message stringlengths 2 433k | message_type stringclasses 2
values | message_id int64 0 1 | conversation_id int64 113 108k | cluster float64 12 12 | __index_level_0__ int64 226 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got another problem dealing with arrays. Let's consider an arbitrary sequence containing n (not necessarily different) integers a1, a2, ..., an. We are interested in all possible pairs of numbers (ai, aj), (1 β€ i, j β€ n). In other words, let's consider all n2 pairs of numbers, picked from the given array.
For example, in sequence a = {3, 1, 5} are 9 pairs of numbers: (3, 3), (3, 1), (3, 5), (1, 3), (1, 1), (1, 5), (5, 3), (5, 1), (5, 5).
Let's sort all resulting pairs lexicographically by non-decreasing. Let us remind you that pair (p1, q1) is lexicographically less than pair (p2, q2) only if either p1 < p2, or p1 = p2 and q1 < q2.
Then the sequence, mentioned above, will be sorted like that: (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)
Let's number all the pair in the sorted list from 1 to n2. Your task is formulated like this: you should find the k-th pair in the ordered list of all possible pairs of the array you've been given.
Input
The first line contains two integers n and k (1 β€ n β€ 105, 1 β€ k β€ n2). The second line contains the array containing n integers a1, a2, ..., an ( - 109 β€ ai β€ 109). The numbers in the array can coincide. All numbers are separated with spaces.
Please do not use the %lld specificator to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout, streams or the %I64d specificator instead.
Output
In the single line print two numbers β the sought k-th pair.
Examples
Input
2 4
2 1
Output
2 2
Input
3 2
3 1 5
Output
1 3
Note
In the first sample the sorted sequence for the given array looks as: (1, 1), (1, 2), (2, 1), (2, 2). The 4-th of them is pair (2, 2).
The sorted sequence for the array from the second sample is given in the statement. The 2-nd pair there is (1, 3).
Submitted Solution:
```
import sys
INF = 10**20
MOD = 10**9 + 7
I = lambda:list(map(int,input().split()))
from math import gcd
from math import ceil
from collections import defaultdict as dd, Counter
from bisect import bisect_left as bl, bisect_right as br
"""
Facts and Data representation
Constructive? Top bottom up down
"""
n, k = I()
a = sorted(I())
cnt = dd(int)
for i in a:
cnt[i] += 1
cur = 0
for i in sorted(cnt.keys()):
cur += cnt[i] * n
if cur < k:
continue
ans = [0, 0]
cur -= cnt[i] * n
r = k - cur
ans[0] = i
ans[1] = a[(r - 1) // cnt[i]]
break
print(*ans)
``` | instruction | 0 | 71,923 | 12 | 143,846 |
Yes | output | 1 | 71,923 | 12 | 143,847 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got another problem dealing with arrays. Let's consider an arbitrary sequence containing n (not necessarily different) integers a1, a2, ..., an. We are interested in all possible pairs of numbers (ai, aj), (1 β€ i, j β€ n). In other words, let's consider all n2 pairs of numbers, picked from the given array.
For example, in sequence a = {3, 1, 5} are 9 pairs of numbers: (3, 3), (3, 1), (3, 5), (1, 3), (1, 1), (1, 5), (5, 3), (5, 1), (5, 5).
Let's sort all resulting pairs lexicographically by non-decreasing. Let us remind you that pair (p1, q1) is lexicographically less than pair (p2, q2) only if either p1 < p2, or p1 = p2 and q1 < q2.
Then the sequence, mentioned above, will be sorted like that: (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)
Let's number all the pair in the sorted list from 1 to n2. Your task is formulated like this: you should find the k-th pair in the ordered list of all possible pairs of the array you've been given.
Input
The first line contains two integers n and k (1 β€ n β€ 105, 1 β€ k β€ n2). The second line contains the array containing n integers a1, a2, ..., an ( - 109 β€ ai β€ 109). The numbers in the array can coincide. All numbers are separated with spaces.
Please do not use the %lld specificator to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout, streams or the %I64d specificator instead.
Output
In the single line print two numbers β the sought k-th pair.
Examples
Input
2 4
2 1
Output
2 2
Input
3 2
3 1 5
Output
1 3
Note
In the first sample the sorted sequence for the given array looks as: (1, 1), (1, 2), (2, 1), (2, 2). The 4-th of them is pair (2, 2).
The sorted sequence for the array from the second sample is given in the statement. The 2-nd pair there is (1, 3).
Submitted Solution:
```
n,k=map(int,input().split())
ar=list(map(int,input().split()))
ar=sorted(ar)
summ=0
flag=True
for i in range(n):
if (i+1)*n>=k:
break
x=ar.count(ar[i])
c=ar.index(ar[i])
y=((k-1)-c*n)//x
print(ar[i],ar[y])
``` | instruction | 0 | 71,924 | 12 | 143,848 |
Yes | output | 1 | 71,924 | 12 | 143,849 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got another problem dealing with arrays. Let's consider an arbitrary sequence containing n (not necessarily different) integers a1, a2, ..., an. We are interested in all possible pairs of numbers (ai, aj), (1 β€ i, j β€ n). In other words, let's consider all n2 pairs of numbers, picked from the given array.
For example, in sequence a = {3, 1, 5} are 9 pairs of numbers: (3, 3), (3, 1), (3, 5), (1, 3), (1, 1), (1, 5), (5, 3), (5, 1), (5, 5).
Let's sort all resulting pairs lexicographically by non-decreasing. Let us remind you that pair (p1, q1) is lexicographically less than pair (p2, q2) only if either p1 < p2, or p1 = p2 and q1 < q2.
Then the sequence, mentioned above, will be sorted like that: (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)
Let's number all the pair in the sorted list from 1 to n2. Your task is formulated like this: you should find the k-th pair in the ordered list of all possible pairs of the array you've been given.
Input
The first line contains two integers n and k (1 β€ n β€ 105, 1 β€ k β€ n2). The second line contains the array containing n integers a1, a2, ..., an ( - 109 β€ ai β€ 109). The numbers in the array can coincide. All numbers are separated with spaces.
Please do not use the %lld specificator to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout, streams or the %I64d specificator instead.
Output
In the single line print two numbers β the sought k-th pair.
Examples
Input
2 4
2 1
Output
2 2
Input
3 2
3 1 5
Output
1 3
Note
In the first sample the sorted sequence for the given array looks as: (1, 1), (1, 2), (2, 1), (2, 2). The 4-th of them is pair (2, 2).
The sorted sequence for the array from the second sample is given in the statement. The 2-nd pair there is (1, 3).
Submitted Solution:
```
from sys import stdin, stdout
def read_ints():
return map(int, stdin.readline().split(' '))
n, k = read_ints()
a = list(read_ints())
a.sort()
l = (k - 1) // n
lo = l
while lo > 0 and a[lo - 1] == a[lo]:
lo -= 1
hi = l
while hi + 1 < n and a[hi + 1] == a[hi]:
hi += 1
length = hi - lo + 1
acc = k - lo * n
r = (acc - 1) // length
stdout.write('{} {}'.format(a[l], a[r]))
``` | instruction | 0 | 71,925 | 12 | 143,850 |
Yes | output | 1 | 71,925 | 12 | 143,851 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got another problem dealing with arrays. Let's consider an arbitrary sequence containing n (not necessarily different) integers a1, a2, ..., an. We are interested in all possible pairs of numbers (ai, aj), (1 β€ i, j β€ n). In other words, let's consider all n2 pairs of numbers, picked from the given array.
For example, in sequence a = {3, 1, 5} are 9 pairs of numbers: (3, 3), (3, 1), (3, 5), (1, 3), (1, 1), (1, 5), (5, 3), (5, 1), (5, 5).
Let's sort all resulting pairs lexicographically by non-decreasing. Let us remind you that pair (p1, q1) is lexicographically less than pair (p2, q2) only if either p1 < p2, or p1 = p2 and q1 < q2.
Then the sequence, mentioned above, will be sorted like that: (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)
Let's number all the pair in the sorted list from 1 to n2. Your task is formulated like this: you should find the k-th pair in the ordered list of all possible pairs of the array you've been given.
Input
The first line contains two integers n and k (1 β€ n β€ 105, 1 β€ k β€ n2). The second line contains the array containing n integers a1, a2, ..., an ( - 109 β€ ai β€ 109). The numbers in the array can coincide. All numbers are separated with spaces.
Please do not use the %lld specificator to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout, streams or the %I64d specificator instead.
Output
In the single line print two numbers β the sought k-th pair.
Examples
Input
2 4
2 1
Output
2 2
Input
3 2
3 1 5
Output
1 3
Note
In the first sample the sorted sequence for the given array looks as: (1, 1), (1, 2), (2, 1), (2, 2). The 4-th of them is pair (2, 2).
The sorted sequence for the array from the second sample is given in the statement. The 2-nd pair there is (1, 3).
Submitted Solution:
```
# your code goes here
n, k = map(int, input().split())
series = list(map(int, input().split()))
series.sort()
digit1 = series[(k-1)//n]
ind, cnt = series.index(digit1), series.count(digit1)
digit2_ind = ((k-1) - ind * n)//cnt
digit2 = series[digit2_ind]
print(digit1,digit2)
``` | instruction | 0 | 71,926 | 12 | 143,852 |
Yes | output | 1 | 71,926 | 12 | 143,853 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got another problem dealing with arrays. Let's consider an arbitrary sequence containing n (not necessarily different) integers a1, a2, ..., an. We are interested in all possible pairs of numbers (ai, aj), (1 β€ i, j β€ n). In other words, let's consider all n2 pairs of numbers, picked from the given array.
For example, in sequence a = {3, 1, 5} are 9 pairs of numbers: (3, 3), (3, 1), (3, 5), (1, 3), (1, 1), (1, 5), (5, 3), (5, 1), (5, 5).
Let's sort all resulting pairs lexicographically by non-decreasing. Let us remind you that pair (p1, q1) is lexicographically less than pair (p2, q2) only if either p1 < p2, or p1 = p2 and q1 < q2.
Then the sequence, mentioned above, will be sorted like that: (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)
Let's number all the pair in the sorted list from 1 to n2. Your task is formulated like this: you should find the k-th pair in the ordered list of all possible pairs of the array you've been given.
Input
The first line contains two integers n and k (1 β€ n β€ 105, 1 β€ k β€ n2). The second line contains the array containing n integers a1, a2, ..., an ( - 109 β€ ai β€ 109). The numbers in the array can coincide. All numbers are separated with spaces.
Please do not use the %lld specificator to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout, streams or the %I64d specificator instead.
Output
In the single line print two numbers β the sought k-th pair.
Examples
Input
2 4
2 1
Output
2 2
Input
3 2
3 1 5
Output
1 3
Note
In the first sample the sorted sequence for the given array looks as: (1, 1), (1, 2), (2, 1), (2, 2). The 4-th of them is pair (2, 2).
The sorted sequence for the array from the second sample is given in the statement. The 2-nd pair there is (1, 3).
Submitted Solution:
```
import math
from os import curdir, startfile
import random
from queue import Queue
import time
import heapq
import sys
def main(arr,k):
n=len(arr)
arr.sort()
val=1
first=k//n-val if k%n==0 else k//n
second=k%n-1
if second==-1:
second=first
print(arr[first],arr[second])
n,k=list(map(int,input().split()))
arr=list(map(int,input().split()))
main(arr,k)
``` | instruction | 0 | 71,927 | 12 | 143,854 |
No | output | 1 | 71,927 | 12 | 143,855 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got another problem dealing with arrays. Let's consider an arbitrary sequence containing n (not necessarily different) integers a1, a2, ..., an. We are interested in all possible pairs of numbers (ai, aj), (1 β€ i, j β€ n). In other words, let's consider all n2 pairs of numbers, picked from the given array.
For example, in sequence a = {3, 1, 5} are 9 pairs of numbers: (3, 3), (3, 1), (3, 5), (1, 3), (1, 1), (1, 5), (5, 3), (5, 1), (5, 5).
Let's sort all resulting pairs lexicographically by non-decreasing. Let us remind you that pair (p1, q1) is lexicographically less than pair (p2, q2) only if either p1 < p2, or p1 = p2 and q1 < q2.
Then the sequence, mentioned above, will be sorted like that: (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)
Let's number all the pair in the sorted list from 1 to n2. Your task is formulated like this: you should find the k-th pair in the ordered list of all possible pairs of the array you've been given.
Input
The first line contains two integers n and k (1 β€ n β€ 105, 1 β€ k β€ n2). The second line contains the array containing n integers a1, a2, ..., an ( - 109 β€ ai β€ 109). The numbers in the array can coincide. All numbers are separated with spaces.
Please do not use the %lld specificator to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout, streams or the %I64d specificator instead.
Output
In the single line print two numbers β the sought k-th pair.
Examples
Input
2 4
2 1
Output
2 2
Input
3 2
3 1 5
Output
1 3
Note
In the first sample the sorted sequence for the given array looks as: (1, 1), (1, 2), (2, 1), (2, 2). The 4-th of them is pair (2, 2).
The sorted sequence for the array from the second sample is given in the statement. The 2-nd pair there is (1, 3).
Submitted Solution:
```
n,b=map(int,input().split())
l=list(map(int,input().split()))
b-=1
l.sort()
c=b//n
e=b%n
print(l[c],l[e])
``` | instruction | 0 | 71,928 | 12 | 143,856 |
No | output | 1 | 71,928 | 12 | 143,857 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got another problem dealing with arrays. Let's consider an arbitrary sequence containing n (not necessarily different) integers a1, a2, ..., an. We are interested in all possible pairs of numbers (ai, aj), (1 β€ i, j β€ n). In other words, let's consider all n2 pairs of numbers, picked from the given array.
For example, in sequence a = {3, 1, 5} are 9 pairs of numbers: (3, 3), (3, 1), (3, 5), (1, 3), (1, 1), (1, 5), (5, 3), (5, 1), (5, 5).
Let's sort all resulting pairs lexicographically by non-decreasing. Let us remind you that pair (p1, q1) is lexicographically less than pair (p2, q2) only if either p1 < p2, or p1 = p2 and q1 < q2.
Then the sequence, mentioned above, will be sorted like that: (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)
Let's number all the pair in the sorted list from 1 to n2. Your task is formulated like this: you should find the k-th pair in the ordered list of all possible pairs of the array you've been given.
Input
The first line contains two integers n and k (1 β€ n β€ 105, 1 β€ k β€ n2). The second line contains the array containing n integers a1, a2, ..., an ( - 109 β€ ai β€ 109). The numbers in the array can coincide. All numbers are separated with spaces.
Please do not use the %lld specificator to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout, streams or the %I64d specificator instead.
Output
In the single line print two numbers β the sought k-th pair.
Examples
Input
2 4
2 1
Output
2 2
Input
3 2
3 1 5
Output
1 3
Note
In the first sample the sorted sequence for the given array looks as: (1, 1), (1, 2), (2, 1), (2, 2). The 4-th of them is pair (2, 2).
The sorted sequence for the array from the second sample is given in the statement. The 2-nd pair there is (1, 3).
Submitted Solution:
```
# https://codeforces.com/contest/160/problem/C
"""
Sort the list. The lexicographic order will look like
(a1, a1), ..., (a1, an)
...
(an, a1), ..., (an, an)
Hence we simply need to find the quotient remainder theorem form on k-1 and n.
k-1 = p*n + q. (k-1 as counting from 0.)
"""
n, k = map(int, input().split())
a = sorted(map(int, input().split()))
q = (k - 1) % n
p = (k - 1 - q) // n
print(a[p], a[q])
``` | instruction | 0 | 71,929 | 12 | 143,858 |
No | output | 1 | 71,929 | 12 | 143,859 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got another problem dealing with arrays. Let's consider an arbitrary sequence containing n (not necessarily different) integers a1, a2, ..., an. We are interested in all possible pairs of numbers (ai, aj), (1 β€ i, j β€ n). In other words, let's consider all n2 pairs of numbers, picked from the given array.
For example, in sequence a = {3, 1, 5} are 9 pairs of numbers: (3, 3), (3, 1), (3, 5), (1, 3), (1, 1), (1, 5), (5, 3), (5, 1), (5, 5).
Let's sort all resulting pairs lexicographically by non-decreasing. Let us remind you that pair (p1, q1) is lexicographically less than pair (p2, q2) only if either p1 < p2, or p1 = p2 and q1 < q2.
Then the sequence, mentioned above, will be sorted like that: (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)
Let's number all the pair in the sorted list from 1 to n2. Your task is formulated like this: you should find the k-th pair in the ordered list of all possible pairs of the array you've been given.
Input
The first line contains two integers n and k (1 β€ n β€ 105, 1 β€ k β€ n2). The second line contains the array containing n integers a1, a2, ..., an ( - 109 β€ ai β€ 109). The numbers in the array can coincide. All numbers are separated with spaces.
Please do not use the %lld specificator to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout, streams or the %I64d specificator instead.
Output
In the single line print two numbers β the sought k-th pair.
Examples
Input
2 4
2 1
Output
2 2
Input
3 2
3 1 5
Output
1 3
Note
In the first sample the sorted sequence for the given array looks as: (1, 1), (1, 2), (2, 1), (2, 2). The 4-th of them is pair (2, 2).
The sorted sequence for the array from the second sample is given in the statement. The 2-nd pair there is (1, 3).
Submitted Solution:
```
from math import ceil,floor
n,k = map(int,input().split())
a = list(map(int,input().split()))
a.sort()
x = ceil(k/n)
m = k%n
print(a[x-1],a[m-1])
``` | instruction | 0 | 71,930 | 12 | 143,860 |
No | output | 1 | 71,930 | 12 | 143,861 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3 | instruction | 0 | 71,987 | 12 | 143,974 |
Tags: brute force, implementation, math
Correct Solution:
```
n=int(input())
l=list(map(int,input().split()))
k,t=0,0
for i in range(n):
if i == l[i]:k+=1
elif i == l[l[i]]:t=1
print(min(k+1+t,n))
``` | output | 1 | 71,987 | 12 | 143,975 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3 | instruction | 0 | 71,988 | 12 | 143,976 |
Tags: brute force, implementation, math
Correct Solution:
```
def main():
n = map(int,input().split())
a = list(map(int,input().split()))
cnt = 0
for i in range(len(a)):
if a[i]==i:
cnt+=1
if cnt==len(a):
print(cnt)
return
for i in range(len(a)):
if a[i]!=i:
if i==a[a[i]]:
print(cnt+2)
return
print(cnt+1)
return
main()
``` | output | 1 | 71,988 | 12 | 143,977 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3 | instruction | 0 | 71,989 | 12 | 143,978 |
Tags: brute force, implementation, math
Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
c=0
f=0
for i in range(n):
if a[i]==i:
c+=1
for i in range(n):
if a[i]!=i:
if a[a[i]]==i:
f=1
break
if f==0 and c!=n:
c+=1
elif f==1 and c!=n:
c+=2
print(c)
``` | output | 1 | 71,989 | 12 | 143,979 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3 | instruction | 0 | 71,990 | 12 | 143,980 |
Tags: brute force, implementation, math
Correct Solution:
```
n = int(input())
a = [int(i) for i in input().split()]
count = 0
add = 0
for i in range(n):
if (a[i] == i):
count += 1
else:
if (a[a[i]] == i):
add = 1
if (count != n):
add += 1
print (count + add)
``` | output | 1 | 71,990 | 12 | 143,981 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3 | instruction | 0 | 71,991 | 12 | 143,982 |
Tags: brute force, implementation, math
Correct Solution:
```
n=int(input());a=list(map(int,input().split()));o,ot=0,0
for i in range(n):
if(a[i]==i):o+=1
for i in range(n):
if(a[i]!=i):
if(i==a[a[i]]):ot=2
else:ot=max(ot,1)
print(ot+o)
``` | output | 1 | 71,991 | 12 | 143,983 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3 | instruction | 0 | 71,992 | 12 | 143,984 |
Tags: brute force, implementation, math
Correct Solution:
```
n=int(input())
a=[int(num) for num in input().split()]
max=0
flag=0
for i in range(0,n):
if a[i]==i:
max=max+1
elif a[a[i]]==i and flag!=1:
temp=a[i]
a[i]=a[temp]
a[temp]=temp
max=max+1
flag=1
elif flag!=1:
flag=2
if flag==2:
max=max+1
print(max)
``` | output | 1 | 71,992 | 12 | 143,985 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3 | instruction | 0 | 71,993 | 12 | 143,986 |
Tags: brute force, implementation, math
Correct Solution:
```
def fixed_points(n, a):
count = 0
fixed = 0
for i, j in enumerate(a):
if i == j:
fixed += 1
elif a[j] == i:
count = 2
elif count == 0:
count = 1
return fixed + count
if __name__ == "__main__":
n = int(input())
a = list(map(int, input().split()))
result = fixed_points(n, a)
print(result)
``` | output | 1 | 71,993 | 12 | 143,987 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3 | instruction | 0 | 71,994 | 12 | 143,988 |
Tags: brute force, implementation, math
Correct Solution:
```
s, k, n = 0, 0, int(input())
t = list(map(int, input().split()))
for i in range(n):
if i == t[i]: s += 1
elif k < 2:
if t[t[i]] == i: k = 2
else: k = 1
print(s + k)
``` | output | 1 | 71,994 | 12 | 143,989 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3
Submitted Solution:
```
n = int(input())
l = list(map(int, input().split(' ')))
certos = 0
achou_2 = False
errados = 0
for i in range(len(l)):
if l[i] == i:
certos += 1
else:
errados += 1
if l[l[i]] == i:
achou_2 = True
if errados > 1:
if achou_2:
certos += 2
else:
certos += 1
print(certos)
# 1518733072890
``` | instruction | 0 | 71,995 | 12 | 143,990 |
Yes | output | 1 | 71,995 | 12 | 143,991 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
ans = 0
ans1 = 0
for i in range(len(a)):
if a[i] == i:
ans += 1
ans1 += 1
if ans != n:
for i in range(len(a)):
if a[i] != i:
if a[a[i]] == i:
ans += 2
break
if ans == ans1:
ans += 1
print(ans)
``` | instruction | 0 | 71,996 | 12 | 143,992 |
Yes | output | 1 | 71,996 | 12 | 143,993 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3
Submitted Solution:
```
from sys import stdin
def max_nb_fixed_points(n, permutation):
pos_for_val = {}
initial_fixed = 0
double_swap = False
single_swap = False
for i in range(n):
if i == permutation[i]:
initial_fixed += 1
continue
if not double_swap:
if i in pos_for_val:
j = pos_for_val[i]
if permutation[i] == j:
double_swap = True
else:
single_swap = True
pos_for_val[permutation[i]] = i
if double_swap:
return initial_fixed + 2
if single_swap:
return initial_fixed + 1
return initial_fixed
if __name__ == "__main__":
n = int(stdin.readline())
permutation = [int(c) for c in stdin.readline().split(" ")]
print(max_nb_fixed_points(n, permutation))
``` | instruction | 0 | 71,997 | 12 | 143,994 |
Yes | output | 1 | 71,997 | 12 | 143,995 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3
Submitted Solution:
```
def solve (n,seq) :
times = 0
temp_fixed = 0
done = 0
s = list(enumerate(seq))
for i,j in s :
if i == j :
times += 1
elif done == 0 :
if s[j][1] == i and j == s[j][0] :
temp_fixed = 2
done = 1
elif s[j][1] == i or j == s[j][0] :
temp_fixed = 1
return times + temp_fixed
n = int(input())
seq = list(map(int,input().split()))
print (solve(n,seq))
``` | instruction | 0 | 71,998 | 12 | 143,996 |
Yes | output | 1 | 71,998 | 12 | 143,997 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3
Submitted Solution:
```
n = int(input())
ai = list(map(int,input().split()))
cnt = 0
for i in range(0,len(ai)):
if ai[i] <= i:
cnt += 1
print(cnt)
``` | instruction | 0 | 71,999 | 12 | 143,998 |
No | output | 1 | 71,999 | 12 | 143,999 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3
Submitted Solution:
```
n = int(input())
a = []
inp = input()
a = [int(x) for x in inp.split(' ')]
result = 0
swaped = False
for i in range(len(a)):
if i == a[i]:
result += 1
if a[a[i]] == i:
result += 2
swaped = True
break
if swaped:
pass
else:
result +=1
print(result)
``` | instruction | 0 | 72,000 | 12 | 144,000 |
No | output | 1 | 72,000 | 12 | 144,001 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3
Submitted Solution:
```
# import math
# import bisect
import sys
from collections import Counter
input = sys.stdin.readline
def inp():
return(int(input()))
def inlt():
return(list(map(int,input().split())))
def insr():
s = input()
return(s[:len(s)-1])
def invr():
return(map(int,input().split()))
# list1, list2 = zip(*sorted(zip(list1, list2)))
N = inp()
L = inlt()
out = 0
fl = True
for n in range(N):
if n == L[n]:
out += 1
if fl and L[L[n]] == n:
out += 1
fl = False
print(out)
``` | instruction | 0 | 72,001 | 12 | 144,002 |
No | output | 1 | 72,001 | 12 | 144,003 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, sequence [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer i is a fixed point of permutation a0, a1, ..., an - 1 if and only if ai = i. For example, permutation [0, 2, 1] has 1 fixed point and permutation [0, 1, 2] has 3 fixed points.
You are given permutation a. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation.
Input
The first line contains a single integer n (1 β€ n β€ 105). The second line contains n integers a0, a1, ..., an - 1 β the given permutation.
Output
Print a single integer β the maximum possible number of fixed points in the permutation after at most one swap operation.
Examples
Input
5
0 1 3 4 2
Output
3
Submitted Solution:
```
x=int(input())
x=input().split()
y=[int(p) for p in x]
fpts=[]
nfpts=[]
for x in y:
if( x==y.index(x)):
fpts.append(x)
else:nfpts.append(x)
for x in nfpts :
if(y[x]==y.index(x)):
print(len(fpts)+2)
break;
else:
print(len(fpts)+1)
if(len(nfpts)==0):
print(len(fpts))
``` | instruction | 0 | 72,002 | 12 | 144,004 |
No | output | 1 | 72,002 | 12 | 144,005 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A permutation p of length n is a sequence of distinct integers p1, p2, ..., pn (1 β€ pi β€ n). A permutation is an identity permutation, if for any i the following equation holds pi = i.
A swap (i, j) is the operation that swaps elements pi and pj in the permutation. Let's assume that f(p) is the minimum number of swaps that you need to make the permutation p an identity permutation.
Valera wonders, how he can transform permutation p into any permutation q, such that f(q) = m, using the minimum number of swaps. Help him do that.
Input
The first line contains integer n (1 β€ n β€ 3000) β the length of permutation p. The second line contains n distinct integers p1, p2, ..., pn (1 β€ pi β€ n) β Valera's initial permutation. The last line contains integer m (0 β€ m < n).
Output
In the first line, print integer k β the minimum number of swaps.
In the second line, print 2k integers x1, x2, ..., x2k β the description of the swap sequence. The printed numbers show that you need to consecutively make swaps (x1, x2), (x3, x4), ..., (x2k - 1, x2k).
If there are multiple sequence swaps of the minimum length, print the lexicographically minimum one.
Examples
Input
5
1 2 3 4 5
2
Output
2
1 2 1 3
Input
5
2 1 4 5 3
2
Output
1
1 2
Note
Sequence x1, x2, ..., xs is lexicographically smaller than sequence y1, y2, ..., ys, if there is such integer r (1 β€ r β€ s), that x1 = y1, x2 = y2, ..., xr - 1 = yr - 1 and xr < yr.
Submitted Solution:
```
n=int(input())
L=list(map(int,input().split()))
Pos=[0]*n
y=0
for i in range(n):
L[i]-=1
Pos[L[i]]=i
if(L[i]!=i):
y+=1
Ans=[]
m=int(input())
Ans=[]
if(y>m+1 and n!=1):
e=y-m-1
while(e>=1):
q1=0
while(L[q1]==q1):
q1+=1
q2=q1+1
cont=False
while(cont or L[q2]==q2):
cont=False
q2+=1
if(q2!=L[q2] and L[q2]==q1 and e==1):
cont=True
numx=L[q1]
posx=q1
numy=L[q2]
posy=q2
if(posx==numy):
e-=2
Ans.append((posx,posy))
L[numx]=numx
Pos[numx]=numx
L[numy]=numy
Pos[numy]=numy
else:
e-=1
Ans.append((posx,posy))
L[numx]=numx
Pos[numx]=numx
L[posx]=numy
Pos[numy]=posx
if(y<m+1 and n!=1):
e=m+1-y
while(e>=1):
q1=0
while(L[q1]!=q1):
q1+=1
q2=q1+1
cont=True
q2=0
while(1):
if(q2==q1):
q2+=1
continue
if(L[q2]==q2 and e==1):
q2+=1
continue
break
numx=L[q1]
posx=q1
numy=L[q2]
posy=q2
b=min(posx,posy)
c=max(posx,posy)
Ans.append((b,c))
L[posx],L[posy]=L[posy],L[posx]
Pos[numx],Pos[numy]=Pos[numy],Pos[numx]
e-=2
print(len(Ans))
for i in range(len(Ans)):
print(Ans[i][0]+1,Ans[i][1]+1,end=" ")
``` | instruction | 0 | 72,033 | 12 | 144,066 |
No | output | 1 | 72,033 | 12 | 144,067 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A permutation p of length n is a sequence of distinct integers p1, p2, ..., pn (1 β€ pi β€ n). A permutation is an identity permutation, if for any i the following equation holds pi = i.
A swap (i, j) is the operation that swaps elements pi and pj in the permutation. Let's assume that f(p) is the minimum number of swaps that you need to make the permutation p an identity permutation.
Valera wonders, how he can transform permutation p into any permutation q, such that f(q) = m, using the minimum number of swaps. Help him do that.
Input
The first line contains integer n (1 β€ n β€ 3000) β the length of permutation p. The second line contains n distinct integers p1, p2, ..., pn (1 β€ pi β€ n) β Valera's initial permutation. The last line contains integer m (0 β€ m < n).
Output
In the first line, print integer k β the minimum number of swaps.
In the second line, print 2k integers x1, x2, ..., x2k β the description of the swap sequence. The printed numbers show that you need to consecutively make swaps (x1, x2), (x3, x4), ..., (x2k - 1, x2k).
If there are multiple sequence swaps of the minimum length, print the lexicographically minimum one.
Examples
Input
5
1 2 3 4 5
2
Output
2
1 2 1 3
Input
5
2 1 4 5 3
2
Output
1
1 2
Note
Sequence x1, x2, ..., xs is lexicographically smaller than sequence y1, y2, ..., ys, if there is such integer r (1 β€ r β€ s), that x1 = y1, x2 = y2, ..., xr - 1 = yr - 1 and xr < yr.
Submitted Solution:
```
def ID(L):
x=0
for i in range(n):
Pos[L[i]]=i
for i in range(n):
if(Pos[i]==i):
continue
e=Pos[i]
q=L[i]
L[i],L[Pos[i]]=L[Pos[i]],L[i]
Pos[i],Pos[q]=i,e
x+=1
return x
n=int(input())
L=list(map(int,input().split()))
Pos=[0]*3001
for i in range(n):
L[i]-=1
y=ID(list(L))
for i in range(n):
Pos[L[i]]=i
Ans=[]
m=int(input())
Ans=[]
if(y>m and n!=1):
e=y-m
while(e>=1):
q1=0
while(L[q1]==q1):
q1+=1
q2=q1+1
while(L[q2]==q2):
q2+=1
numx=L[q1]
posx=q1
numy=L[q2]
posy=q2
if(posx==numy):
e-=1
Ans.append((posx,posy))
L[numx]=numx
Pos[numx]=numx
L[numy]=numy
Pos[numy]=numy
else:
e-=1
Ans.append((posx,posy))
L[numx]=numx
Pos[numx]=numx
L[posx]=numy
Pos[numy]=posx
if(y<m and n!=1):
e=m-y
#print(L)
while(e>=1):
q1=0
while(L[q1]!=q1):
q1+=1
q2=q1+1
cont=True
q2=0
while(1):
if(q2==q1):
q2+=1
continue
if(L[q2]!=q2 and e>1):
q2+=1
continue
break
numx=L[q1]
posx=q1
numy=L[q2]
posy=q2
b=min(posx,posy)
c=max(posx,posy)
Ans.append((b,c))
L[posx],L[posy]=L[posy],L[posx]
Pos[numx],Pos[numy]=Pos[numy],Pos[numx]
e-=1
print(len(Ans))
for i in range(len(Ans)):
print(Ans[i][0]+1,Ans[i][1]+1,end=" ")
``` | instruction | 0 | 72,034 | 12 | 144,068 |
No | output | 1 | 72,034 | 12 | 144,069 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3 | instruction | 0 | 72,137 | 12 | 144,274 |
Tags: dp, greedy, implementation
Correct Solution:
```
for _ in range(1):
n=int(input())
# n,k=map(int,input().split())
a=list(map(int,input().split()))
mn=1
mx=1
i=0
while(i<n-1):
if(a[i]<a[i+1]):
mn=mn+1
i=i+1
else:
i=i+1
mn=1
if(mn>mx):
mx=mn
print(mx)
``` | output | 1 | 72,137 | 12 | 144,275 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3 | instruction | 0 | 72,138 | 12 | 144,276 |
Tags: dp, greedy, implementation
Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
big=1
c=1
for i in range(n-1):
if a[i+1]>a[i]:
c+=1
else:
big=max(big,c)
c=1
print(max(big,c))
``` | output | 1 | 72,138 | 12 | 144,277 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3 | instruction | 0 | 72,139 | 12 | 144,278 |
Tags: dp, greedy, implementation
Correct Solution:
```
n = int(input())
a = list([int(x) for x in input().split()])
i = 1
res = 1
ans = 1
while i != n:
if a[i-1] < a[i]:
res += 1
else:
ans = max(res, ans)
res = 1
i += 1
ans = max(res, ans)
print(ans)
``` | output | 1 | 72,139 | 12 | 144,279 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3 | instruction | 0 | 72,140 | 12 | 144,280 |
Tags: dp, greedy, implementation
Correct Solution:
```
n, a, b, c = input(), 0, 0, 0
for x in list(map(int, input().split())):
c = c + 1 if x > a else 1
b = max(c, b)
a = x
print(b)
``` | output | 1 | 72,140 | 12 | 144,281 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3 | instruction | 0 | 72,141 | 12 | 144,282 |
Tags: dp, greedy, implementation
Correct Solution:
```
n = int(input())
a = input().split()
b = [1 for i in range(n)]
a[0] = int(a[0])
for i in range(1, n):
a[i] = int(a[i])
if a[i] > a[i-1]:
b[i] += b[i-1]
k = b[0]
for i in range(n):
k = max(k, b[i])
print(k)
``` | output | 1 | 72,141 | 12 | 144,283 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3 | instruction | 0 | 72,142 | 12 | 144,284 |
Tags: dp, greedy, implementation
Correct Solution:
```
import sys
input = sys.stdin.readline
def inp():
return int(input())
def inlt():
return list(map(int, input().split()))
def insr():
s = input()
return list(s[:len(s) - 1])
def invr():
return map(int, input().split())
def solve(ip):
i = 0
j = i + 1
max = 1
while (i <= j) and j < len(ip):
current = 1
while i < j < len(ip) and (ip[i] < ip[j]) :
current = current + 1
j = j + 1
i = i+1
if current > max:
max = current
i = i + 1
j = j + 1
print(max)
n = inp()
ip = inlt()
solve(ip)
``` | output | 1 | 72,142 | 12 | 144,285 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3 | instruction | 0 | 72,143 | 12 | 144,286 |
Tags: dp, greedy, implementation
Correct Solution:
```
n = int(input())
l = list(map(int, input().split()))
ans = 0
tmp = 1
for i in range(1, n):
if l[i] > l[i - 1]:
tmp += 1
else:
if tmp > ans:
ans = tmp
tmp = 1
if tmp > ans:
ans = tmp
print (ans)
``` | output | 1 | 72,143 | 12 | 144,287 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3 | instruction | 0 | 72,144 | 12 | 144,288 |
Tags: dp, greedy, implementation
Correct Solution:
```
n = int(input())
v = list(map(int, input().split()))
mx = 1
dp = [0]*n
dp[0] = 1
for i in range(1, n):
if v[i] > v[i-1]:
dp[i] = dp[i-1]+1
else:
dp[i] = 1
mx = max(dp[i], mx)
print(mx)
``` | output | 1 | 72,144 | 12 | 144,289 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3
Submitted Solution:
```
n = int(input())
a = list(map(int,input().split()))
max_l = 1
l = 1
for i in range(n-1):
if(a[i+1] > a[i]):
l += 1
if(l > max_l):
max_l=l
else:
l = 1
print(max_l)
``` | instruction | 0 | 72,145 | 12 | 144,290 |
Yes | output | 1 | 72,145 | 12 | 144,291 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3
Submitted Solution:
```
n=int(input())
s=str(input()).split()
l=list()
for i in s:
l.append(int(i))
nl=list()
c=1
for k in range(len(l)-1):
if l[k]<l[k+1]:
c=c+1
nl.append(c)
else:
c=1
if len(nl)!=0:
print(max(nl))
else:
print(1)
``` | instruction | 0 | 72,146 | 12 | 144,292 |
Yes | output | 1 | 72,146 | 12 | 144,293 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3
Submitted Solution:
```
import math
x = list(map(int, input().split()))
s = []
s = list(map(int, input().split()))
q_temp = 1
q = 1
for i in range(1,x[0]):
if s[i] <= s[i-1]:
q_temp = 1
else:
q_temp += 1
q = max(q,q_temp)
print(q)
``` | instruction | 0 | 72,147 | 12 | 144,294 |
Yes | output | 1 | 72,147 | 12 | 144,295 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3
Submitted Solution:
```
n=int(input());j=1;r=0
L=list(map(int,input().split()))+[-1]
for k in range(n):
if(L[k]<L[k+1]):
j+=1
else:
if(j>r):
r=j
j=1
print(r)
``` | instruction | 0 | 72,148 | 12 | 144,296 |
Yes | output | 1 | 72,148 | 12 | 144,297 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3
Submitted Solution:
```
str = int(input())
str = input()
Array = [int(x) for x in str.split()]
pred = Array[0]
count=1
for i in Array[1:]:
if i>pred:
count+=1
pred = i
else:
count = 1
print(count)
``` | instruction | 0 | 72,149 | 12 | 144,298 |
No | output | 1 | 72,149 | 12 | 144,299 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3
Submitted Solution:
```
input()
#cons = [int(x) for x in input().split()]
cons = list(map(int, input().split()))
backitem = 0
count = 1
for item in cons:
if item > backitem:
count += 1
else:
count = 1
backitem = item
print(count)
``` | instruction | 0 | 72,150 | 12 | 144,300 |
No | output | 1 | 72,150 | 12 | 144,301 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3
Submitted Solution:
```
n=int(input())
z=list(map(int,input().split()))
arr=[]
count=1
for i in range(n-1) :
if z[i]<z[i+1] :
count+=1
else :
arr.append(count)
count=1
print(max(arr))
``` | instruction | 0 | 72,151 | 12 | 144,302 |
No | output | 1 | 72,151 | 12 | 144,303 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.
A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.
Input
The first line contains single positive integer n (1 β€ n β€ 105) β the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print the maximum length of an increasing subarray of the given array.
Examples
Input
5
1 7 2 11 15
Output
3
Input
6
100 100 100 100 100 100
Output
1
Input
3
1 2 3
Output
3
Submitted Solution:
```
n = int(input())
count = 1
maxCount = 1
nums = [int(num) for num in input().split()]
for i in range(1,n):
if nums[i] > nums[i-1]:
count += 1
else:
maxCount = max(maxCount,count)
count = 1
print(maxCount)
``` | instruction | 0 | 72,152 | 12 | 144,304 |
No | output | 1 | 72,152 | 12 | 144,305 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a table consisting of n rows and m columns.
Numbers in each row form a permutation of integers from 1 to m.
You are allowed to pick two elements in one row and swap them, but no more than once for each row. Also, no more than once you are allowed to pick two columns and swap them. Thus, you are allowed to perform from 0 to n + 1 actions in total. Operations can be performed in any order.
You have to check whether it's possible to obtain the identity permutation 1, 2, ..., m in each row. In other words, check if one can perform some of the operation following the given rules and make each row sorted in increasing order.
Input
The first line of the input contains two integers n and m (1 β€ n, m β€ 20) β the number of rows and the number of columns in the given table.
Each of next n lines contains m integers β elements of the table. It's guaranteed that numbers in each line form a permutation of integers from 1 to m.
Output
If there is a way to obtain the identity permutation in each row by following the given rules, print "YES" (without quotes) in the only line of the output. Otherwise, print "NO" (without quotes).
Examples
Input
2 4
1 3 2 4
1 3 4 2
Output
YES
Input
4 4
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
Output
NO
Input
3 6
2 1 3 4 5 6
1 2 4 3 5 6
1 2 3 4 6 5
Output
YES
Note
In the first sample, one can act in the following way:
1. Swap second and third columns. Now the table is 1 2 3 4 1 4 3 2
2. In the second row, swap the second and the fourth elements. Now the table is 1 2 3 4 1 2 3 4 | instruction | 0 | 72,153 | 12 | 144,306 |
Tags: brute force, greedy, implementation, math
Correct Solution:
```
import sys
def swapC(c1, c2):
for r in range(n):
swap(r, c1, c2)
def swap(r, c1, c2):
nums[r][c1], nums[r][c2] = nums[r][c2], nums[r][c1]
def checkRow(r):
bad = []
for i in range(m):
if nums[r][i] != i:
bad.append(i)
if len(bad) == 0:
return True
if len(bad) != 2:
return False
x0, x1 = nums[r][bad[0]], nums[r][bad[1]]
return bad[0] == x1 and bad[1] == x0
def checkAll():
for r in range(n):
if not checkRow(r):
return False
return True
n, m = map(int, input().split())
nums = [list(map(lambda x: int(x) - 1, input().split())) for i in range(n)]
flag = False
for c1 in range(m):
for c2 in range(c1, m):
swapC(c1, c2)
if checkAll():
print("YES")
flag = True
break
swapC(c1, c2)
if flag:
break
else:
print("NO")
``` | output | 1 | 72,153 | 12 | 144,307 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a table consisting of n rows and m columns.
Numbers in each row form a permutation of integers from 1 to m.
You are allowed to pick two elements in one row and swap them, but no more than once for each row. Also, no more than once you are allowed to pick two columns and swap them. Thus, you are allowed to perform from 0 to n + 1 actions in total. Operations can be performed in any order.
You have to check whether it's possible to obtain the identity permutation 1, 2, ..., m in each row. In other words, check if one can perform some of the operation following the given rules and make each row sorted in increasing order.
Input
The first line of the input contains two integers n and m (1 β€ n, m β€ 20) β the number of rows and the number of columns in the given table.
Each of next n lines contains m integers β elements of the table. It's guaranteed that numbers in each line form a permutation of integers from 1 to m.
Output
If there is a way to obtain the identity permutation in each row by following the given rules, print "YES" (without quotes) in the only line of the output. Otherwise, print "NO" (without quotes).
Examples
Input
2 4
1 3 2 4
1 3 4 2
Output
YES
Input
4 4
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
Output
NO
Input
3 6
2 1 3 4 5 6
1 2 4 3 5 6
1 2 3 4 6 5
Output
YES
Note
In the first sample, one can act in the following way:
1. Swap second and third columns. Now the table is 1 2 3 4 1 4 3 2
2. In the second row, swap the second and the fourth elements. Now the table is 1 2 3 4 1 2 3 4 | instruction | 0 | 72,154 | 12 | 144,308 |
Tags: brute force, greedy, implementation, math
Correct Solution:
```
n, m = map(int, input().split())
a = [input().split() for _ in range(n)]
for l in range(m):
for r in range(l, m):
for s in a:
s1 = s.copy()
s1[l], s1[r] = s1[r], s1[l]
if sum(int(s1[i]) != i + 1 for i in range(m)) > 2:
break
else:
print('YES')
exit()
print('NO')
``` | output | 1 | 72,154 | 12 | 144,309 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a table consisting of n rows and m columns.
Numbers in each row form a permutation of integers from 1 to m.
You are allowed to pick two elements in one row and swap them, but no more than once for each row. Also, no more than once you are allowed to pick two columns and swap them. Thus, you are allowed to perform from 0 to n + 1 actions in total. Operations can be performed in any order.
You have to check whether it's possible to obtain the identity permutation 1, 2, ..., m in each row. In other words, check if one can perform some of the operation following the given rules and make each row sorted in increasing order.
Input
The first line of the input contains two integers n and m (1 β€ n, m β€ 20) β the number of rows and the number of columns in the given table.
Each of next n lines contains m integers β elements of the table. It's guaranteed that numbers in each line form a permutation of integers from 1 to m.
Output
If there is a way to obtain the identity permutation in each row by following the given rules, print "YES" (without quotes) in the only line of the output. Otherwise, print "NO" (without quotes).
Examples
Input
2 4
1 3 2 4
1 3 4 2
Output
YES
Input
4 4
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
Output
NO
Input
3 6
2 1 3 4 5 6
1 2 4 3 5 6
1 2 3 4 6 5
Output
YES
Note
In the first sample, one can act in the following way:
1. Swap second and third columns. Now the table is 1 2 3 4 1 4 3 2
2. In the second row, swap the second and the fourth elements. Now the table is 1 2 3 4 1 2 3 4 | instruction | 0 | 72,155 | 12 | 144,310 |
Tags: brute force, greedy, implementation, math
Correct Solution:
```
def solve():
n, m = map(int, input().split())
tab = [list(map(int, input().split())) for _ in range(n)]
def ordered(l):
for i in range(len(l) - 1):
if l[i] > l[i + 1]: return False
return True
def canswap(l):
if ordered(l): return True
for i in range(len(l)):
for j in range(i + 1, len(l)):
lc = list(l)
lc[i], lc[j] = lc[j], lc[i]
if ordered(lc):
return True
return False
works = True
for row in tab:
if not canswap(row):
works = False
if works: return True
for coli in range(m):
for colj in range(coli, m):
works = True
for rowref in tab:
row = list(rowref)
row[coli], row[colj] = row[colj], row[coli]
if ordered(row):
continue
good = False
for i in range(m):
if good: break
for j in range(m):
row = list(rowref)
row[i], row[j] = row[j], row[i]
row[coli], row[colj] = row[colj], row[coli]
if ordered(row):
good = True
break
row = list(rowref)
row[coli], row[colj] = row[colj], row[coli]
row[i], row[j] = row[j], row[i]
if ordered(row):
good = True
break
if not good:
works = False
break
if works:
return True
return False
res = solve()
print("YES" if res else "NO")
``` | output | 1 | 72,155 | 12 | 144,311 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a table consisting of n rows and m columns.
Numbers in each row form a permutation of integers from 1 to m.
You are allowed to pick two elements in one row and swap them, but no more than once for each row. Also, no more than once you are allowed to pick two columns and swap them. Thus, you are allowed to perform from 0 to n + 1 actions in total. Operations can be performed in any order.
You have to check whether it's possible to obtain the identity permutation 1, 2, ..., m in each row. In other words, check if one can perform some of the operation following the given rules and make each row sorted in increasing order.
Input
The first line of the input contains two integers n and m (1 β€ n, m β€ 20) β the number of rows and the number of columns in the given table.
Each of next n lines contains m integers β elements of the table. It's guaranteed that numbers in each line form a permutation of integers from 1 to m.
Output
If there is a way to obtain the identity permutation in each row by following the given rules, print "YES" (without quotes) in the only line of the output. Otherwise, print "NO" (without quotes).
Examples
Input
2 4
1 3 2 4
1 3 4 2
Output
YES
Input
4 4
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
Output
NO
Input
3 6
2 1 3 4 5 6
1 2 4 3 5 6
1 2 3 4 6 5
Output
YES
Note
In the first sample, one can act in the following way:
1. Swap second and third columns. Now the table is 1 2 3 4 1 4 3 2
2. In the second row, swap the second and the fourth elements. Now the table is 1 2 3 4 1 2 3 4 | instruction | 0 | 72,156 | 12 | 144,312 |
Tags: brute force, greedy, implementation, math
Correct Solution:
```
import copy
n,m = map(int,input().split())
l = []
for i in range(n) :
l.append(list(map(int,input().split())))
def test_matrix(l) :
test = 1
for i in range(n) :
rem = 0
k = 1
for j in range(m) :
if l[i][j] != j+1 and rem == 0 :
rem = {j+1,l[i][j]}
elif l[i][j] != j+1 and (l[i][j] not in rem) :
k = 0
break
if k == 0 :
test = 0
break
if test == 0 :
return False
else :
return True
ola = 0
if test_matrix(l) == True :
ola = 1
for i in range(m) :
for j in range(i+1,m) :
b = copy.deepcopy(l)
for p in range(n) :
b[p][i],b[p][j] = b[p][j],b[p][i]
if test_matrix(b) == True :
ola = 1
break
if ola == 1 :
break
if ola == 1 :
print('YES')
else :
print('NO')
``` | output | 1 | 72,156 | 12 | 144,313 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a table consisting of n rows and m columns.
Numbers in each row form a permutation of integers from 1 to m.
You are allowed to pick two elements in one row and swap them, but no more than once for each row. Also, no more than once you are allowed to pick two columns and swap them. Thus, you are allowed to perform from 0 to n + 1 actions in total. Operations can be performed in any order.
You have to check whether it's possible to obtain the identity permutation 1, 2, ..., m in each row. In other words, check if one can perform some of the operation following the given rules and make each row sorted in increasing order.
Input
The first line of the input contains two integers n and m (1 β€ n, m β€ 20) β the number of rows and the number of columns in the given table.
Each of next n lines contains m integers β elements of the table. It's guaranteed that numbers in each line form a permutation of integers from 1 to m.
Output
If there is a way to obtain the identity permutation in each row by following the given rules, print "YES" (without quotes) in the only line of the output. Otherwise, print "NO" (without quotes).
Examples
Input
2 4
1 3 2 4
1 3 4 2
Output
YES
Input
4 4
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
Output
NO
Input
3 6
2 1 3 4 5 6
1 2 4 3 5 6
1 2 3 4 6 5
Output
YES
Note
In the first sample, one can act in the following way:
1. Swap second and third columns. Now the table is 1 2 3 4 1 4 3 2
2. In the second row, swap the second and the fourth elements. Now the table is 1 2 3 4 1 2 3 4 | instruction | 0 | 72,157 | 12 | 144,314 |
Tags: brute force, greedy, implementation, math
Correct Solution:
```
def no(k):
s=[]
for j in range (len(k)):
if k[j]!=j+1:
s.append(j)
return(s)
def summ(k,n,i):
s=0
for j in range(n):
s+=k[j][i]
return(s)
def numcol(k,n):
d=0
s=no(k[0])
for i in s:
if summ(k,n,i)==n*k[0][i]:
d+=1
return(d)
def notin(k,m):
s=0
for j in range(m):
if k[j]!=j+1:
s+=1
return(s)
def somme(k,n,m):
g=0
for i in range(n):
g+=notin(k[i],m)
return(g)
def op(k,n,m):
for i in range(n):
if notin(k[i],m)>2:
return(False)
return(True)
def tr(l,n,m,i,j):
c=l.copy()
for s in range(n):
c[s][i],c[s][j]=c[s][j],c[s][i]
f=op(c,n,m)
for s in range(n):
c[s][i],c[s][j]=c[s][j],c[s][i]
return(f)
def main ():
n,m=map(int,input().split())
k=[]
for i in range (n):
k.append(list(map(int,input().split(' '))))
g=somme(k,n,m)
h=-1
f=-1
for i in range(n):
if notin(k[i],m) > 4 :
return("NO")
elif notin(k[i],m) == 4:
f=i
elif notin(k[i],m) == 3:
h=i
if n <3 and m<3:
return("YES")
elif h==-1 and f==-1:
return("YES")
elif h !=-1:
p=no(k[h])
if tr(k,n,m,p[0],p[1])or tr(k,n,m,p[0],p[2])or tr(k,n,m,p[1],p[2]):
return("YES")
else :
return("NO")
elif h==-1:
p=no(k[f])
if tr(k,n,m,p[0],p[1])or tr(k,n,m,p[0],p[2])or tr(k,n,m,p[0],p[3])or tr(k,n,m,p[1],p[2])or tr(k,n,m,p[1],p[3])or tr(k,n,m,p[2],p[3]):
return("YES")
else :
return("NO")
print(main())
``` | output | 1 | 72,157 | 12 | 144,315 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a table consisting of n rows and m columns.
Numbers in each row form a permutation of integers from 1 to m.
You are allowed to pick two elements in one row and swap them, but no more than once for each row. Also, no more than once you are allowed to pick two columns and swap them. Thus, you are allowed to perform from 0 to n + 1 actions in total. Operations can be performed in any order.
You have to check whether it's possible to obtain the identity permutation 1, 2, ..., m in each row. In other words, check if one can perform some of the operation following the given rules and make each row sorted in increasing order.
Input
The first line of the input contains two integers n and m (1 β€ n, m β€ 20) β the number of rows and the number of columns in the given table.
Each of next n lines contains m integers β elements of the table. It's guaranteed that numbers in each line form a permutation of integers from 1 to m.
Output
If there is a way to obtain the identity permutation in each row by following the given rules, print "YES" (without quotes) in the only line of the output. Otherwise, print "NO" (without quotes).
Examples
Input
2 4
1 3 2 4
1 3 4 2
Output
YES
Input
4 4
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
Output
NO
Input
3 6
2 1 3 4 5 6
1 2 4 3 5 6
1 2 3 4 6 5
Output
YES
Note
In the first sample, one can act in the following way:
1. Swap second and third columns. Now the table is 1 2 3 4 1 4 3 2
2. In the second row, swap the second and the fourth elements. Now the table is 1 2 3 4 1 2 3 4 | instruction | 0 | 72,158 | 12 | 144,316 |
Tags: brute force, greedy, implementation, math
Correct Solution:
```
n, m = map(int, input().split())
a = []
for i in range(n):
a.append(list(map(int, input().split())))
def check(x, y):
for i in range(n):
k = 0
for j in range(m):
if (j == x):
if (a[i][y] != j + 1):
k += 1
elif (j == y):
if (a[i][x] != j + 1):
k += 1
elif (a[i][j] != j + 1):
k += 1
if k > 2:
return False
return True
for e in range(m):
for r in range(m):
if check(e, r):
print('YES')
exit()
print('NO')
``` | output | 1 | 72,158 | 12 | 144,317 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a table consisting of n rows and m columns.
Numbers in each row form a permutation of integers from 1 to m.
You are allowed to pick two elements in one row and swap them, but no more than once for each row. Also, no more than once you are allowed to pick two columns and swap them. Thus, you are allowed to perform from 0 to n + 1 actions in total. Operations can be performed in any order.
You have to check whether it's possible to obtain the identity permutation 1, 2, ..., m in each row. In other words, check if one can perform some of the operation following the given rules and make each row sorted in increasing order.
Input
The first line of the input contains two integers n and m (1 β€ n, m β€ 20) β the number of rows and the number of columns in the given table.
Each of next n lines contains m integers β elements of the table. It's guaranteed that numbers in each line form a permutation of integers from 1 to m.
Output
If there is a way to obtain the identity permutation in each row by following the given rules, print "YES" (without quotes) in the only line of the output. Otherwise, print "NO" (without quotes).
Examples
Input
2 4
1 3 2 4
1 3 4 2
Output
YES
Input
4 4
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
Output
NO
Input
3 6
2 1 3 4 5 6
1 2 4 3 5 6
1 2 3 4 6 5
Output
YES
Note
In the first sample, one can act in the following way:
1. Swap second and third columns. Now the table is 1 2 3 4 1 4 3 2
2. In the second row, swap the second and the fourth elements. Now the table is 1 2 3 4 1 2 3 4 | instruction | 0 | 72,159 | 12 | 144,318 |
Tags: brute force, greedy, implementation, math
Correct Solution:
```
def check(matrix, getindex = False, isfirst = False):
indices = set()
canbe = True
for row in matrix:
count = 0
for i, value in enumerate(row):
if value != i+1 :
indices.update([i])
count += 1
if count >2:
canbe = False
if count >4 and isfirst:
print("NO")
exit()
if getindex:
return list(indices)
return canbe
n, m = map(int, input().split())
matrix = []
for i in range(n):
row = [int(x) for x in input().split()]
matrix.append(row)
indices = check(matrix, True, True)
canbesort = check(matrix)
for i in indices:
if canbesort:
break
for j in indices[1:]:
for k in range(n):
matrix[k][i], matrix[k][j] = matrix[k][j], matrix[k][i]
canbesort = check(matrix)
if canbesort:
break
for k in range(n):
matrix[k][i], matrix[k][j] = matrix[k][j], matrix[k][i]
print(canbesort and 'YES' or 'NO')
``` | output | 1 | 72,159 | 12 | 144,319 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a table consisting of n rows and m columns.
Numbers in each row form a permutation of integers from 1 to m.
You are allowed to pick two elements in one row and swap them, but no more than once for each row. Also, no more than once you are allowed to pick two columns and swap them. Thus, you are allowed to perform from 0 to n + 1 actions in total. Operations can be performed in any order.
You have to check whether it's possible to obtain the identity permutation 1, 2, ..., m in each row. In other words, check if one can perform some of the operation following the given rules and make each row sorted in increasing order.
Input
The first line of the input contains two integers n and m (1 β€ n, m β€ 20) β the number of rows and the number of columns in the given table.
Each of next n lines contains m integers β elements of the table. It's guaranteed that numbers in each line form a permutation of integers from 1 to m.
Output
If there is a way to obtain the identity permutation in each row by following the given rules, print "YES" (without quotes) in the only line of the output. Otherwise, print "NO" (without quotes).
Examples
Input
2 4
1 3 2 4
1 3 4 2
Output
YES
Input
4 4
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
Output
NO
Input
3 6
2 1 3 4 5 6
1 2 4 3 5 6
1 2 3 4 6 5
Output
YES
Note
In the first sample, one can act in the following way:
1. Swap second and third columns. Now the table is 1 2 3 4 1 4 3 2
2. In the second row, swap the second and the fourth elements. Now the table is 1 2 3 4 1 2 3 4 | instruction | 0 | 72,160 | 12 | 144,320 |
Tags: brute force, greedy, implementation, math
Correct Solution:
```
n, m = map(int, input().split(' '))
a = []
for i in range(n):
a.append(list(map(int, input().split(' '))))
p = []
possible = True
col_swap = False
#print('swaps:')
for r in a:
x = []
j = 0
swaps = []
while j < len(r) and len(swaps) < 3:
if r[j] != j + 1:
tmp = r[j]
r[j] = r[tmp - 1]
r[tmp - 1] = tmp
swaps.append((j, tmp - 1))
else:
j += 1
#print(swaps)
if len(swaps) > 2:
possible = False
break
if len(swaps) == 2:
col_swap = True
if len(swaps) > 0:
x = swaps
if len(swaps) == 2 and swaps[0][0] == swaps[1][0]:
x.append((
min(swaps[0][1], swaps[1][1]),
max(swaps[0][1], swaps[1][1])
))
p.append(x)
#print('possible:', possible, 'p:', p, 'col_swap:', col_swap)
if possible and col_swap and p:
c = set(p[0])
for x in p:
c = c.intersection(x)
possible = bool(c)
#print('c:', c)
if possible:
print('YES')
else:
print('NO')
``` | output | 1 | 72,160 | 12 | 144,321 |
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