pos][idx] == value
return False
def __iter__(self):
"""Return an iterator over the sorted list."""
return (value for _list in self._lists for value in _list)
def __reversed__(self):
"""Return a reverse iterator over the sorted list."""
return (value for _list in reversed(self._lists) for value in reversed(_list))
def __repr__(self):
"""Return string representation of sorted list."""
return 'SortedList({0})'.format(list(self))
def ncr(n, r, p):
num = den = 1
for i in range(r):
num = (num * (n - i)) % p
den = (den * (i + 1)) % p
return (num * pow(den,
p - 2, p)) % p
def sol(n):
seti = set()
for i in range(1,int(sqrt(n))+1):
if n%i == 0:
seti.add(n//i)
seti.add(i)
return seti
def lcm(a,b):
return (a*b)//gcd(a,b)
#
# n,p = map(int,input().split())
#
# s = input()
#
# if n <=2:
# if n == 1:
# pass
# if n == 2:
# pass
# i = n-1
# idx = -1
# while i>=0:
# z = ord(s[i])-96
# k = chr(z+1+96)
# flag = 1
# if i-1>=0:
# if s[i-1]!=k:
# flag+=1
# else:
# flag+=1
# if i-2>=0:
# if s[i-2]!=k:
# flag+=1
# else:
# flag+=1
# if flag == 2:
# idx = i
# s[i] = k
# break
# if idx == -1:
# print('NO')
# exit()
# for i in range(idx+1,n):
# if
#
def moore_voting(l):
count1 = 0
count2 = 0
first = 10**18
second = 10**18
n = len(l)
for i in range(n):
if l[i] == first:
count1+=1
elif l[i] == second:
count2+=1
elif count1 == 0:
count1+=1
first = l[i]
elif count2 == 0:
count2+=1
second = l[i]
else:
count1-=1
count2-=1
for i in range(n):
if l[i] == first:
count1+=1
elif l[i] == second:
count2+=1
if count1>n//3:
return first
if count2>n//3:
return second
return -1
def dijkstra(n,tot,hash):
hea = [[0,n]]
dis = [10**18]*(tot+1)
dis[n] = 0
boo = defaultdict(bool)
while hea:
a,b = heapq.heappop(hea)
if boo[b]:
continue
boo[b] = True
for i,w in hash[b]:
if dis[b]+w<dis[i]:
dis[i] = dis[b]+w
heapq.heappush(hea,[dis[i],i])
return dis
def find_parent(u,parent):
if u!=parent[u]:
parent[u] = find_parent(parent[u],parent)
return parent[u]
def dis_union(n):
par = [i for i in range(n+1)]
rank = [1]*(n+1)
k = int(input())
for i in range(k):
a,b = map(int,input().split())
z1,z2 = find_parent(a,par),find_parent(b,par)
if z1!=z2:
par[z1] = z2
rank[z2]+=rank[z1]
a = int(input())
l = list(input())
n = int(len(l))
hash = defaultdict(int)
for i in range(n):
tot = 0
for j in range(i,n):
tot+=int(l[j])
hash[tot]+=1
ans = 0
if a == 0:
ans+=hash[0]*hash[0]
for i in hash:
if not i:
continue
ans+=hash[0]*hash[i]*2
print(ans)
exit()
for i in hash:
if i and a%i == 0 and a//i in hash:
ans+=hash[a//i]*hash[i]
print(ans)
```
| 95,623 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Tags: combinatorics, data structures, implementation
Correct Solution:
```
from collections import Counter
a=int(input())
string=input()
arr=[0]
count1=0
count2=0
for i in range(len(string)):
arr+=[int(string[i])]
for i in range(1,len(arr)):
arr[i]+=arr[i-1]
#print(arr)
temparr=[]
#sumset.add(arr[0])
for i in range(len(arr)):
for j in range(i+1,len(arr)):
temparr+=[(arr[j]-arr[i])]
sumset=Counter(temparr)
#print(sumset)
possums=0
for i in (sumset):
possums+=sumset[i]
for i in (sumset):
#print(str(i)+"###")
if i!=0 and a%i==0 and i**2!=a:
count1+=sumset[i]*sumset[a//i]
elif i==0 and a==0:
count1+=sumset[i]*possums
elif i!=0 and a%i==0 and i**2==a:
#print(str(i)+"***")
count2+=sumset[i]*sumset[a//i]
print(count1+count2)
```
| 95,624 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Tags: combinatorics, data structures, implementation
Correct Solution:
```
sm = [0] * 40000
n = int(input())
s = input()
l = len(s)
for i in range(l):
ss = 0
for j in range(i,l):
ss += int(s[j])
sm[ss] += 1
if n == 0:
ans = 0
for i in range(1,40000):
ans += sm[0] * sm[i] * 2
ans += sm[0]*sm[0]
print(ans)
else:
ans = 0
u = int(n**.5)
for i in range(1,u+1):
if n % i == 0:
if n // i < 40000:
ans += sm[i] * sm[n//i]
ans *= 2
if u ** 2 == n:
ans -= sm[u] ** 2
print(ans)
```
| 95,625 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Tags: combinatorics, data structures, implementation
Correct Solution:
```
a=int(input())
s=input()
di = {}
for i in range(len(s)):
total=0
for j in range(i, len(s)):
total += int(s[j])
di[total] = 1 if total not in di else di[total]+1
ans=0
if a==0:
ans=0
if 0 in di:
ans +=di[0]*di[0]
for each in di:
if not each:continue
ans += di[each]*di[0]*2
print(ans)
quit()
for p in di:
if p and a % p == 0 and (a//p) in di:
ans += di[a//p]*di[p]
print(ans)
```
| 95,626 |
Provide tags and a correct Python 2 solution for this coding contest problem.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Tags: combinatorics, data structures, implementation
Correct Solution:
```
from sys import stdin, stdout
from collections import Counter, defaultdict
from itertools import permutations, combinations
raw_input = stdin.readline
pr = stdout.write
def in_num():
return int(raw_input())
def in_arr():
return map(int,raw_input().strip())
def pr_num(n):
stdout.write(str(n)+'\n')
def pr_arr(arr):
pr(' '.join(map(str,arr))+'\n')
# fast read function for total integer input
def inp():
# this function returns whole input of
# space/line seperated integers
# Use Ctrl+D to flush stdin.
return map(int,stdin.read().split())
range = xrange # not for python 3.0+
# main code
a=input()
l=in_arr()
n=len(l)
dp=[0]*(n+1)
for i in range(1,n+1):
dp[i]=dp[i-1]+l[i-1]
d=Counter()
for i in range(n+1):
for j in range(i+1,n+1):
d[dp[j]-dp[i]]+=1
ans=0
if a==0:
ans = ((n*(n+1))/2)*d[0]
#exit()
#ans=0
for i in d:
if i!=0 and a%i==0:
ans+=(d[i]*d[a/i])
pr_num(ans)
```
| 95,627 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Submitted Solution:
```
from collections import defaultdict
a=int(input())
s=list(input())
n=len(s)
for i in range(n):
s[i]=int(s[i])
cs=[0]+s
for i in range(1,n+1):
cs[i]+=cs[i-1]
cnt=defaultdict(int)
key=set()
for l in range(1,n+1):
for r in range(l,n+1):
cnt[cs[r]-cs[l-1]]+=1
key.add(cs[r]-cs[l-1])
if a==0:
if 0 in cnt:
y=n*(n+1)//2
print(y*cnt[0]+cnt[0]*(y-cnt[0]))
else:
print(0)
exit()
ans=0
for x in key:
if x>0 and a%x==0 and a//x in key:
ans+=cnt[x]*cnt[a//x]
print(ans)
```
Yes
| 95,628 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Submitted Solution:
```
def divisors(x):
def f(y, q):
t = -len(r)
while not y % q:
y //= q
for i in range(t, 0):
r.append(r[t] * q)
return y
r, p = [1], 7
x = f(f(f(x, 2), 3), 5)
while x >= p * p:
for s in 4, 2, 4, 2, 4, 6, 2, 6:
if not x % p:
x = f(x, p)
p += s
if x > 1:
f(x, x)
return r
def main():
a, s = int(input()), input()
if not a:
z = sum(x * (x + 1) for x in map(len, s.translate(
str.maketrans('123456789', ' ')).split())) // 2
x = len(s)
print((x * (x + 1) - z) * z)
return
sums, x, cnt = {}, 0, 1
for u in map(int, s):
if u:
sums[x] = cnt
x += u
cnt = 1
else:
cnt += 1
if x * x < a:
print(0)
return
sums[x], u = cnt, a // x
l = [v for v in divisors(a) if v <= x]
z = a // max(l)
d = {x: 0 for x in l if z <= x}
for x in d:
for k, v in sums.items():
u = sums.get(k + x, 0)
if u:
d[x] += v * u
print(sum(u * d[a // x] for x, u in d.items()))
if __name__ == '__main__':
main()
```
Yes
| 95,629 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Submitted Solution:
```
def f(t, k):
i, j = 0, 1
s, d = 0, t[0]
n = len(t)
while j <= n:
if d > k:
d -= t[i]
i += 1
elif d == k:
if t[i] and (j == n or t[j]): s += 1
else:
a, b = i - 1, j - 1
while j < n and t[j] == 0: j += 1
while t[i] == 0: i += 1
s += (i - a) * (j - b)
if j < n: d += t[j]
d -= t[i]
i += 1
j += 1
else:
if j < n: d += t[j]
j += 1
return s
s, n = 0, int(input())
t = list(map(int, input()))
if n:
k = sum(t)
if k == 0: print(0)
else:
p = [(i, n // i) for i in range(max(1, n // k), int(n ** 0.5) + 1) if n % i == 0]
for a, b in p:
if a != b: s += 2 * f(t, a) * f(t, b)
else:
k = f(t, a)
s += k * k
print(s)
else:
n = len(t)
m = n * (n + 1)
s = j = 0
while j < n:
if t[j] == 0:
i = j
j += 1
while j < n and t[j] == 0: j += 1
k = ((j - i) * (j - i + 1)) // 2
s += k
j += 1
print((m - s) * s)
```
Yes
| 95,630 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Submitted Solution:
```
import sys
import itertools as it
import bisect as bi
import math as mt
import collections as cc
import sys
I=lambda:list(map(int,input().split()))
a,=I()
s=list(input().strip())
n=len(s)
s=[int(s[i]) for i in range(len(s))]
f=cc.defaultdict(int)
for i in range(n):
tem=0
for j in range(i,n):
tem+=s[j]
f[tem]+=1
temp=list(f.keys())
if a==0:
tot=n*(n+1)//2
tot=tot**2
if f[0]:
del f[0]
tem=sum(f.values())
for i in f:
tot-=(tem*f[i])
print(tot)
else:
ans=0
for i in temp:
if i!=0:
if a%i==0:
j=a//i
if f[i]>0 and f[j]>0:
ans+=f[i]*f[j]
print(ans)
```
Yes
| 95,631 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Submitted Solution:
```
def f(t, k):
i, j = 0, 1
s, d = 0, t[0]
n = len(t)
while j <= n:
if d > k:
d -= t[i]
i += 1
elif d == k:
if t[i] and (j == n or t[j]): s += 1
else:
a, b = i - 1, j - 1
while j < n and t[j] == 0: j += 1
while t[i] == 0: i += 1
s += (i - a) * (j - b)
if j < n: d += t[j]
d -= t[i]
i += 1
j += 1
else:
if j < n: d += t[j]
j += 1
return s
s, n = 0, int(input())
t = list(map(int, input()))
if n:
k = sum(t)
if k == 0: print(0)
else:
p = [(i, n // i) for i in range(max(1, n // k), int(n ** 0.5) + 1) if n % i == 0]
for a, b in p:
if a != b: s += 2 * f(t, a) * f(t, b)
else:
k = f(t, a)
s += k * k
print(s)
else:
n = len(t)
m = n * (n + 1)
s = j = 0
while j < n:
if t[j] == 0:
i = j
j += 1
while j < n and t[j] == 0: j += 1
k = ((j - i) * (j - i + 1)) // 2
s += (m - k) * k
j += 1
print(s)
```
No
| 95,632 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Submitted Solution:
```
a = int(input())
s = input()
if a == 0:
c = []
t = 0
for i in range(len(s)):
if s[i] == '0':
t += 1
else:
if t != 0:
c.append(t)
t = 0
if t != 0:
c.append(t)
r = 1
for f in c:
r *= (f*(f+1))//2
print(r)
else:
sm ={}
for i in range(len(s)):
for j in range(i,len(s)):
if j== i:
t = int(s[j])
else:
t += int(s[j])
if t in sm:
sm[t] += 1
else:
sm[t] = 1
c = 0
for f in sm:
if f != 0 and a % f == 0 and (a//f) in sm:
c += sm[f] * sm[a//f]
print(c)
```
No
| 95,633 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Submitted Solution:
```
a=int(input())
b=[int(i) for i in input()]+[0]
n=len(b)-1
f=0
for k in range(1,int(a**0.5)+1):
if a%k==0:
d=e=0
i,j=0,-1
c=0
while j<n:
if c<k:
j+=1
c+=b[j]
elif c==k:
d+=1
j+=1
c+=b[j]
else:
c-=b[i]
i+=1
i,j=0,-1
c=0
while j<n:
if c<a//k:
j+=1
c+=b[j]
elif c==a//k:
e+=1
j+=1
c+=b[j]
else:
c-=b[i]
i+=1
f+=d*e
if k!=a//k:
f+=d*e
print(f)
```
No
| 95,634 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a string of decimal digits s. Let's define bij = siΒ·sj. Find in matrix b the number of such rectangles that the sum bij for all cells (i, j) that are the elements of the rectangle equals a in each rectangle.
A rectangle in a matrix is a group of four integers (x, y, z, t) (x β€ y, z β€ t). The elements of the rectangle are all cells (i, j) such that x β€ i β€ y, z β€ j β€ t.
Input
The first line contains integer a (0 β€ a β€ 109), the second line contains a string of decimal integers s (1 β€ |s| β€ 4000).
Output
Print a single integer β the answer to a problem.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
10
12345
Output
6
Input
16
439873893693495623498263984765
Output
40
Submitted Solution:
```
from math import *
#from bisect import *
#from collections import *
#from random import *
#from decimal import *"""
#from heapq import *
#from random import *
import sys
input=sys.stdin.readline
#sys.setrecursionlimit(3*(10**5))
global flag
def inp():
return int(input())
def st():
return input().rstrip('\n')
def lis():
return list(map(int,input().split()))
def ma():
return map(int,input().split())
t=1
def pos(su,le):
if(su>=0 and su<=(9*le)):
return 1
return 0
while(t):
t-=1
a=inp()
s=st()
di={}
for i in range(len(s)):
su=0
for j in range(i,len(s)):
su+=int(s[j])
try:
di[su]+=1
except:
di[su]=1
co=0
for i in di.keys():
if(a==0 and i==0):
co+=di[0]*((len(s)*(len(s)+1))//2)*2
co-=di[0]*di[0]
if(i and a%i==0 and (a//i) in di and a):
co+=di[i]*di[a//i]
if(a==0):
if(0 in di):
co+=(di[0]*di[0] -1 )//2
print(co)
```
No
| 95,635 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
George is a cat, so he loves playing very much.
Vitaly put n cards in a row in front of George. Each card has one integer written on it. All cards had distinct numbers written on them. Let's number the cards from the left to the right with integers from 1 to n. Then the i-th card from the left contains number pi (1 β€ pi β€ n).
Vitaly wants the row to have exactly k cards left. He also wants the i-th card from left to have number bi written on it. Vitaly gave a task to George, to get the required sequence of cards using the remove operation n - k times.
In one remove operation George can choose w (1 β€ w; w is not greater than the current number of cards in the row) contiguous cards (contiguous subsegment of cards). Let's denote the numbers written on these card as x1, x2, ..., xw (from the left to the right). After that, George can remove the card xi, such that xi β€ xj for each j (1 β€ j β€ w). After the described operation George gets w pieces of sausage.
George wondered: what maximum number of pieces of sausage will he get in total if he reaches his goal and acts optimally well? Help George, find an answer to his question!
Input
The first line contains integers n and k (1 β€ k β€ n β€ 106) β the initial and the final number of cards.
The second line contains n distinct space-separated integers p1, p2, ..., pn (1 β€ pi β€ n) β the initial row of cards.
The third line contains k space-separated integers b1, b2, ..., bk β the row of cards that you need to get. It is guaranteed that it's possible to obtain the given row by using the remove operation for n - k times.
Output
Print a single integer β the maximum number of pieces of sausage that George can get if he acts optimally well.
Examples
Input
3 2
2 1 3
1 3
Output
1
Input
10 5
1 2 3 4 5 6 7 8 9 10
2 4 6 8 10
Output
30
Submitted Solution:
```
__author__ = 'allen'
n, k = (int(x) for x in (input().split(" ")))
p = [int(x) for x in (input().split(" "))]
b = [int(x) for x in (input().split(" "))]
r = list(set(p)-set(b))
r.sort()
r.append(-1)
ps = [(i, p[i]) for i in range(len(p))]
def second(inp):
return inp[1]
ps.sort(key=second)
position = [-1, n]
def bin_find(pos, i, j, k):
m = i+(j-i)//2
if i > j:
return i
if pos[m] == k or i == j:
return m
elif k < pos[m]:
return bin_find(pos, i, m-1, k)
elif k > pos[m]:
return bin_find(pos, m+1, j, k)
def find_pie(pos, i):
m = bin_find(pos, 0, len(pos)-1, i)
if i > pos[m]:
pos.insert(m+1, i)
return pos[m+2]-pos[m]-1
else:
pos.insert(m, i)
return pos[m+1]-pos[m-1]-1
it_b = 0
s = 0
for it_p in range(n):
if r[it_b] == ps[it_p][1]:
it_b += 1
s += find_pie(position, ps[it_p][0])
else:
find_pie(position, ps[it_p][0])
print(s)
```
No
| 95,636 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Tags: brute force, geometry, implementation, math
Correct Solution:
```
def pitagoras(k):
casos_possiveis = []
for n in range(1,k):
m = int((k**2 - n**2)**(0.5))
if((n**2 + m**2) == k**2):
casos_possiveis.append([n, m])
return casos_possiveis
def possivelRepresntar(k):
for n in range(1, k):
m = int((k**2 - n**2)**(0.5))
if ((n ** 2 + m ** 2) == k ** 2):
return True
def tangentes(v):
tangentes = []
for p in v:
tangente = p[0]/p[1]
tangentes.append(tangente)
return tangentes
def vetorSemRepeticao(v1, v2):
v = []
v3 = v1 + v2
for p in v3:
if(p not in v):
v.append(p)
return v
def vetorUtil(v1, v2):
v_util = []
v3 = vetorSemRepeticao(v1,v2)
for vx in v3:
if(vx in v1 and vx in v2):
v_util.append(vx)
return v_util
def td_diferente(a,b,c,x,y,z):
if(a!=b and a!=c and b!=c and x!=y and x!=z and y!=z):
return True
else:
return False
a , b = input().split()
a = int(a)
b = int(b)
deu_certo = False
e3 = 0
e4 = 0
e5 = 0
if(possivelRepresntar(a) and possivelRepresntar(b)):
p1 = pitagoras(a)
p2 = pitagoras(b)
t1 = tangentes(pitagoras(a))
t2 = tangentes(pitagoras(b))
t_util = vetorUtil(t1, t2)
if(len(t_util) != 0):
for case in t_util:
caso = case
e1 = p1[(t1.index(caso))]
e2 = p2[(t2.index(1/caso))]
e4 = [0 ,e1[0]]
e5 = [e1[1],0]
e3 = [e1[1]+e2[1], e2[0]]
if(td_diferente(e3[0],e4[0],e5[0],e3[1],e4[1],e5[1])):
deu_certo = True
print("YES")
print("{} {}".format(e3[0], e3[1]))
print("{} {}".format(e4[0], e4[1]))
print("{} {}".format(e5[0], e5[1]))
break
if(not deu_certo):
print("NO")
else:
print("NO")
else:
print("NO")
```
| 95,637 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Tags: brute force, geometry, implementation, math
Correct Solution:
```
import math
def square(a):
lis=[]
for k in range(a+1):
if math.sqrt(a**2-k **2)==int(math.sqrt(a**2-k **2)):
lis.append((k,int(math.sqrt(a**2-k **2))))
return lis
def check(a):
boo=1
if len(square(a))==2 and int(math.sqrt(a))==math.sqrt(a):
boo=0
return boo
a,b=input().split()
a=int(a)
b=int(b)
if check(a)*check(b)==0:
print('NO')
else:
v=0
lisA=[]
lisB=[]
lisa=square(a)
lisb=square(b)
lisa.remove((a,0))
lisa.remove((0,a))
lisb.remove((b,0))
lisb.remove((0,b))
for A in lisa:
for B in lisb:
if A[0]*B[0]-A[1]*B[1]==0 and A[1]!=B[1]:
v=1
lisA.append(A)
lisB.append(B)
if v==1:
print('YES')
print(0,0)
print(-int(lisA[0][0]),int(lisA[0][1]))
print(int(lisB[0][0]),int(lisB[0][1]))
else:
print('NO')
```
| 95,638 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Tags: brute force, geometry, implementation, math
Correct Solution:
```
# Made By Mostafa_Khaled
bot = True
a,b=map(int,input().split())
def get(a):
return list([i,j] for i in range(1,a) for j in range(1,a) if i*i+j*j==a*a)
A=get(a)
B=get(b)
for [a,b] in A:
for [c,d] in B:
if a*c==b*d and b!=d:
print("YES\n0 0\n%d %d\n%d %d" %(-a,b,c,d))
exit(0)
print("NO")
# Made By Mostafa_Khaled
```
| 95,639 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Tags: brute force, geometry, implementation, math
Correct Solution:
```
a, b = input().strip().split()
a, b = int(a), int(b)
import math
import functools
@functools.lru_cache(None)
def check(a):
ans = set()
for i in range(1, a):
for j in range(i, a):
if i ** 2 + j ** 2 == a ** 2:
ans.add((i, j))
ans.add((j, i))
return list(ans)
sq1, sq2 = check(a), check(b)
if sq1 and sq2:
# print(sq1, sq2)
for x1, y1 in sq1:
for x2, y2 in sq2:
if (x1 * x2) / (y1 * y2) == 1:
a1, b1 = -x1, y1
a2, b2 = x2, y2
if not (a1 == a2 or b1 == b2):
print('YES')
print(a1, b1)
print(0, 0)
print(a2, b2)
import sys
sys.exit()
elif (x1 * y2) / (x2 * y1) == 1:
a1, b1 = -x1, y1
a2, b2 = y2, x2
if not (a1 == a2 or b1 == b2):
print('YES')
print(a1, b1)
print(0, 0)
print(a2, b2)
import sys
sys.exit()
print('NO')
else:
print('NO')
```
| 95,640 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Tags: brute force, geometry, implementation, math
Correct Solution:
```
a, b = map(int, input().split())
a, b = min(a, b), max(a, b)
for x in range(1, a):
if ((a ** 2 - x ** 2) ** 0.5) % 1 < 10 ** -5:
y = round((a ** 2 - x ** 2) ** 0.5)
if x > 0 and y > 0 and (y * b) % a == 0 and (x * b) % a == 0:
print('YES')
print(0, 0)
print(x, y)
print(y * b // a, -x * b // a)
exit(0)
print('NO')
```
| 95,641 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Tags: brute force, geometry, implementation, math
Correct Solution:
```
a,b=map(int,input().split())
A=[]
B=[]
for x in range(1,a):
y=(a*a-x*x)**.5
if int(y)==y:A.append((x,int(y)))
for x in range(1,b):
y=(b*b-x*x)**.5
if int(y)==y:B.append((-x,int(y)))
for x,y in A:
for c,d in B:
if (x-c)**2+(y-d)**2==a*a+b*b:
if y==d or x==c:c=-c;d=-d
if y==d or x==c:c=-c;d=-d;continue
print('YES\n0 0\n'+str(x),y,'\n'+str(c),d);exit()
print('NO')
```
| 95,642 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Tags: brute force, geometry, implementation, math
Correct Solution:
```
a,b = list(map(int,input().split()))
t = a*a
for x in range(-a,a+1):
y = t-(x**2)
z = int(y**0.5)
if z*z==y:
y = z
# print(x,y)
if x!=0 and y!=0:
den = x**2 + y**2
num = b*y
z = int(den**0.5)
if z*z==den:
den = z
if num%den==0:
x1 = num//den
num = x*x1
den = y
if num%den==0:
y1 = num//den
y1 = -y1
if y1-y!=0:
print("YES")
print(0,0)
print(x,y)
print(x1,y1)
exit()
y = -z
if x!=0 and y!=0:
den = x**2 + y**2
num = b*y
z = int(den**0.5)
if z*z==den:
if num%den==0:
x1 = num//den
num = x*x1
den = y
if num%den==0:
y1 = num//den
y1 = -y1
if y1-y!=0:
print("YES")
print(0,0)
print(x,y)
print(x1,y1)
exit()
print("NO")
```
| 95,643 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Tags: brute force, geometry, implementation, math
Correct Solution:
```
a,b=map(int,input().split())
x1=0
x2=0
for x1 in range(1,a):
for x2 in range(1,b):
i=(a*a-x1*x1)**0.5
if int(i)==i:
j=(b*b-x2*x2)**0.5
if int(j)==j:
if i!=j and (-x2-x1)**2+(i-j)**2==a*a+b*b:
print('YES')
print(0,0)
print(x1,int(i))
print(-x2,int(j))
exit(0)
print('NO')
```
| 95,644 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Submitted Solution:
```
a, b = map(int, input().split())
for x in range(1, b):
y = (b * b - x * x) ** 0.5
if y != int(y): continue
y = int(y)
if (a * y) % b or (a * x) % b: continue
if -(a * y) // b == x or (a * x) // b == y: continue
print("YES")
print(0, 0)
print(x, y)
print(-(a * y) // b, (a * x) // b)
exit()
print("NO")
```
Yes
| 95,645 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Submitted Solution:
```
a,b=map(int,input().split(" "))
lia,lib=[],[]
for i in range(1,a):
for j in range(1,a):
if i*i + j*j == a*a:
lia.append([i,j])
fl=0
ans="NO"
for i in range(1,b):
for j in range(1,b):
if i*i + j*j == b*b:
lib.append([i,j])
for [a,b] in lia:
for [c,d] in lib:
if a*c==b*d and b!=d:
fl=1
ans="YES"
break
if fl==1:
break
print(ans)
if fl==1:
print(0,0)
print(-a,b)
print(c,d)
```
Yes
| 95,646 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Submitted Solution:
```
def pitagoras(k):
casos_possiveis = []
for n in range(1,k):
m = int((k**2 - n**2)**(0.5))
if((n**2 + m**2) == k**2):
casos_possiveis.append([n, m])
return casos_possiveis
def possivelRepresntar(k):
for n in range(1, k):
m = int((k**2 - n**2)**(0.5))
if ((n ** 2 + m ** 2) == k ** 2):
return True
def tangentes(v):
tangentes = []
for p in v:
tangente = p[0]/p[1]
tangentes.append(tangente)
return tangentes
def vetorSemRepeticao(v1, v2):
v = []
v3 = v1 + v2
for p in v3:
if(p not in v):
v.append(p)
return v
def vetorUtil(v1, v2):
v_util = []
v3 = vetorSemRepeticao(v1,v2)
for vx in v3:
if(vx in v1 and vx in v2):
v_util.append(vx)
return v_util
def td_diferente(a,b,c,x,y,z):
if(a!=b and a!=c and b!=c and x!=y and x!=z and y!=z):
return True
else:
return False
a , b = input().split()
a = int(a)
b = int(b)
deu_certo = False
e3 = 0
e4 = 0
e5 = 00
if(possivelRepresntar(a) and possivelRepresntar(b)):
p1 = pitagoras(a)
p2 = pitagoras(b)
t1 = tangentes(pitagoras(a))
t2 = tangentes(pitagoras(b))
t_util = vetorUtil(t1, t2)
if(len(t_util) != 0):
for case in t_util:
caso = case
e1 = p1[(t1.index(caso))]
e2 = p2[(t2.index(1/caso))]
e4 = [0 ,e1[0]]
e5 = [e1[1],0]
e3 = [e1[1]+e2[1], e2[0]]
if(td_diferente(e3[0],e4[0],e5[0],e3[1],e4[1],e5[1])):
deu_certo = True
print("YES")
print("{} {}".format(e3[0], e3[1]))
print("{} {}".format(e4[0], e4[1]))
print("{} {}".format(e5[0], e5[1]))
break
if(not deu_certo):
print("NO")
else:
print("NO")
else:
print("NO")
```
Yes
| 95,647 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Submitted Solution:
```
def dist(a, b):
return (a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2
a, b = map(int, input().split())
pnt_a, pnt_b = [], []
for i in range(1, 1000):
j = 1
while j*j + i*i <= 1000000:
if i*i + j*j == a*a: pnt_a.append((i, j))
if i*i + j*j == b*b: pnt_b.append((-i, j))
j += 1
for i in pnt_a:
for j in pnt_b:
if i[1] != j[1] and dist(i, j) == a*a + b*b:
print("YES")
print("0 0")
print(i[0], i[1])
print(j[0], j[1])
exit()
print("NO")
```
Yes
| 95,648 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Submitted Solution:
```
import math
a,b=map(int,input().split())
alpha=b/a
c=0
for i in range(1,a):
if math.floor(math.sqrt(a**2)-(i**2))-(math.sqrt(a**2)-(i**2))==0:
c=i
if c==0:
print("NO")
else:
print("YES")
print(0,0)
print(str(int(c))+" "+str(int(math.sqrt((a**2)-(c**2)))))
print(str(int(alpha*(math.sqrt((a**2)-(c**2)))))+" "+str(int(-(alpha*c))))
```
No
| 95,649 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Submitted Solution:
```
#!/usr/bin/python3 -SOO
from math import sqrt,sin,cos,asin
a,b = map(int,input().strip().split())
for i in range(1,a):
x = a*a - i*i
if x<=0 or int(sqrt(x) + 0.5)**2 != x: continue
t = asin(i/a)
u = b*sin(t)
v = b*cos(t)
if abs(u-int(u)) < 0.0005 and abs(v-int(v)) < 0.0005:
print('YES')
print('0 0')
print('%d %d'%(-int(u),-int(v)))
print('%d %d'%(int(sqrt(x)),i))
break
else:
print('NO')
```
No
| 95,650 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Submitted Solution:
```
'''input
10 15
'''
# practicing a skill right after sleep improves it a lot quickly
from sys import stdin, setrecursionlimit
import math
def check(num):
return math.sqrt(num) == int(math.sqrt(num))
def pythagoreanTriplets():
mydict = dict()
for i in range(1, 1001):
for j in range(1, 1001):
num = i ** 2 + j ** 2
if check(num):
mydict[int(math.sqrt(num))] = str(i) + ' ' + str(j)
return mydict
# main starts
mydict = pythagoreanTriplets()
a, b = list(map(int, stdin.readline().split()))
if a in mydict and b in mydict:
print("YES")
a_f, a_s = list(map(int, mydict[a].split()))
b_f, b_s = list(map(int, mydict[b].split()))
print(0, a_s)
print(a_f, 0)
if b_f/b_s == a_f/a_s:
print(b_s, a_s + b_f)
else:
print(b_f, a_s + b_s)
else:
print("NO")
```
No
| 95,651 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.
Input
The first line contains two integers a, b (1 β€ a, b β€ 1000), separated by a single space.
Output
In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers β the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.
Examples
Input
1 1
Output
NO
Input
5 5
Output
YES
2 1
5 5
-2 4
Input
5 10
Output
YES
-10 4
-2 -2
1 2
Submitted Solution:
```
def isquare(n):
h = n
l = 1
while h-l>1:
m = (h+l)//2
if m*m<=n:
l = m
elif m*m>n:
h = m
return l
a,b = map(int,input().split())
p,q,r,s = -1,-1,-1,-1
for i in range(3,a):
if isquare(a*a-i*i)**2==a*a-i*i:
p,q = i,isquare(a*a-i*i)
break
for i in range(3,b):
if isquare(b*b-i*i)**2==b*b-i*i:
r,s = i,isquare(b*b-i*i)
break
if p==-1 or q==-1 or r==-1 or s==-1:
print("NO")
else:
if p*r==q*s:
print("YES\n",0,0,'\n',p,q,'\n',-r,s)
elif p*s==q*r:
print("YES\n",0,0,'\n',p,q,'\n',-s,r)
else:
print("NO")
```
No
| 95,652 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya tries to break in a safe. He knows that a code consists of n numbers, and every number is a 0 or a 1. Vasya has made m attempts to enter the code. After each attempt the system told him in how many position stand the right numbers. It is not said in which positions the wrong numbers stand. Vasya has been so unlucky that he hasnβt entered the code where would be more than 5 correct numbers. Now Vasya is completely bewildered: he thinks thereβs a mistake in the system and it is self-contradictory. Help Vasya β calculate how many possible code variants are left that do not contradict the previous system responses.
Input
The first input line contains two integers n and m (6 β€ n β€ 35, 1 β€ m β€ 10) which represent the number of numbers in the code and the number of attempts made by Vasya. Then follow m lines, each containing space-separated si and ci which correspondingly indicate Vasyaβs attempt (a line containing n numbers which are 0 or 1) and the systemβs response (an integer from 0 to 5 inclusively).
Output
Print the single number which indicates how many possible code variants that do not contradict the m system responses are left.
Examples
Input
6 2
000000 2
010100 4
Output
6
Input
6 3
000000 2
010100 4
111100 0
Output
0
Input
6 3
000000 2
010100 4
111100 2
Output
1
Tags: brute force
Correct Solution:
```
import itertools
n,m=map(int,input().split())
def gen(s,d):
ans=[]
a=int(str(s),2)
A=int(a)
for i in itertools.combinations(list(range(n)), d):
c=A
for e in i:c=c ^ 1<<e
ans.append(c)
return ans
a,b=map(int,input().split())
cur=gen(a,b)
#print(cur)
for i in range(m-1):
a,b=map(int,input().split())
cur=[x for x in cur if(bin(x^int(str(a),2)).count("1")==b)]
#print(*cur)
print(len(cur))
```
| 95,653 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya tries to break in a safe. He knows that a code consists of n numbers, and every number is a 0 or a 1. Vasya has made m attempts to enter the code. After each attempt the system told him in how many position stand the right numbers. It is not said in which positions the wrong numbers stand. Vasya has been so unlucky that he hasnβt entered the code where would be more than 5 correct numbers. Now Vasya is completely bewildered: he thinks thereβs a mistake in the system and it is self-contradictory. Help Vasya β calculate how many possible code variants are left that do not contradict the previous system responses.
Input
The first input line contains two integers n and m (6 β€ n β€ 35, 1 β€ m β€ 10) which represent the number of numbers in the code and the number of attempts made by Vasya. Then follow m lines, each containing space-separated si and ci which correspondingly indicate Vasyaβs attempt (a line containing n numbers which are 0 or 1) and the systemβs response (an integer from 0 to 5 inclusively).
Output
Print the single number which indicates how many possible code variants that do not contradict the m system responses are left.
Examples
Input
6 2
000000 2
010100 4
Output
6
Input
6 3
000000 2
010100 4
111100 0
Output
0
Input
6 3
000000 2
010100 4
111100 2
Output
1
Tags: brute force
Correct Solution:
```
import sys
from array import array # noqa: F401
from itertools import combinations
def input():
return sys.stdin.buffer.readline().decode('utf-8')
n, m = map(int, input().split())
s = set()
x = set()
for i in range(m):
a, k = input().split()
k = int(k)
a = int(a, 2)
x.add(str(a))
cur_s = set()
for c in combinations(range(n), r=k):
mask = 0
for j in c:
mask |= (1 << j)
cur_s.add(str(a ^ mask))
if i == 0:
s = cur_s
else:
s.intersection_update(cur_s)
print(len(s - x))
```
| 95,654 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya tries to break in a safe. He knows that a code consists of n numbers, and every number is a 0 or a 1. Vasya has made m attempts to enter the code. After each attempt the system told him in how many position stand the right numbers. It is not said in which positions the wrong numbers stand. Vasya has been so unlucky that he hasnβt entered the code where would be more than 5 correct numbers. Now Vasya is completely bewildered: he thinks thereβs a mistake in the system and it is self-contradictory. Help Vasya β calculate how many possible code variants are left that do not contradict the previous system responses.
Input
The first input line contains two integers n and m (6 β€ n β€ 35, 1 β€ m β€ 10) which represent the number of numbers in the code and the number of attempts made by Vasya. Then follow m lines, each containing space-separated si and ci which correspondingly indicate Vasyaβs attempt (a line containing n numbers which are 0 or 1) and the systemβs response (an integer from 0 to 5 inclusively).
Output
Print the single number which indicates how many possible code variants that do not contradict the m system responses are left.
Examples
Input
6 2
000000 2
010100 4
Output
6
Input
6 3
000000 2
010100 4
111100 0
Output
0
Input
6 3
000000 2
010100 4
111100 2
Output
1
Tags: brute force
Correct Solution:
```
from itertools import combinations
def calculate(s, dif):
x = int(s, 2)
for j in combinations(range(len(s)), dif):
y = x
for k in j:
y ^= (2**k)
yield y
def calculate2(s, dif, arr):
y = int(s, 2)
for x in arr:
if(bin(y ^ x).count('1') == dif):
yield x
n, m = map(int, input().split())
result = []
(st, dif) = input().split()
total = calculate(st, int(dif))
for i in range(1, m):
st, dif = input().split()
total = calculate2(st, int(dif), total)
print(len(list(total)))
```
| 95,655 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya tries to break in a safe. He knows that a code consists of n numbers, and every number is a 0 or a 1. Vasya has made m attempts to enter the code. After each attempt the system told him in how many position stand the right numbers. It is not said in which positions the wrong numbers stand. Vasya has been so unlucky that he hasnβt entered the code where would be more than 5 correct numbers. Now Vasya is completely bewildered: he thinks thereβs a mistake in the system and it is self-contradictory. Help Vasya β calculate how many possible code variants are left that do not contradict the previous system responses.
Input
The first input line contains two integers n and m (6 β€ n β€ 35, 1 β€ m β€ 10) which represent the number of numbers in the code and the number of attempts made by Vasya. Then follow m lines, each containing space-separated si and ci which correspondingly indicate Vasyaβs attempt (a line containing n numbers which are 0 or 1) and the systemβs response (an integer from 0 to 5 inclusively).
Output
Print the single number which indicates how many possible code variants that do not contradict the m system responses are left.
Examples
Input
6 2
000000 2
010100 4
Output
6
Input
6 3
000000 2
010100 4
111100 0
Output
0
Input
6 3
000000 2
010100 4
111100 2
Output
1
Tags: brute force
Correct Solution:
```
import os,io
from sys import stdout
# import collections
# import random
# import math
# from operator import itemgetter
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
# from collections import Counter
# from decimal import Decimal
# import heapq
# from functools import lru_cache
# import sys
# import threading
# sys.setrecursionlimit(10**6)
# threading.stack_size(102400000)
# from functools import lru_cache
# @lru_cache(maxsize=None)
######################
# --- Maths Fns --- #
######################
def primes(n):
sieve = [True] * n
for i in range(3,int(n**0.5)+1,2):
if sieve[i]:
sieve[i*i::2*i]=[False]*((n-i*i-1)//(2*i)+1)
return [2] + [i for i in range(3,n,2) if sieve[i]]
def binomial_coefficient(n, k):
if 0 <= k <= n:
ntok = 1
ktok = 1
for t in range(1, min(k, n - k) + 1):
ntok *= n
ktok *= t
n -= 1
return ntok // ktok
else:
return 0
def powerOfK(k, max):
if k == 1:
return [1]
if k == -1:
return [-1, 1]
result = []
n = 1
while n <= max:
result.append(n)
n *= k
return result
def divisors(n):
i = 1
result = []
while i*i <= n:
if n%i == 0:
if n/i == i:
result.append(i)
else:
result.append(i)
result.append(n/i)
i+=1
return result
# @lru_cache(maxsize=None)
def digitsSum(n):
if n == 0:
return 0
r = 0
while n > 0:
r += n % 10
n //= 10
return r
######################
# ---- GRID Fns ---- #
######################
def isValid(i, j, n, m):
return i >= 0 and i < n and j >= 0 and j < m
def print_grid(grid):
for line in grid:
print(" ".join(map(str,line)))
######################
# ---- MISC Fns ---- #
######################
def kadane(a,size):
max_so_far = 0
max_ending_here = 0
for i in range(0, size):
max_ending_here = max_ending_here + a[i]
if (max_so_far < max_ending_here):
max_so_far = max_ending_here
if max_ending_here < 0:
max_ending_here = 0
return max_so_far
def prefixSum(arr):
for i in range(1, len(arr)):
arr[i] = arr[i] + arr[i-1]
return arr
def ceil(n, d):
if n % d == 0:
return n // d
else:
return (n // d) + 1
# INPUTS --------------------------
# s = input().decode('utf-8').strip()
# n = int(input())
# l = list(map(int, input().split()))
# t = int(input())
# for _ in range(t):
# for _ in range(t):
n, k = list(map(int, input().split()))
q = []
for _ in range(k):
a, b = list(map(lambda x: x.decode('utf-8').strip(), input().split()))
q.append((list(map(int, a)), int(b)))
code, correct = max(q, key=lambda x: x[1])
codeb = int("".join(map(str, code)), 2)
possibles = set()
def generate(n, correct, codeb, l, s):
if correct == 0:
while len(l) < n:
l.append(1)
p = int("".join(map(str, l)), 2)
s.add(p)
return
if n - len(l) < correct:
return
generate(n, correct-1, codeb, l+[0], s)
generate(n, correct, codeb, l+[1], s)
result = None
memo = {}
for code, correct in q:
codeb = int("".join(map(str, code)), 2)
newSetOfPossibles = set()
if correct in memo:
newSetOfPossibles = memo[correct]
else:
generate(n, correct, codeb, [], newSetOfPossibles)
memo[correct] = newSetOfPossibles
newSetOfPossibles = set(list(map(lambda x: x^codeb, list(newSetOfPossibles))))
if not result:
result = newSetOfPossibles
else:
result = result.intersection(newSetOfPossibles)
print(len(result))
```
| 95,656 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya tries to break in a safe. He knows that a code consists of n numbers, and every number is a 0 or a 1. Vasya has made m attempts to enter the code. After each attempt the system told him in how many position stand the right numbers. It is not said in which positions the wrong numbers stand. Vasya has been so unlucky that he hasnβt entered the code where would be more than 5 correct numbers. Now Vasya is completely bewildered: he thinks thereβs a mistake in the system and it is self-contradictory. Help Vasya β calculate how many possible code variants are left that do not contradict the previous system responses.
Input
The first input line contains two integers n and m (6 β€ n β€ 35, 1 β€ m β€ 10) which represent the number of numbers in the code and the number of attempts made by Vasya. Then follow m lines, each containing space-separated si and ci which correspondingly indicate Vasyaβs attempt (a line containing n numbers which are 0 or 1) and the systemβs response (an integer from 0 to 5 inclusively).
Output
Print the single number which indicates how many possible code variants that do not contradict the m system responses are left.
Examples
Input
6 2
000000 2
010100 4
Output
6
Input
6 3
000000 2
010100 4
111100 0
Output
0
Input
6 3
000000 2
010100 4
111100 2
Output
1
Submitted Solution:
```
import os,io
from sys import stdout
# import collections
# import random
# import math
# from operator import itemgetter
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
# from collections import Counter
# from decimal import Decimal
# import heapq
# from functools import lru_cache
# import sys
# import threading
# sys.setrecursionlimit(10**6)
# threading.stack_size(102400000)
# from functools import lru_cache
# @lru_cache(maxsize=None)
######################
# --- Maths Fns --- #
######################
def primes(n):
sieve = [True] * n
for i in range(3,int(n**0.5)+1,2):
if sieve[i]:
sieve[i*i::2*i]=[False]*((n-i*i-1)//(2*i)+1)
return [2] + [i for i in range(3,n,2) if sieve[i]]
def binomial_coefficient(n, k):
if 0 <= k <= n:
ntok = 1
ktok = 1
for t in range(1, min(k, n - k) + 1):
ntok *= n
ktok *= t
n -= 1
return ntok // ktok
else:
return 0
def powerOfK(k, max):
if k == 1:
return [1]
if k == -1:
return [-1, 1]
result = []
n = 1
while n <= max:
result.append(n)
n *= k
return result
def divisors(n):
i = 1
result = []
while i*i <= n:
if n%i == 0:
if n/i == i:
result.append(i)
else:
result.append(i)
result.append(n/i)
i+=1
return result
# @lru_cache(maxsize=None)
def digitsSum(n):
if n == 0:
return 0
r = 0
while n > 0:
r += n % 10
n //= 10
return r
######################
# ---- GRID Fns ---- #
######################
def isValid(i, j, n, m):
return i >= 0 and i < n and j >= 0 and j < m
def print_grid(grid):
for line in grid:
print(" ".join(map(str,line)))
######################
# ---- MISC Fns ---- #
######################
def kadane(a,size):
max_so_far = 0
max_ending_here = 0
for i in range(0, size):
max_ending_here = max_ending_here + a[i]
if (max_so_far < max_ending_here):
max_so_far = max_ending_here
if max_ending_here < 0:
max_ending_here = 0
return max_so_far
def prefixSum(arr):
for i in range(1, len(arr)):
arr[i] = arr[i] + arr[i-1]
return arr
def ceil(n, d):
if n % d == 0:
return n // d
else:
return (n // d) + 1
# INPUTS --------------------------
# s = input().decode('utf-8').strip()
# n = int(input())
# l = list(map(int, input().split()))
# t = int(input())
# for _ in range(t):
# for _ in range(t):
n, k = list(map(int, input().split()))
q = []
for _ in range(k):
a, b = list(map(lambda x: x.decode('utf-8').strip(), input().split()))
q.append((list(map(int, a)), int(b)))
code, correct = max(q, key=lambda x: x[1])
codeb = int("".join(map(str, code)), 2)
possibles = set()
def generate(n, correct, l):
if correct == 0:
while len(l) < n:
l.append(1)
p = int("".join(map(str, l)), 2)
possibles.add(p^codeb)
return
if n - len(l) < correct:
return
generate(n, correct-1, l+[0])
generate(n, correct, l+[1])
generate(n, correct, [])
impossible = set()
total = 0
for possibleCode in possibles:
for attempt, match in q:
attempt = "".join(list(map(str, attempt)))
attempt = int(attempt, base=2)
r = (possibleCode^attempt)
r = "{0:{f}{w}b}".format(r, w=n, f='0')
t = r.count('0')
if t != match:
impossible.add(possibleCode)
break
total += 1
print(total)
```
No
| 95,657 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After Misha's birthday he had many large numbers left, scattered across the room. Now it's time to clean up and Misha needs to put them in a basket. He ordered this task to his pet robot that agreed to complete the task at certain conditions. Before the robot puts a number x to the basket, Misha should answer the question: is it possible to choose one or multiple numbers that already are in the basket, such that their XOR sum equals x?
If the answer is positive, you also need to give the indexes of these numbers. If there are multiple options of choosing numbers, you are allowed to choose any correct option. After Misha's answer the robot puts the number to the basket.
Initially the basket is empty. Each integer you put in the basket takes some number. The first integer you put into the basket take number 0, the second integer takes number 1 and so on.
Misha needs to clean up the place as soon as possible but unfortunately, he isn't that good at mathematics. He asks you to help him.
Input
The first line contains number m (1 β€ m β€ 2000), showing how many numbers are scattered around the room.
The next m lines contain the numbers in the order in which the robot puts them in the basket. Each number is a positive integer strictly less than 10600 that doesn't contain leading zeroes.
Output
For each number either print a 0 on the corresponding line, if the number cannot be represented as a XOR sum of numbers that are in the basket, or print integer k showing how many numbers are in the representation and the indexes of these numbers. Separate the numbers by spaces. Each number can occur in the representation at most once.
Examples
Input
7
7
6
5
4
3
2
1
Output
0
0
0
3 0 1 2
2 1 2
2 0 2
2 0 1
Input
2
5
5
Output
0
1 0
Note
The XOR sum of numbers is the result of bitwise sum of numbers modulo 2.
Tags: bitmasks
Correct Solution:
```
m = int(input())
values = []
idx = []
for i in range(m):
x = int(input())
ans = 0
for xx,ii in zip(values,idx):
if (xx^x) < x:
x^=xx
ans^=ii
if x == 0:
anss = []
for j in range(i):
if (ans&1)==1:
anss.append(j)
ans>>=1
print(len(anss),*anss)
else:
print(0)
values.append(x)
idx.append(ans^(2**i))
```
| 95,658 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After Misha's birthday he had many large numbers left, scattered across the room. Now it's time to clean up and Misha needs to put them in a basket. He ordered this task to his pet robot that agreed to complete the task at certain conditions. Before the robot puts a number x to the basket, Misha should answer the question: is it possible to choose one or multiple numbers that already are in the basket, such that their XOR sum equals x?
If the answer is positive, you also need to give the indexes of these numbers. If there are multiple options of choosing numbers, you are allowed to choose any correct option. After Misha's answer the robot puts the number to the basket.
Initially the basket is empty. Each integer you put in the basket takes some number. The first integer you put into the basket take number 0, the second integer takes number 1 and so on.
Misha needs to clean up the place as soon as possible but unfortunately, he isn't that good at mathematics. He asks you to help him.
Input
The first line contains number m (1 β€ m β€ 2000), showing how many numbers are scattered around the room.
The next m lines contain the numbers in the order in which the robot puts them in the basket. Each number is a positive integer strictly less than 10600 that doesn't contain leading zeroes.
Output
For each number either print a 0 on the corresponding line, if the number cannot be represented as a XOR sum of numbers that are in the basket, or print integer k showing how many numbers are in the representation and the indexes of these numbers. Separate the numbers by spaces. Each number can occur in the representation at most once.
Examples
Input
7
7
6
5
4
3
2
1
Output
0
0
0
3 0 1 2
2 1 2
2 0 2
2 0 1
Input
2
5
5
Output
0
1 0
Note
The XOR sum of numbers is the result of bitwise sum of numbers modulo 2.
Tags: bitmasks
Correct Solution:
```
import sys, os
numbs = [int(x) for x in sys.stdin.buffer.read().split()]
n = numbs.pop(0)
base = []
out = []
for i in range(n):
x = numbs[i]
how = 0
for b,rep in base:
if x.bit_length() == b.bit_length():
x ^= b
how ^= rep
if x:
how |= 1 << i
a = 0
b = len(base)
while a < b:
c = a + b >> 1
if base[c][0] > x:
a = c + 1
else:
b = c
base.insert(a, (x, how))
out.append(0)
else:
outind = len(out)
out.append(-1)
y = bin(how).encode('ascii')
ylen = len(y)
for i in range(2,len(y)):
if y[i] == 49:
out.append(ylen - 1 - i)
out[outind] = len(out) - 1 - outind
os.write(1, b'\n'.join(str(x).encode('ascii') for x in out))
```
| 95,659 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After Misha's birthday he had many large numbers left, scattered across the room. Now it's time to clean up and Misha needs to put them in a basket. He ordered this task to his pet robot that agreed to complete the task at certain conditions. Before the robot puts a number x to the basket, Misha should answer the question: is it possible to choose one or multiple numbers that already are in the basket, such that their XOR sum equals x?
If the answer is positive, you also need to give the indexes of these numbers. If there are multiple options of choosing numbers, you are allowed to choose any correct option. After Misha's answer the robot puts the number to the basket.
Initially the basket is empty. Each integer you put in the basket takes some number. The first integer you put into the basket take number 0, the second integer takes number 1 and so on.
Misha needs to clean up the place as soon as possible but unfortunately, he isn't that good at mathematics. He asks you to help him.
Input
The first line contains number m (1 β€ m β€ 2000), showing how many numbers are scattered around the room.
The next m lines contain the numbers in the order in which the robot puts them in the basket. Each number is a positive integer strictly less than 10600 that doesn't contain leading zeroes.
Output
For each number either print a 0 on the corresponding line, if the number cannot be represented as a XOR sum of numbers that are in the basket, or print integer k showing how many numbers are in the representation and the indexes of these numbers. Separate the numbers by spaces. Each number can occur in the representation at most once.
Examples
Input
7
7
6
5
4
3
2
1
Output
0
0
0
3 0 1 2
2 1 2
2 0 2
2 0 1
Input
2
5
5
Output
0
1 0
Note
The XOR sum of numbers is the result of bitwise sum of numbers modulo 2.
Tags: bitmasks
Correct Solution:
```
m = int(input())
values = []
idx = []
for i in range(m):
x = int(input())
ans = 0
for j,xx in enumerate(values):
if (xx^x) < x:
x^=xx
ans^=idx[j]
if x == 0:
anss = []
for j in range(i):
if (ans&1)!=0:
anss.append(j)
ans>>=1
print(len(anss),*anss)
else:
print(0)
values.append(x)
idx.append(ans^(2**i))
```
| 95,660 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After Misha's birthday he had many large numbers left, scattered across the room. Now it's time to clean up and Misha needs to put them in a basket. He ordered this task to his pet robot that agreed to complete the task at certain conditions. Before the robot puts a number x to the basket, Misha should answer the question: is it possible to choose one or multiple numbers that already are in the basket, such that their XOR sum equals x?
If the answer is positive, you also need to give the indexes of these numbers. If there are multiple options of choosing numbers, you are allowed to choose any correct option. After Misha's answer the robot puts the number to the basket.
Initially the basket is empty. Each integer you put in the basket takes some number. The first integer you put into the basket take number 0, the second integer takes number 1 and so on.
Misha needs to clean up the place as soon as possible but unfortunately, he isn't that good at mathematics. He asks you to help him.
Input
The first line contains number m (1 β€ m β€ 2000), showing how many numbers are scattered around the room.
The next m lines contain the numbers in the order in which the robot puts them in the basket. Each number is a positive integer strictly less than 10600 that doesn't contain leading zeroes.
Output
For each number either print a 0 on the corresponding line, if the number cannot be represented as a XOR sum of numbers that are in the basket, or print integer k showing how many numbers are in the representation and the indexes of these numbers. Separate the numbers by spaces. Each number can occur in the representation at most once.
Examples
Input
7
7
6
5
4
3
2
1
Output
0
0
0
3 0 1 2
2 1 2
2 0 2
2 0 1
Input
2
5
5
Output
0
1 0
Note
The XOR sum of numbers is the result of bitwise sum of numbers modulo 2.
Tags: bitmasks
Correct Solution:
```
m = int(input())
b = []
k = []
for i in range(m):
x = int(input())
c = 0
for j in range(len(b)):
v = b[j]
d = k[j]
if (x ^ v) < x:
x ^= v
c ^= d
if x != 0:
print(0)
c ^= 2 ** i
b.append(x)
k.append(c)
else:
a = []
for j in range(m):
if c & 1 == 1:
a.append(j)
c >>= 1
print(len(a), end='')
for v in a:
print(' ', v, sep='', end='')
print()
```
| 95,661 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After Misha's birthday he had many large numbers left, scattered across the room. Now it's time to clean up and Misha needs to put them in a basket. He ordered this task to his pet robot that agreed to complete the task at certain conditions. Before the robot puts a number x to the basket, Misha should answer the question: is it possible to choose one or multiple numbers that already are in the basket, such that their XOR sum equals x?
If the answer is positive, you also need to give the indexes of these numbers. If there are multiple options of choosing numbers, you are allowed to choose any correct option. After Misha's answer the robot puts the number to the basket.
Initially the basket is empty. Each integer you put in the basket takes some number. The first integer you put into the basket take number 0, the second integer takes number 1 and so on.
Misha needs to clean up the place as soon as possible but unfortunately, he isn't that good at mathematics. He asks you to help him.
Input
The first line contains number m (1 β€ m β€ 2000), showing how many numbers are scattered around the room.
The next m lines contain the numbers in the order in which the robot puts them in the basket. Each number is a positive integer strictly less than 10600 that doesn't contain leading zeroes.
Output
For each number either print a 0 on the corresponding line, if the number cannot be represented as a XOR sum of numbers that are in the basket, or print integer k showing how many numbers are in the representation and the indexes of these numbers. Separate the numbers by spaces. Each number can occur in the representation at most once.
Examples
Input
7
7
6
5
4
3
2
1
Output
0
0
0
3 0 1 2
2 1 2
2 0 2
2 0 1
Input
2
5
5
Output
0
1 0
Note
The XOR sum of numbers is the result of bitwise sum of numbers modulo 2.
Tags: bitmasks
Correct Solution:
```
buck = [[0, 0] for i in range(2201)]
m = int(input())
for i in range(m):
a = int(input())
ok = True
br = 0
for j in range(2200, -1, -1):
if a & (1 << j):
if(buck[j][0]):
a ^= buck[j][0]
br ^= buck[j][1]
else:
ok = False
buck[j][0] = a
buck[j][1] = br | (1 << i)
break
if not ok:
print("0")
else:
lst = []
for j in range(2201):
if br & (1 << j):
lst.append(j)
print(len(lst), end = ' ')
for j in lst:
print(j, end = ' ')
print('\n', end='')
```
| 95,662 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After Misha's birthday he had many large numbers left, scattered across the room. Now it's time to clean up and Misha needs to put them in a basket. He ordered this task to his pet robot that agreed to complete the task at certain conditions. Before the robot puts a number x to the basket, Misha should answer the question: is it possible to choose one or multiple numbers that already are in the basket, such that their XOR sum equals x?
If the answer is positive, you also need to give the indexes of these numbers. If there are multiple options of choosing numbers, you are allowed to choose any correct option. After Misha's answer the robot puts the number to the basket.
Initially the basket is empty. Each integer you put in the basket takes some number. The first integer you put into the basket take number 0, the second integer takes number 1 and so on.
Misha needs to clean up the place as soon as possible but unfortunately, he isn't that good at mathematics. He asks you to help him.
Input
The first line contains number m (1 β€ m β€ 2000), showing how many numbers are scattered around the room.
The next m lines contain the numbers in the order in which the robot puts them in the basket. Each number is a positive integer strictly less than 10600 that doesn't contain leading zeroes.
Output
For each number either print a 0 on the corresponding line, if the number cannot be represented as a XOR sum of numbers that are in the basket, or print integer k showing how many numbers are in the representation and the indexes of these numbers. Separate the numbers by spaces. Each number can occur in the representation at most once.
Examples
Input
7
7
6
5
4
3
2
1
Output
0
0
0
3 0 1 2
2 1 2
2 0 2
2 0 1
Input
2
5
5
Output
0
1 0
Note
The XOR sum of numbers is the result of bitwise sum of numbers modulo 2.
Tags: bitmasks
Correct Solution:
```
n = int(input())
b = []
bb =[]
for i in range(n):
x=int(input())
idx = 0
for j in range(len(b)):
nxt = b[j] ^ x
if nxt < x :
x = nxt
idx ^= bb[j]
if x == 0:
cnt = 0
v = []
for k in range(2000):
if idx & (1 << k) :
v.append(k)
print(len(v),end=' ')
for e in v:
print(e,end=' ')
print()
else :
print(0)
idx ^= 1 << i
b.append(x)
bb.append(idx)
```
| 95,663 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After Misha's birthday he had many large numbers left, scattered across the room. Now it's time to clean up and Misha needs to put them in a basket. He ordered this task to his pet robot that agreed to complete the task at certain conditions. Before the robot puts a number x to the basket, Misha should answer the question: is it possible to choose one or multiple numbers that already are in the basket, such that their XOR sum equals x?
If the answer is positive, you also need to give the indexes of these numbers. If there are multiple options of choosing numbers, you are allowed to choose any correct option. After Misha's answer the robot puts the number to the basket.
Initially the basket is empty. Each integer you put in the basket takes some number. The first integer you put into the basket take number 0, the second integer takes number 1 and so on.
Misha needs to clean up the place as soon as possible but unfortunately, he isn't that good at mathematics. He asks you to help him.
Input
The first line contains number m (1 β€ m β€ 2000), showing how many numbers are scattered around the room.
The next m lines contain the numbers in the order in which the robot puts them in the basket. Each number is a positive integer strictly less than 10600 that doesn't contain leading zeroes.
Output
For each number either print a 0 on the corresponding line, if the number cannot be represented as a XOR sum of numbers that are in the basket, or print integer k showing how many numbers are in the representation and the indexes of these numbers. Separate the numbers by spaces. Each number can occur in the representation at most once.
Examples
Input
7
7
6
5
4
3
2
1
Output
0
0
0
3 0 1 2
2 1 2
2 0 2
2 0 1
Input
2
5
5
Output
0
1 0
Note
The XOR sum of numbers is the result of bitwise sum of numbers modulo 2.
Tags: bitmasks
Correct Solution:
```
n = int(input())
t = [0 for i in range(2000)]
c = [0 for i in range(2000)]
for i in range(n) :
x = int(input())
r = 0
ok = False
for j in range(2000) :
if x >> j & 1 :
if t[j] != 0 :
x ^= t[j]
r ^= c[j]
else :
t[j] = x
c[j] = r ^ (1 << i)
ok = True
break
if ok :
print(0)
continue
a = []
for j in range(2000) :
if r >> j & 1 :
a.append(j)
print(len(a))
for y in a :
print(y)
```
| 95,664 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After Misha's birthday he had many large numbers left, scattered across the room. Now it's time to clean up and Misha needs to put them in a basket. He ordered this task to his pet robot that agreed to complete the task at certain conditions. Before the robot puts a number x to the basket, Misha should answer the question: is it possible to choose one or multiple numbers that already are in the basket, such that their XOR sum equals x?
If the answer is positive, you also need to give the indexes of these numbers. If there are multiple options of choosing numbers, you are allowed to choose any correct option. After Misha's answer the robot puts the number to the basket.
Initially the basket is empty. Each integer you put in the basket takes some number. The first integer you put into the basket take number 0, the second integer takes number 1 and so on.
Misha needs to clean up the place as soon as possible but unfortunately, he isn't that good at mathematics. He asks you to help him.
Input
The first line contains number m (1 β€ m β€ 2000), showing how many numbers are scattered around the room.
The next m lines contain the numbers in the order in which the robot puts them in the basket. Each number is a positive integer strictly less than 10600 that doesn't contain leading zeroes.
Output
For each number either print a 0 on the corresponding line, if the number cannot be represented as a XOR sum of numbers that are in the basket, or print integer k showing how many numbers are in the representation and the indexes of these numbers. Separate the numbers by spaces. Each number can occur in the representation at most once.
Examples
Input
7
7
6
5
4
3
2
1
Output
0
0
0
3 0 1 2
2 1 2
2 0 2
2 0 1
Input
2
5
5
Output
0
1 0
Note
The XOR sum of numbers is the result of bitwise sum of numbers modulo 2.
Tags: bitmasks
Correct Solution:
```
m = int(input())
values = []
idx = []
for i in range(m):
x = int(input())
ans = 0
for xx,ii in zip(values,idx):
if (xx^x) < x:
x^=xx
ans^=ii
if x == 0:
anss = []
for j in range(i):
if (ans&1)!=0:
anss.append(j)
ans>>=1
print(len(anss),*anss)
else:
print(0)
values.append(x)
idx.append(ans^(2**i))
```
| 95,665 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After Misha's birthday he had many large numbers left, scattered across the room. Now it's time to clean up and Misha needs to put them in a basket. He ordered this task to his pet robot that agreed to complete the task at certain conditions. Before the robot puts a number x to the basket, Misha should answer the question: is it possible to choose one or multiple numbers that already are in the basket, such that their XOR sum equals x?
If the answer is positive, you also need to give the indexes of these numbers. If there are multiple options of choosing numbers, you are allowed to choose any correct option. After Misha's answer the robot puts the number to the basket.
Initially the basket is empty. Each integer you put in the basket takes some number. The first integer you put into the basket take number 0, the second integer takes number 1 and so on.
Misha needs to clean up the place as soon as possible but unfortunately, he isn't that good at mathematics. He asks you to help him.
Input
The first line contains number m (1 β€ m β€ 2000), showing how many numbers are scattered around the room.
The next m lines contain the numbers in the order in which the robot puts them in the basket. Each number is a positive integer strictly less than 10600 that doesn't contain leading zeroes.
Output
For each number either print a 0 on the corresponding line, if the number cannot be represented as a XOR sum of numbers that are in the basket, or print integer k showing how many numbers are in the representation and the indexes of these numbers. Separate the numbers by spaces. Each number can occur in the representation at most once.
Examples
Input
7
7
6
5
4
3
2
1
Output
0
0
0
3 0 1 2
2 1 2
2 0 2
2 0 1
Input
2
5
5
Output
0
1 0
Note
The XOR sum of numbers is the result of bitwise sum of numbers modulo 2.
Submitted Solution:
```
m = int(input())
b = []
k = []
for i in range(m):
x = int(input())
c = 0
for i in range(len(b)):
v = b[i]
d = k[i]
if (x ^ v) < x:
x ^= v
c ^= d
if x != 0:
print(0)
c ^= 2 ** i
b.append(x)
k.append(c)
else:
a = []
for j in range(m):
if c & 1 == 1:
a.append(j)
c >>= 1
print(len(a), end='')
for v in a:
print(' ', v, sep='', end='')
print()
```
No
| 95,666 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After Misha's birthday he had many large numbers left, scattered across the room. Now it's time to clean up and Misha needs to put them in a basket. He ordered this task to his pet robot that agreed to complete the task at certain conditions. Before the robot puts a number x to the basket, Misha should answer the question: is it possible to choose one or multiple numbers that already are in the basket, such that their XOR sum equals x?
If the answer is positive, you also need to give the indexes of these numbers. If there are multiple options of choosing numbers, you are allowed to choose any correct option. After Misha's answer the robot puts the number to the basket.
Initially the basket is empty. Each integer you put in the basket takes some number. The first integer you put into the basket take number 0, the second integer takes number 1 and so on.
Misha needs to clean up the place as soon as possible but unfortunately, he isn't that good at mathematics. He asks you to help him.
Input
The first line contains number m (1 β€ m β€ 2000), showing how many numbers are scattered around the room.
The next m lines contain the numbers in the order in which the robot puts them in the basket. Each number is a positive integer strictly less than 10600 that doesn't contain leading zeroes.
Output
For each number either print a 0 on the corresponding line, if the number cannot be represented as a XOR sum of numbers that are in the basket, or print integer k showing how many numbers are in the representation and the indexes of these numbers. Separate the numbers by spaces. Each number can occur in the representation at most once.
Examples
Input
7
7
6
5
4
3
2
1
Output
0
0
0
3 0 1 2
2 1 2
2 0 2
2 0 1
Input
2
5
5
Output
0
1 0
Note
The XOR sum of numbers is the result of bitwise sum of numbers modulo 2.
Submitted Solution:
```
buck = [[0, 0] for i in range(2500)]
m = int(input())
for i in range(m):
a = int(input())
lst = []
for j in range(2500):
if a & (1 << j):
if(buck[j][0]):
a ^= buck[j][0]
lst.append(buck[j][1])
else:
lst = [0]
buck[j][0] = a
buck[j][1] = i+1
break
if len(lst) == 1 and lst[0] == 0:
print(0)
else:
print(len(lst), end = ' ')
for ind in lst:
print(ind, end=' ')
print('\n', end='')
```
No
| 95,667 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After Misha's birthday he had many large numbers left, scattered across the room. Now it's time to clean up and Misha needs to put them in a basket. He ordered this task to his pet robot that agreed to complete the task at certain conditions. Before the robot puts a number x to the basket, Misha should answer the question: is it possible to choose one or multiple numbers that already are in the basket, such that their XOR sum equals x?
If the answer is positive, you also need to give the indexes of these numbers. If there are multiple options of choosing numbers, you are allowed to choose any correct option. After Misha's answer the robot puts the number to the basket.
Initially the basket is empty. Each integer you put in the basket takes some number. The first integer you put into the basket take number 0, the second integer takes number 1 and so on.
Misha needs to clean up the place as soon as possible but unfortunately, he isn't that good at mathematics. He asks you to help him.
Input
The first line contains number m (1 β€ m β€ 2000), showing how many numbers are scattered around the room.
The next m lines contain the numbers in the order in which the robot puts them in the basket. Each number is a positive integer strictly less than 10600 that doesn't contain leading zeroes.
Output
For each number either print a 0 on the corresponding line, if the number cannot be represented as a XOR sum of numbers that are in the basket, or print integer k showing how many numbers are in the representation and the indexes of these numbers. Separate the numbers by spaces. Each number can occur in the representation at most once.
Examples
Input
7
7
6
5
4
3
2
1
Output
0
0
0
3 0 1 2
2 1 2
2 0 2
2 0 1
Input
2
5
5
Output
0
1 0
Note
The XOR sum of numbers is the result of bitwise sum of numbers modulo 2.
Submitted Solution:
```
m = int(input())
values = []
idx = []
for i in range(m):
x = int(input())
ans = 0
for j,xx in enumerate(values):
if (xx^x) < x:
x^=xx
ans^=idx[j]
if x == 0:
anss = []
for j,xx in enumerate(values):
if (ans&1)!=0:
anss.append(j)
ans>>=1
print(len(anss),*anss)
else:
print(0)
values.append(x)
idx.append(ans^(2**i))
```
No
| 95,668 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After Misha's birthday he had many large numbers left, scattered across the room. Now it's time to clean up and Misha needs to put them in a basket. He ordered this task to his pet robot that agreed to complete the task at certain conditions. Before the robot puts a number x to the basket, Misha should answer the question: is it possible to choose one or multiple numbers that already are in the basket, such that their XOR sum equals x?
If the answer is positive, you also need to give the indexes of these numbers. If there are multiple options of choosing numbers, you are allowed to choose any correct option. After Misha's answer the robot puts the number to the basket.
Initially the basket is empty. Each integer you put in the basket takes some number. The first integer you put into the basket take number 0, the second integer takes number 1 and so on.
Misha needs to clean up the place as soon as possible but unfortunately, he isn't that good at mathematics. He asks you to help him.
Input
The first line contains number m (1 β€ m β€ 2000), showing how many numbers are scattered around the room.
The next m lines contain the numbers in the order in which the robot puts them in the basket. Each number is a positive integer strictly less than 10600 that doesn't contain leading zeroes.
Output
For each number either print a 0 on the corresponding line, if the number cannot be represented as a XOR sum of numbers that are in the basket, or print integer k showing how many numbers are in the representation and the indexes of these numbers. Separate the numbers by spaces. Each number can occur in the representation at most once.
Examples
Input
7
7
6
5
4
3
2
1
Output
0
0
0
3 0 1 2
2 1 2
2 0 2
2 0 1
Input
2
5
5
Output
0
1 0
Note
The XOR sum of numbers is the result of bitwise sum of numbers modulo 2.
Submitted Solution:
```
buck = [[0, 0] for i in range(2500)]
m = int(input())
for i in range(m):
a = int(input())
ok = True
br = 1
for j in range(2500, -1, -1):
if a & (1 << j):
if(buck[j][0]):
a ^= buck[j][0]
br ^= buck[j][1]
else:
ok = False
buck[j][0] = a
buck[j][1] = br | (1 << i)
break
if not ok:
print("0")
else:
lst = []
for j in range(2501):
if br & (1 << j):
lst.append(j)
print(len(lst), end = ' ')
for j in lst:
print(j, end = ' ')
print('\n', end='')
```
No
| 95,669 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Tags: data structures, dp, greedy, implementation, sortings
Correct Solution:
```
#!/usr/bin/env python
# coding=utf-8
n = int(input())
l = []
for i in range(n):
x, y = map(int, input().split())
l += [(x + y, x - y)]
l.sort()
r = -2000000000
a = 0
for u in l:
if u[1] >= r:
a += 1
r = u[0]
print(a)
# Made By Mostafa_Khaled
```
| 95,670 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Tags: data structures, dp, greedy, implementation, sortings
Correct Solution:
```
def on(l1, l2):
return(abs(l1[0]-l2[0])>=l1[1]+l2[1])
n = int(input())
inf = []
for i in range(n):
a,b = map(int,input().split())
inf.append([a+b,a-b])
inf.sort()
res = 1
last = 0
for i in range(1,n):
if inf[i][1] >= inf[last][0]:
res+=1
last = i
print(res)
```
| 95,671 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Tags: data structures, dp, greedy, implementation, sortings
Correct Solution:
```
from sys import stdin,setrecursionlimit
import threading
def main():
n = int(stdin.readline())
line = []
for i in range(n):
x, w = [int(x) for x in stdin.readline().split()]
line.append((x-w,x+w))
line.sort()
def best(ind, line):
r = line[ind][1]
nxt = ind+1
while nxt < len(line):
nL, nR = line[nxt]
if nL >= r:
return best(nxt, line)+1
elif nR < r:
return best(nxt,line)
nxt += 1
return 1
print(best(0,line))
if __name__ == "__main__":
setrecursionlimit(10**6)
threading.stack_size(10**8)
t = threading.Thread(target=main)
t.start()
t.join()
```
| 95,672 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Tags: data structures, dp, greedy, implementation, sortings
Correct Solution:
```
from sys import stdin
from sys import stdout
from collections import defaultdict
n=int(stdin.readline())
a=[map(int,stdin.readline().split(),(10,10)) for i in range(n)]
v=defaultdict(list)
for i,e in enumerate(a,1):
q,f=e
v[q-f].append(i)
v[q+f-1].append(-i)
sa=set()
rez=0
for j in sorted(v.keys()):
for d in v[j]:
if d>0:
sa.add(d)
for d in v[j]:
if -d in sa:
sa.clear()
rez+=1
stdout.write(str(rez))
```
| 95,673 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Tags: data structures, dp, greedy, implementation, sortings
Correct Solution:
```
from operator import itemgetter
class CodeforcesTask528BSolution:
def __init__(self):
self.result = ''
self.n = 0
self.points = []
def read_input(self):
self.n = int(input())
for _ in range(self.n):
self.points.append([int(x) for x in input().split(" ")])
self.points[-1].append(sum(self.points[-1]))
def process_task(self):
self.points.sort(key=itemgetter(2))
last = 0
ans = 1
for i in range(1, self.n):
if self.points[i][0] - self.points[i][1] >= self.points[last][0] + self.points[last][1]:
last = i
ans += 1
self.result = str(ans)
def get_result(self):
return self.result
if __name__ == "__main__":
Solution = CodeforcesTask528BSolution()
Solution.read_input()
Solution.process_task()
print(Solution.get_result())
```
| 95,674 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Tags: data structures, dp, greedy, implementation, sortings
Correct Solution:
```
import sys
readline = sys.stdin.readline
def main():
N = int(input())
itvs = []
for _ in range(N):
x, w = map(int, input().split())
itvs.append((x - w, x + w))
itvs.sort(key=lambda x: x[1])
ans = 0
end = -(10**9 + 1)
for l, r in itvs:
if end <= l:
ans += 1
end = r
print(ans)
if __name__ == "__main__":
main()
```
| 95,675 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Tags: data structures, dp, greedy, implementation, sortings
Correct Solution:
```
from bisect import bisect
import sys
readlines = sys.stdin.buffer.readlines
readline = sys.stdin.buffer.readline
def solve(X,W):
'''
(X[j]>X[i]) and (X[j]-W[j] >= X[i]+W[i]) <=> i,j are connected
'''
XW = sorted((x,w) for x,w in zip(X,W))
dp = [2*10**9+1]*len(X)
n = 0
for x,w in XW:
i = bisect(dp,x-w,hi=n)
if x+w < dp[i]:
dp[i] = x+w
n += i==n
return n
if __name__ == '__main__':
n = int(readline())
X,W = [None]*n,[None]*n
for i,s in enumerate(readlines()):
x,w = map(int,s.split())
X[i] = x
W[i] = w
print(solve(X,W))
```
| 95,676 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Tags: data structures, dp, greedy, implementation, sortings
Correct Solution:
```
n = int(input())
d = []
for i in range(n):
xx, ww = [int(i) for i in input().split()]
d.append([xx-ww, xx+ww])
d.sort(key=lambda x:x[0])
last = -100000000000
ans = 0
for i in range(n):
if last <= d[i][0]:
last = d[i][1]
ans += 1
elif last > d[i][1]:
last = d[i][1]
print(ans)
```
| 95,677 |
Provide tags and a correct Python 2 solution for this coding contest problem.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Tags: data structures, dp, greedy, implementation, sortings
Correct Solution:
```
from sys import stdin, stdout
from collections import Counter, defaultdict
from itertools import permutations, combinations
from fractions import Fraction
raw_input = stdin.readline
pr = stdout.write
mod=10**9+7
def ni():
return int(raw_input())
def li():
return map(int,raw_input().split())
def pn(n):
stdout.write(str(n)+'\n')
def pa(arr):
pr(' '.join(map(str,arr))+'\n')
# fast read function for total integer input
def inp():
# this function returns whole input of
# space/line seperated integers
# Use Ctrl+D to flush stdin.
return map(int,stdin.read().split())
range = xrange # not for python 3.0+
# main code
n=ni()
l=[]
for i in range(n):
l.append(tuple(li()))
l.sort(key=lambda x:sum(x))
id=0
ans=1
for i in range(1,n):
if l[i][0]-l[i][1]>=sum(l[id]):
id=i
ans+=1
pn(ans)
```
| 95,678 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Submitted Solution:
```
def solve():
from sys import stdin
f_i = stdin
n = int(f_i.readline())
segments = []
for i in range(n):
x, w = map(int, f_i.readline().split())
segments.append((x + w, x - w)) # (end, start)
segments.sort()
ans = 0
t = segments[0][1]
for end, start in segments:
if t <= start:
ans += 1
t = end
print(ans)
solve()
```
Yes
| 95,679 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Submitted Solution:
```
import sys
n = int(input())
ranges = []
for xw in sys.stdin:
x, w = map(int, xw.split())
ranges.append((x + w, x - w))
ranges.sort()
result = 0
end = - float('inf')
for e, b in ranges:
if b >= end:
result += 1
end = e
print(result)
```
Yes
| 95,680 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Submitted Solution:
```
n = int(input())
ls= [list(map(int, input().split())) for i in range(n)]
lsr = [[max(ls[i][0]-ls[i][1], 0), ls[i][0]+ls[i][1]] for i in range(n)]
lsr.sort(key=lambda x: x[1])
idx = 0
ans = 0
for l in lsr:
if idx <= l[0]:
idx = l[1]
ans+=1
print(ans)
```
Yes
| 95,681 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Submitted Solution:
```
MOD = 10 ** 9 + 7
INF = 10 ** 10
import sys
sys.setrecursionlimit(100000000)
dy = (-1,0,1,0)
dx = (0,1,0,-1)
def main():
n = int(input())
P = [tuple(map(int,input().split())) for _ in range(n)]
P.sort(key = lambda x:sum(x))
ans = 0
X,W = -INF,0
for x,w in P:
if abs(x - X) >= W + w:
ans += 1
X = x
W = w
print(ans)
if __name__ == '__main__':
main()
```
Yes
| 95,682 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Submitted Solution:
```
# -*- coding: utf-8 -*-
"""
Created on Fri Feb 15 17:39:24 2019
@author: avina
"""
n = int(input())
l = []
for _ in range(n):
k,m = map(int, input().strip().split())
l.append((k,m))
l.sort(key=lambda x:x[0])
ma = 1
for i in range(n):
cou = 1
for j in range(n):
if abs(l[i][0] - l[j][0]) >= l[i][1] + l[i][1]:
cou+=1
ma = max(cou, ma)
print(ma)
```
No
| 95,683 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Submitted Solution:
```
import io
import os
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
n = int(input())
endpoints = []
for x in range(n):
p, w = map(int, input().split())
endpoints.append([p-w, p+w])
#bruh
endpoints.sort(key=lambda sublist: (-sublist[0], sublist[1]))
res = 0
#print(endpoints)
bottom = 10**18 * -1
for pt in range(len(endpoints)):
if endpoints[pt][0] >= bottom:
res += 1
bottom = endpoints[pt][1]
print(res)
```
No
| 95,684 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Submitted Solution:
```
# -*- coding: utf-8 -*-
"""
Created on Fri Feb 15 17:39:24 2019
@author: avina
"""
n = int(input())
l = []
for _ in range(n):
k,m = map(int, input().strip().split())
l.append((k,m))
l.sort(key=lambda x:x[0])
ma = 0
for i in range(n):
cou = 0
for j in range(n):
if abs(l[i][0] - l[j][0]) >= l[i][1] + l[i][1]:
cou+=1
ma = max(cou, ma)
print(ma)
```
No
| 95,685 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.
Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i, j), such that the distance between them is not less than the sum of their weights, or more formally: |xi - xj| β₯ wi + wj.
Find the size of the maximum clique in such graph.
Input
The first line contains the integer n (1 β€ n β€ 200 000) β the number of points.
Each of the next n lines contains two numbers xi, wi (0 β€ xi β€ 109, 1 β€ wi β€ 109) β the coordinate and the weight of a point. All xi are different.
Output
Print a single number β the number of vertexes in the maximum clique of the given graph.
Examples
Input
4
2 3
3 1
6 1
0 2
Output
3
Note
If you happen to know how to solve this problem without using the specific properties of the graph formulated in the problem statement, then you are able to get a prize of one million dollars!
The picture for the sample test.
<image>
Submitted Solution:
```
length = int(input())
root = []
vertices = []
for i in range(length):
a, b = map(int, input().split(" "))
s, e = a - b, a + b
root.append([s, 0])
root.append([e, 1])
root.sort()
ini_area = length
answer = 0
temp_v = 0
for i, v in enumerate(root):
if v[1] == 0:
temp_v += 1
answer = max(answer, min(temp_v + 1, ini_area + 1))
elif v[1] == 1:
ini_area -= 1
print(answer)
```
No
| 95,686 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and L, and they move towards each other with speed v1 and v2, respectively. Luke has width d and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive.
Input
The first line of the input contains four integers d, L, v1, v2 (1 β€ d, L, v1, v2 β€ 10 000, d < L) β Luke's width, the initial position of the second press and the speed of the first and second presses, respectively.
Output
Print a single real value β the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
2 6 2 2
Output
1.00000000000000000000
Input
1 9 1 2
Output
2.66666666666666650000
Note
In the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.
In the second sample he needs to occupy the position <image>. In this case both presses move to his edges at the same time.
Tags: math
Correct Solution:
```
# Input: d, L, v1, v2
# d = Lukes width
# L= position of second presser (first one is at 0)
# v1 = speed of first presser
# v2 = speed of second presser
# Output:
# Max time luke can curvive for
def saveLuke():
var = input().strip()
var = var.split(' ')
d = int(var[0])
L = int(var[1])
v1 = int(var[2])
v2 = int(var[3])
v = v1 + v2
s = L - d
print(s/v)
saveLuke()
```
| 95,687 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and L, and they move towards each other with speed v1 and v2, respectively. Luke has width d and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive.
Input
The first line of the input contains four integers d, L, v1, v2 (1 β€ d, L, v1, v2 β€ 10 000, d < L) β Luke's width, the initial position of the second press and the speed of the first and second presses, respectively.
Output
Print a single real value β the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
2 6 2 2
Output
1.00000000000000000000
Input
1 9 1 2
Output
2.66666666666666650000
Note
In the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.
In the second sample he needs to occupy the position <image>. In this case both presses move to his edges at the same time.
Tags: math
Correct Solution:
```
s = lambda: list(map(int,input().split()))
val = s()
print((val[1]-val[0])/(val[2]+val[3]))
```
| 95,688 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and L, and they move towards each other with speed v1 and v2, respectively. Luke has width d and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive.
Input
The first line of the input contains four integers d, L, v1, v2 (1 β€ d, L, v1, v2 β€ 10 000, d < L) β Luke's width, the initial position of the second press and the speed of the first and second presses, respectively.
Output
Print a single real value β the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
2 6 2 2
Output
1.00000000000000000000
Input
1 9 1 2
Output
2.66666666666666650000
Note
In the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.
In the second sample he needs to occupy the position <image>. In this case both presses move to his edges at the same time.
Tags: math
Correct Solution:
```
'''input
1 9 1 2
'''
d, l, v1, v2 = map(int, input().split())
print((l-d) / (v1+v2))
```
| 95,689 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and L, and they move towards each other with speed v1 and v2, respectively. Luke has width d and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive.
Input
The first line of the input contains four integers d, L, v1, v2 (1 β€ d, L, v1, v2 β€ 10 000, d < L) β Luke's width, the initial position of the second press and the speed of the first and second presses, respectively.
Output
Print a single real value β the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
2 6 2 2
Output
1.00000000000000000000
Input
1 9 1 2
Output
2.66666666666666650000
Note
In the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.
In the second sample he needs to occupy the position <image>. In this case both presses move to his edges at the same time.
Tags: math
Correct Solution:
```
x = input()
x = x.split()
d = int(x[0])
L = int(x[1])
v1 = int(x[2])
v2 = int(x[3])
ans = (L-d)/(v1+v2)
print (ans)
```
| 95,690 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and L, and they move towards each other with speed v1 and v2, respectively. Luke has width d and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive.
Input
The first line of the input contains four integers d, L, v1, v2 (1 β€ d, L, v1, v2 β€ 10 000, d < L) β Luke's width, the initial position of the second press and the speed of the first and second presses, respectively.
Output
Print a single real value β the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
2 6 2 2
Output
1.00000000000000000000
Input
1 9 1 2
Output
2.66666666666666650000
Note
In the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.
In the second sample he needs to occupy the position <image>. In this case both presses move to his edges at the same time.
Tags: math
Correct Solution:
```
d, L, v1, v2 = [int(s) for s in input().split(' ')]
print((L - d) / (v1 + v2))
```
| 95,691 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and L, and they move towards each other with speed v1 and v2, respectively. Luke has width d and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive.
Input
The first line of the input contains four integers d, L, v1, v2 (1 β€ d, L, v1, v2 β€ 10 000, d < L) β Luke's width, the initial position of the second press and the speed of the first and second presses, respectively.
Output
Print a single real value β the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
2 6 2 2
Output
1.00000000000000000000
Input
1 9 1 2
Output
2.66666666666666650000
Note
In the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.
In the second sample he needs to occupy the position <image>. In this case both presses move to his edges at the same time.
Tags: math
Correct Solution:
```
d, L, a1, a2 = map(int, input().split())
print ((L - d) / (a1+a2))
```
| 95,692 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and L, and they move towards each other with speed v1 and v2, respectively. Luke has width d and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive.
Input
The first line of the input contains four integers d, L, v1, v2 (1 β€ d, L, v1, v2 β€ 10 000, d < L) β Luke's width, the initial position of the second press and the speed of the first and second presses, respectively.
Output
Print a single real value β the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
2 6 2 2
Output
1.00000000000000000000
Input
1 9 1 2
Output
2.66666666666666650000
Note
In the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.
In the second sample he needs to occupy the position <image>. In this case both presses move to his edges at the same time.
Tags: math
Correct Solution:
```
string = input()
numbers = list(map(int, string.split()))
a = numbers[0]
b = numbers[1]
v1 = numbers[2]
v2 = numbers[3]
print((b - a) / (v1 + v2))
```
| 95,693 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and L, and they move towards each other with speed v1 and v2, respectively. Luke has width d and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive.
Input
The first line of the input contains four integers d, L, v1, v2 (1 β€ d, L, v1, v2 β€ 10 000, d < L) β Luke's width, the initial position of the second press and the speed of the first and second presses, respectively.
Output
Print a single real value β the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
2 6 2 2
Output
1.00000000000000000000
Input
1 9 1 2
Output
2.66666666666666650000
Note
In the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.
In the second sample he needs to occupy the position <image>. In this case both presses move to his edges at the same time.
Tags: math
Correct Solution:
```
import sys
def main():
d, l, v1, v2 = map(int, input().split())
t = (l - d) / (v1 + v2)
print("{0:.7f}".format(t))
main()
```
| 95,694 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and L, and they move towards each other with speed v1 and v2, respectively. Luke has width d and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive.
Input
The first line of the input contains four integers d, L, v1, v2 (1 β€ d, L, v1, v2 β€ 10 000, d < L) β Luke's width, the initial position of the second press and the speed of the first and second presses, respectively.
Output
Print a single real value β the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
2 6 2 2
Output
1.00000000000000000000
Input
1 9 1 2
Output
2.66666666666666650000
Note
In the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.
In the second sample he needs to occupy the position <image>. In this case both presses move to his edges at the same time.
Submitted Solution:
```
width, right, v1, v2=map(int, input().split())
left=0;t=0
##Here distance between the blocks are decreased at a speed of v1+v2##
d=right-width
v=v1+v2
##The required distance to decrease will be right(L)-0, and Luke has a width, the distance travelled by presses would be L-d
##[Simple Physics]
print(d/v)
```
Yes
| 95,695 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and L, and they move towards each other with speed v1 and v2, respectively. Luke has width d and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive.
Input
The first line of the input contains four integers d, L, v1, v2 (1 β€ d, L, v1, v2 β€ 10 000, d < L) β Luke's width, the initial position of the second press and the speed of the first and second presses, respectively.
Output
Print a single real value β the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
2 6 2 2
Output
1.00000000000000000000
Input
1 9 1 2
Output
2.66666666666666650000
Note
In the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.
In the second sample he needs to occupy the position <image>. In this case both presses move to his edges at the same time.
Submitted Solution:
```
d , L , s1 , s2 = map(int,input().strip().split())
ans = (L-d)/(s1+s2)
print(ans)
```
Yes
| 95,696 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and L, and they move towards each other with speed v1 and v2, respectively. Luke has width d and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive.
Input
The first line of the input contains four integers d, L, v1, v2 (1 β€ d, L, v1, v2 β€ 10 000, d < L) β Luke's width, the initial position of the second press and the speed of the first and second presses, respectively.
Output
Print a single real value β the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
2 6 2 2
Output
1.00000000000000000000
Input
1 9 1 2
Output
2.66666666666666650000
Note
In the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.
In the second sample he needs to occupy the position <image>. In this case both presses move to his edges at the same time.
Submitted Solution:
```
R = lambda : map(int, input().split())
d,L,v1,v2 = R()
print((L-d)/(v2+v1))
```
Yes
| 95,697 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and L, and they move towards each other with speed v1 and v2, respectively. Luke has width d and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive.
Input
The first line of the input contains four integers d, L, v1, v2 (1 β€ d, L, v1, v2 β€ 10 000, d < L) β Luke's width, the initial position of the second press and the speed of the first and second presses, respectively.
Output
Print a single real value β the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
2 6 2 2
Output
1.00000000000000000000
Input
1 9 1 2
Output
2.66666666666666650000
Note
In the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.
In the second sample he needs to occupy the position <image>. In this case both presses move to his edges at the same time.
Submitted Solution:
```
def solve(d, L, v1, v2):
return (v1*(L - d))/(v1 + v2)/v1
def main():
d, L, v1, v2 = list(map(int, input().split()))
print(solve(d, L, v1, v2))
main()
```
Yes
| 95,698 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and L, and they move towards each other with speed v1 and v2, respectively. Luke has width d and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive.
Input
The first line of the input contains four integers d, L, v1, v2 (1 β€ d, L, v1, v2 β€ 10 000, d < L) β Luke's width, the initial position of the second press and the speed of the first and second presses, respectively.
Output
Print a single real value β the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.
Examples
Input
2 6 2 2
Output
1.00000000000000000000
Input
1 9 1 2
Output
2.66666666666666650000
Note
In the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.
In the second sample he needs to occupy the position <image>. In this case both presses move to his edges at the same time.
Submitted Solution:
```
d,L,v1,v2 = list(map(int,input().split()))
k=v1+v2
s1=(L/(v1+v2))*v1
s2=(L/(v1+v2))*v2
t1i=s1/v1
t2i=s2/v2
t1k=((d/(v1+v2))*v1)
t2k=((d/(v1+v2))*v2)
su1=(t1i+t2i)
su2=(t1k+t2k)
ras=su1-su2
print(ras)
```
No
| 95,699 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.