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 |
|---|---|---|---|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array a of length n and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array a, only if array a can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array a, sorted by non-decreasing, himself.
Input
The first line contains a single integer n (2 ≤ n ≤ 105) — the size of array a. The next line contains n positive integers, separated by single spaces and not exceeding 109, — array a.
Note that the elements of the array are not necessarily distinct numbers.
Output
In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise.
Examples
Input
2
1 2
Output
YES
Input
3
3 2 1
Output
YES
Input
4
4 3 2 1
Output
NO
Note
In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO". | instruction | 0 | 6,914 | 12 | 13,828 |
Tags: implementation, sortings
Correct Solution:
```
from collections import Counter
n=int(input())
a=list(map(int,input().split()))
b=a.copy()
a.sort()
for i in range(n):
a[i]=abs(a[i]-b[i])
k=Counter(a)
if(k[0]>=n-2):
print("YES")
else:
print("NO")
``` | output | 1 | 6,914 | 12 | 13,829 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array a of length n and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array a, only if array a can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array a, sorted by non-decreasing, himself.
Input
The first line contains a single integer n (2 ≤ n ≤ 105) — the size of array a. The next line contains n positive integers, separated by single spaces and not exceeding 109, — array a.
Note that the elements of the array are not necessarily distinct numbers.
Output
In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise.
Examples
Input
2
1 2
Output
YES
Input
3
3 2 1
Output
YES
Input
4
4 3 2 1
Output
NO
Note
In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO". | instruction | 0 | 6,915 | 12 | 13,830 |
Tags: implementation, sortings
Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
b = sorted(a)
res = 0
for i in range(n):
if a[i] != b[i]:
res += 1
print('YES' if res <= 2 else 'NO')
``` | output | 1 | 6,915 | 12 | 13,831 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array a of length n and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array a, only if array a can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array a, sorted by non-decreasing, himself.
Input
The first line contains a single integer n (2 ≤ n ≤ 105) — the size of array a. The next line contains n positive integers, separated by single spaces and not exceeding 109, — array a.
Note that the elements of the array are not necessarily distinct numbers.
Output
In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise.
Examples
Input
2
1 2
Output
YES
Input
3
3 2 1
Output
YES
Input
4
4 3 2 1
Output
NO
Note
In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO". | instruction | 0 | 6,916 | 12 | 13,832 |
Tags: implementation, sortings
Correct Solution:
```
n=int(input())
from itertools import permutations as pem
List=list(map(int, input().split()))
newlist=sorted(List)
count=0
for i in range(n):
if newlist[i]!=List[i]:
count+=1
if count<=2:
print("YES")
else:
print("NO")
``` | output | 1 | 6,916 | 12 | 13,833 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array a of length n and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array a, only if array a can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array a, sorted by non-decreasing, himself.
Input
The first line contains a single integer n (2 ≤ n ≤ 105) — the size of array a. The next line contains n positive integers, separated by single spaces and not exceeding 109, — array a.
Note that the elements of the array are not necessarily distinct numbers.
Output
In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise.
Examples
Input
2
1 2
Output
YES
Input
3
3 2 1
Output
YES
Input
4
4 3 2 1
Output
NO
Note
In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO". | instruction | 0 | 6,917 | 12 | 13,834 |
Tags: implementation, sortings
Correct Solution:
```
import sys
import math
import itertools
import functools
import collections
def ii(): return int(input())
def mi(): return map(int, input().split())
def li(): return list(map(int, input().split()))
def lcm(a, b): return abs(a * b) // math.gcd(a, b)
def wr(arr): return ' '.join(map(str, arr))
def revn(n): return str(n)[::-1]
def dd(): return collections.defaultdict(int)
def ddl(): return collections.defaultdict(list)
def sieve(n):
if n < 2: return list()
prime = [True for _ in range(n + 1)]
p = 3
while p * p <= n:
if prime[p]:
for i in range(p * 2, n + 1, p):
prime[i] = False
p += 2
r = [2]
for p in range(3, n + 1, 2):
if prime[p]:
r.append(p)
return r
def divs(n, start=1):
r = []
for i in range(start, int(math.sqrt(n) + 1)):
if (n % i == 0):
if (n / i == i):
r.append(i)
else:
r.extend([i, n // i])
return r
def divn(n, primes):
divs_number = 1
for i in primes:
if n == 1:
return divs_number
t = 1
while n % i == 0:
t += 1
n //= i
divs_number *= t
def prime(n):
if n == 2: return True
if n % 2 == 0 or n <= 1: return False
sqr = int(math.sqrt(n)) + 1
for d in range(3, sqr, 2):
if n % d == 0: return False
return True
def convn(number, base):
newnumber = 0
while number > 0:
newnumber += number % base
number //= base
return newnumber
def cdiv(n, k): return n // k + (n % k != 0)
n = ii()
a = li()
b = sorted(a)
ans = 0
for i in range(n):
if a[i] != b[i]:
ans += 1
if ans == 0 or ans == 2:
print('YES')
else:
print('NO')
``` | output | 1 | 6,917 | 12 | 13,835 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array a of length n and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array a, only if array a can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array a, sorted by non-decreasing, himself.
Input
The first line contains a single integer n (2 ≤ n ≤ 105) — the size of array a. The next line contains n positive integers, separated by single spaces and not exceeding 109, — array a.
Note that the elements of the array are not necessarily distinct numbers.
Output
In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise.
Examples
Input
2
1 2
Output
YES
Input
3
3 2 1
Output
YES
Input
4
4 3 2 1
Output
NO
Note
In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO".
Submitted Solution:
```
def issort(l):
return all(l[i] <= l[i+1] for i in range(len(l)-1))
sa = int(input())
array = list(map(int, input().split(' ')))
array2 = array[:]
array2.sort()
count = 0
mislist=[]
for i in range(sa):
if array[i] != array2[i]:
count += 1
if count <= 2:
mislist.append(i)
if count > 2:
print("NO")
else:
if mislist == []:
print("YES")
elif len(mislist) == 1:
if issort(array):
print("YES")
else:
print("NO")
else:
array[mislist[0]], array[mislist[1]] = array[mislist[1]], array[mislist[0]]
if issort(array):
print("YES")
else:
print("NO")
``` | instruction | 0 | 6,918 | 12 | 13,836 |
Yes | output | 1 | 6,918 | 12 | 13,837 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array a of length n and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array a, only if array a can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array a, sorted by non-decreasing, himself.
Input
The first line contains a single integer n (2 ≤ n ≤ 105) — the size of array a. The next line contains n positive integers, separated by single spaces and not exceeding 109, — array a.
Note that the elements of the array are not necessarily distinct numbers.
Output
In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise.
Examples
Input
2
1 2
Output
YES
Input
3
3 2 1
Output
YES
Input
4
4 3 2 1
Output
NO
Note
In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO".
Submitted Solution:
```
import sys
input = sys.stdin.readline
n = int(input())
a = list(map(int,input().split()))
b = sorted(a)
ans = 0
for i in range(n):
if a[i] != b[i]:
ans += 1
print('YES' if ans <= 2 else 'NO')
``` | instruction | 0 | 6,919 | 12 | 13,838 |
Yes | output | 1 | 6,919 | 12 | 13,839 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array a of length n and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array a, only if array a can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array a, sorted by non-decreasing, himself.
Input
The first line contains a single integer n (2 ≤ n ≤ 105) — the size of array a. The next line contains n positive integers, separated by single spaces and not exceeding 109, — array a.
Note that the elements of the array are not necessarily distinct numbers.
Output
In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise.
Examples
Input
2
1 2
Output
YES
Input
3
3 2 1
Output
YES
Input
4
4 3 2 1
Output
NO
Note
In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO".
Submitted Solution:
```
def arr_inp(n):
if n == 1:
return [int(x) for x in stdin.readline().split()]
elif n == 2:
return [float(x) for x in stdin.readline().split()]
else:
return [str(x) for x in stdin.readline().split()]
from sys import stdin
n, a = int(input()), arr_inp(1)
a1, c, ix = sorted(a.copy()), 0, 0
for i in range(n):
if a[i] != a1[i]:
if c == 0:
c += 1
ix = i
elif c > 2:
exit(print('NO'))
else:
if a1[ix] == a[i]:
c += 1
else:
exit(print('NO'))
print('YES')
``` | instruction | 0 | 6,920 | 12 | 13,840 |
Yes | output | 1 | 6,920 | 12 | 13,841 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array a of length n and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array a, only if array a can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array a, sorted by non-decreasing, himself.
Input
The first line contains a single integer n (2 ≤ n ≤ 105) — the size of array a. The next line contains n positive integers, separated by single spaces and not exceeding 109, — array a.
Note that the elements of the array are not necessarily distinct numbers.
Output
In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise.
Examples
Input
2
1 2
Output
YES
Input
3
3 2 1
Output
YES
Input
4
4 3 2 1
Output
NO
Note
In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO".
Submitted Solution:
```
n=int(input())
l=list(map(int,input().split()))
d=sorted(l)
c=0
for i in range(n):
if(l[i]!=d[i]):
c=c+1
if(c>2):
print("NO")
else:
print("YES")
``` | instruction | 0 | 6,921 | 12 | 13,842 |
Yes | output | 1 | 6,921 | 12 | 13,843 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array a of length n and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array a, only if array a can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array a, sorted by non-decreasing, himself.
Input
The first line contains a single integer n (2 ≤ n ≤ 105) — the size of array a. The next line contains n positive integers, separated by single spaces and not exceeding 109, — array a.
Note that the elements of the array are not necessarily distinct numbers.
Output
In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise.
Examples
Input
2
1 2
Output
YES
Input
3
3 2 1
Output
YES
Input
4
4 3 2 1
Output
NO
Note
In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO".
Submitted Solution:
```
import sys
input = sys.stdin.readline
n = int(input())
a = list(map(int,input().split()))
ind1 = a.index(max(a))
ind2 = a.index(min(a))
k = 0
f = False
for i in range(n - 1):
if a[i] > a[i + 1]:
k += 1
if k == 2:
f = True
break
if f or ind1 != 0 and ind2 != n - 1:
print('NO')
else:
print('YES')
``` | instruction | 0 | 6,922 | 12 | 13,844 |
No | output | 1 | 6,922 | 12 | 13,845 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array a of length n and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array a, only if array a can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array a, sorted by non-decreasing, himself.
Input
The first line contains a single integer n (2 ≤ n ≤ 105) — the size of array a. The next line contains n positive integers, separated by single spaces and not exceeding 109, — array a.
Note that the elements of the array are not necessarily distinct numbers.
Output
In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise.
Examples
Input
2
1 2
Output
YES
Input
3
3 2 1
Output
YES
Input
4
4 3 2 1
Output
NO
Note
In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO".
Submitted Solution:
```
#https://codeforces.com/contest/221/problem/C
n=int(input())
a=list(map(int,input().split(' ')))
b=[]
for i in range(n):
b.append(a[i])
b.sort()
q=0
R=[]
bhul=True
for i in range(n):
if a[i]!=b[i]:
if q>=2:
print('NO')
bhul=False
break
else:
q+=1
R.append(i)
if bhul:
if q!=2:
print('NO')
else:
print('YES')
``` | instruction | 0 | 6,923 | 12 | 13,846 |
No | output | 1 | 6,923 | 12 | 13,847 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array a of length n and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array a, only if array a can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array a, sorted by non-decreasing, himself.
Input
The first line contains a single integer n (2 ≤ n ≤ 105) — the size of array a. The next line contains n positive integers, separated by single spaces and not exceeding 109, — array a.
Note that the elements of the array are not necessarily distinct numbers.
Output
In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise.
Examples
Input
2
1 2
Output
YES
Input
3
3 2 1
Output
YES
Input
4
4 3 2 1
Output
NO
Note
In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO".
Submitted Solution:
```
import sys
input = sys.stdin.readline
n = int(input())
a = list(map(int,input().split()))
d = {}
for i in range(n):
if a[i] in d:
d[a[i]].add(i)
else:
d[a[i]] = {i}
ans = 0
b = a[:]
a.sort()
cur = set()
for i in range(n):
if i not in d[a[i]]:
cur.add(b[i])
cur.add(a[i])
print('YES' if len(cur) <= 2 else 'NO')
``` | instruction | 0 | 6,924 | 12 | 13,848 |
No | output | 1 | 6,924 | 12 | 13,849 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array a of length n and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array a, only if array a can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array a, sorted by non-decreasing, himself.
Input
The first line contains a single integer n (2 ≤ n ≤ 105) — the size of array a. The next line contains n positive integers, separated by single spaces and not exceeding 109, — array a.
Note that the elements of the array are not necessarily distinct numbers.
Output
In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise.
Examples
Input
2
1 2
Output
YES
Input
3
3 2 1
Output
YES
Input
4
4 3 2 1
Output
NO
Note
In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO".
Submitted Solution:
```
from collections import Counter
n=int(input())
a=list(map(int,input().split()))
b=a.copy()
a.sort()
for i in range(n):
a[i]=abs(a[i]-b[i])
k=Counter(a)
print(k[0])
if(k[0]>=n-2):
print("YES")
else:
print("NO")
``` | instruction | 0 | 6,925 | 12 | 13,850 |
No | output | 1 | 6,925 | 12 | 13,851 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}. | instruction | 0 | 7,249 | 12 | 14,498 |
Tags: implementation
Correct Solution:
```
'''
//Abdurasul
#include<bits/stdc++.h>
using namespace std;
/**
##################################
## ___________________ ##
## | | Abdurasul... | ##
## |▓| _ _ | ##
## |▓| |_||_| | ##
## |▓| |_||_| | ##
## |▓| Microsoft | ##
## |▓|_________________| ##
## |/\ <><><><><><><><> \ ##
## \ \ <><><><><><<<>>> \ ##
## \ \ <<><><><><><><>> \ ##
## \ \__________________\ ##
## \|___________________| ##
##################################
**/
void seti(){
int n, m;
cin >> n >> m;
if(n % 2 == 0 && m % 2 == 0 && n % m == 0) cout << "YES";
else if(n % 2 == 1 && m % 2 == 1 && n % m == 0) cout << "YES";
else if(n % m == 0) cout << "YES";
else cout << "NO";
cout << endl;
}
int main(){
int n = 1;
//freopen("a.txt", "r", stdin);
//freopen("output.txt", "w", stdout);
cin >> n;
for(int i = 0; i < n; i++){
seti();
}
return 0;
}
'''
n = int(input())
a = list(map(int,input().split()))
for i in range(n - 1):
if max(a[i],a[i + 1]) - min(a[i], a[i + 1]) > 1:
print("NO")
exit()
print("YES")
``` | output | 1 | 7,249 | 12 | 14,499 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}. | instruction | 0 | 7,250 | 12 | 14,500 |
Tags: implementation
Correct Solution:
```
_=input()
l = list(map(int, input().split()))
ans=True
for i in range(1, len(l)):
if abs(l[i]-l[i-1])>=2:
ans=False
break
if ans:
print('YES')
else:
print('NO')
``` | output | 1 | 7,250 | 12 | 14,501 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}. | instruction | 0 | 7,251 | 12 | 14,502 |
Tags: implementation
Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
b=list(sorted(a,reverse=True))
c=[]
for i in range(n):
for j in range(n-i-1):
if abs(a[j]-a[j+1])>=2:
print('NO')
exit()
q=max(a)
qi=a.index(q)
c.append(q)
for j in range(i):
if abs(c[j]-c[j+1])>=2:
print('NO')
exit()
del a[qi]
print('YES')
``` | output | 1 | 7,251 | 12 | 14,503 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}. | instruction | 0 | 7,252 | 12 | 14,504 |
Tags: implementation
Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
s=set()
if n==1:
print("YES")
exit(0)
for i in range(1,n):
s.add(abs(a[i]-a[i-1]))
if max(s) >=2:
print("NO")
else:
print("YES")
``` | output | 1 | 7,252 | 12 | 14,505 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}. | instruction | 0 | 7,253 | 12 | 14,506 |
Tags: implementation
Correct Solution:
```
n=int(input())
l=[int(s) for s in input().split()]
z=0
f=0
d=0
e=0
while(len(l)>0):
a=max(l)
if l.index(a)!=0:
d=a-l[l.index(a)-1]
if l.index(a)!=len(l)-1:
e=a-l[l.index(a)+1]
if d>=2:
z=1
break
if e>=2:
f=1
break
else:
l.remove(a)
if z==1 or f==1:
print("NO")
else:
print("YES")
``` | output | 1 | 7,253 | 12 | 14,507 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}. | instruction | 0 | 7,254 | 12 | 14,508 |
Tags: implementation
Correct Solution:
```
n = int(input())
a = [int(n) for n in input().split()]
answer = True
if n != 1:
for i in range(0, n-1):
#print(a[i], a[i+1])
if max(a[i], a[i+1]) - min(a[i+1], a[i]) >= 2:
answer = False
break
if answer:
print("YES")
else:
print("NO")
else:
print("YES")
``` | output | 1 | 7,254 | 12 | 14,509 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}. | instruction | 0 | 7,255 | 12 | 14,510 |
Tags: implementation
Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
ans=True
for i in range(1,n):
if abs(a[i]-a[i-1])>1: ans=False
if ans: print("YES")
else: print("NO")
``` | output | 1 | 7,255 | 12 | 14,511 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}. | instruction | 0 | 7,256 | 12 | 14,512 |
Tags: implementation
Correct Solution:
```
def sign(x):
if x > 0:
return 1
elif x == 0:
return 0
return -1
def bober(a, b):
return sign(a - b) * (a - b)
n = int(input())
a = list(map(int, input().split()))
mx = 0
for i in range(1, n):
mx = max(mx, bober(a[i], a[i - 1]))
if mx <= 1:
print('YES')
else:
print('NO')
``` | output | 1 | 7,256 | 12 | 14,513 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}.
Submitted Solution:
```
n=int(input())
a=list(map(int,input().split()))
print('NO' if any(abs(a[i]-a[i+1])>1 for i in range(n-1))else 'YES')
``` | instruction | 0 | 7,257 | 12 | 14,514 |
Yes | output | 1 | 7,257 | 12 | 14,515 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}.
Submitted Solution:
```
def check(a):
for i in range(len(a) - 1):
if a[i] > 0 and abs(a[i] - a[i + 1]) > 1:
return False
return True
n = int(input())
a = list(map(int, input().split()))
b = []
for i in range(n):
if not check(a):
print("NO")
break
ind = a.index(max(a))
b.append(a.pop(ind))
else:
print("YES")
``` | instruction | 0 | 7,258 | 12 | 14,516 |
Yes | output | 1 | 7,258 | 12 | 14,517 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}.
Submitted Solution:
```
n=int(input())
num=input().split()
flag=1
for i in range(n-1):
if abs((int(num[i]))-(int(num[i+1])))>=2:
flag=0
if flag==1:
print("YES")
else:
print("NO")
``` | instruction | 0 | 7,259 | 12 | 14,518 |
Yes | output | 1 | 7,259 | 12 | 14,519 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}.
Submitted Solution:
```
n = int(input())
stacks = list(map(int,input().strip().split(' ')))
while n:
for i in range(n-1):
if abs(stacks[i] - stacks[i+1]) >= 2:
print('NO')
exit(0)
stacks.remove(max(stacks))
n -= 1
print('YES')
``` | instruction | 0 | 7,260 | 12 | 14,520 |
Yes | output | 1 | 7,260 | 12 | 14,521 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}.
Submitted Solution:
```
def step(xs):
i = xs.pop(xs.index(max(xs)))
return xs + [i]
def f(xs):
while not all(xs[i] <= xs[i+1] for i in range(len(xs)-1)):
for x, y in zip(xs, xs[1:]):
if abs(y - x) > 1:
return False
xs = step(xs)
return True
if __name__ == "__main__":
input()
xs = list(map(int, input().split()))
print("YES" if f(xs) else "NO")
``` | instruction | 0 | 7,261 | 12 | 14,522 |
No | output | 1 | 7,261 | 12 | 14,523 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}.
Submitted Solution:
```
n=int(input())
flag=0
a=[int(x) for x in input().split()]
for i in range(0,len(a)):
for j in range(0,len(a)-1):
if(a[j]>=a[j+1]+2 or a[j]+2<=a[j+1]):
print("NO")
flag=1
break
c=a.index(max(a))
del a[c]
if(flag==0):
print("YES")
``` | instruction | 0 | 7,262 | 12 | 14,524 |
No | output | 1 | 7,262 | 12 | 14,525 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}.
Submitted Solution:
```
import sys
if __name__ == '__main__':
n = int(input())
arr = list(map(int, input().split()))
last_max = -1
for i in range(n):
max = 0
max_index = 0
for j in range(len(arr)):
if arr[j] > max:
max = arr[j]
max_index = j
if max_index < len(arr) - 1 and max_index > 0:
if abs(arr[max_index-1] - arr[max_index+1]) > 1:
print("NO")
sys.exit()
if last_max != -1:
if abs(max - last_max) > 1:
print("NO")
sys.exit()
last_max = max
arr.pop(max_index)
print("YES")
``` | instruction | 0 | 7,263 | 12 | 14,526 |
No | output | 1 | 7,263 | 12 | 14,527 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}.
Submitted Solution:
```
import cmath
import sys
n = int(input())
a = [int(i) for i in input().split()]
ok = True
maxi = -1;
mini = 1000000;
for x in a:
maxi = max(maxi, x)
mini = max(mini, x)
if (maxi - mini < 2):
print('YES')
sys.exit()
for i in range(1, n):
if (a[i] < a[i - 1] or abs(a[i] - a[i - 1]) > 1):
print('NO')
ok = False
break
if (ok == True):
print('YES')
``` | instruction | 0 | 7,264 | 12 | 14,528 |
No | output | 1 | 7,264 | 12 | 14,529 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
Define a function $ f $ that starts with $ 1 $ and takes a sequence of finite lengths as an argument as follows.
$ \ displaystyle f (\\ {a_1, a_2, \ ldots, a_n \\}) = \ sum_ {i = 1} ^ n {a_i} ^ i $
Given a sequence of length $ N $, $ X = \\ {x_1, x_2, \ ldots, x_N \\} $, $ f (X) for all subsequences $ X'$ except empty columns. ') Find $ and output the sum of them divided by $ 998244353 $. However, the subsequence subsequences shall be renumbered starting from $ 1 $ while maintaining the relative order in the original sequence. Also, even if two subsequences are the same as columns, if they are taken out at different positions, they shall be counted separately.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq N \ leq 10 ^ 6 $
* $ 1 \ leq x_i \ leq 10 ^ 6 $
* All inputs are integers
Input
The input is given in the following format.
$ N $
$ x_1 $ $ \ ldots $ $ x_N $
The first line is given the length $ N $. In the second row, the elements of the sequence $ X $ are given, separated by blanks.
Output
Find $ f (X') $ for all subsequences $ X'$ except empty columns, and divide the sum by $ 998244353 $ to output the remainder.
Examples
Input
3
1 2 3
Output
64
Input
5
100 200 300 400 500
Output
935740429 | instruction | 0 | 7,503 | 12 | 15,006 |
"Correct Solution:
```
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
res = list(sys.stdin.readline())
if res[-1] == "\n":
return res[:-1]
return res
def IR(n):
return [I() for i in range(n)]
def LIR(n):
return [LI() for i in range(n)]
def SR(n):
return [S() for i in range(n)]
def LSR(n):
return [LS() for i in range(n)]
sys.setrecursionlimit(1000000)
mod = 998244353
def solve():
n = I()
x = LI()
ans = 0
for i in range(n):
xi = x[i]
ans += pow(2,n-i-1,mod)*xi*pow(xi+1,i,mod)
if ans >= mod:
ans %= mod
print(ans)
return
if __name__ == "__main__":
solve()
``` | output | 1 | 7,503 | 12 | 15,007 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1 | instruction | 0 | 7,505 | 12 | 15,010 |
"Correct Solution:
```
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
from itertools import permutations
import sys
import math
import bisect
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
res = list(sys.stdin.readline())
if res[-1] == "\n":
return res[:-1]
return res
def IR(n):
return [I() for i in range(n)]
def LIR(n):
return [LI() for i in range(n)]
def SR(n):
return [S() for i in range(n)]
def LSR(n):
return [LS() for i in range(n)]
sys.setrecursionlimit(1000000)
mod = 1000000007
def solve():
n = I()
a = IR(n)
dp = [float("inf")]*n
for i in a:
j = bisect.bisect_left(dp,i)
dp[j] = i
print(n-dp.count(float("inf")))
return
#Solve
if __name__ == "__main__":
solve()
``` | output | 1 | 7,505 | 12 | 15,011 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1 | instruction | 0 | 7,506 | 12 | 15,012 |
"Correct Solution:
```
import sys
from bisect import bisect_left
def solve():
n = int(input())
A = [int(input()) for i in range(n)]
inf = 10**9 + 1
dp = [inf] * n
for a in A:
j = bisect_left(dp, a)
dp[j] = a
for i, v in enumerate(dp):
if v == inf:
print(i)
return
print(n)
def debug(x, table):
for name, val in table.items():
if x is val:
print('DEBUG:{} -> {}'.format(name, val), file=sys.stderr)
return None
if __name__ == '__main__':
solve()
``` | output | 1 | 7,506 | 12 | 15,013 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1 | instruction | 0 | 7,507 | 12 | 15,014 |
"Correct Solution:
```
import sys
from bisect import bisect_left
read = sys.stdin.read
readline = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 8)
INF = float('inf')
MOD = 10 ** 9 + 7
def main():
N = int(readline())
A = list(int(readline()) for _ in range(N))
LIS = [INF]*(N+1)
for a in A:
i = bisect_left(LIS,a)
LIS[i] = a
print(LIS.index(INF))
if __name__ == '__main__':
main()
``` | output | 1 | 7,507 | 12 | 15,015 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1 | instruction | 0 | 7,509 | 12 | 15,018 |
"Correct Solution:
```
import bisect
n = int(input())
L = []
for i in range(n):
L.append(int(input()))
dp = [float('inf')]*n
for i in range(n):
k = bisect.bisect_left(dp,L[i])
dp[k] = L[i]
ans = 0
for i in range(n):
if dp[i] != float('inf'):
ans += 1
else:
break
print(ans)
``` | output | 1 | 7,509 | 12 | 15,019 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1 | instruction | 0 | 7,510 | 12 | 15,020 |
"Correct Solution:
```
# -*- coding: utf-8 -*-
import bisect
if __name__ == '__main__':
n = int(input())
a = [int(input()) for _ in range(n)]
L = [None] * n
L[0] = a[0]
length = 1
for i in range(1, n):
if L[length - 1] < a[i]:
L[length] = a[i]
length += 1
else:
indx = bisect.bisect_left(L[:length], a[i])
L[indx] = a[i]
print(length)
``` | output | 1 | 7,510 | 12 | 15,021 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1 | instruction | 0 | 7,511 | 12 | 15,022 |
"Correct Solution:
```
import bisect
n = int(input())
A = [int(input()) for j in range(n)]
dp = A[:1]
for a_i in A[1:]:
if dp[-1] < a_i:
dp.append(a_i)
else:
dp[bisect.bisect_left(dp, a_i)] = a_i
print(len(dp))
``` | output | 1 | 7,511 | 12 | 15,023 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1 | instruction | 0 | 7,512 | 12 | 15,024 |
"Correct Solution:
```
import sys, bisect
def solve():
A = list(map(int, sys.stdin.readlines()))
n = A[0]
A = A[1:]
L = A[:1]
for a_i in A[1:]:
if a_i > L[-1]:
L.append(a_i)
else:
j = bisect.bisect_left(L, a_i)
L[j] = a_i
print(len(L))
solve()
``` | output | 1 | 7,512 | 12 | 15,025 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1
Submitted Solution:
```
from bisect import bisect_left
N = int(input())
A = [int(input()) for _ in range(N)]
LIS = [A[0]] # i番目の成分 = 長さ i+1 の増加部分列の最後の要素の値
for a in A[1:]:
if a > LIS[-1]: # 最大の長さの増加部分列の最後の要素より大きい値なら、これを用いて１つ長い増加部分列を作ることができる。
# 更新前の最長増加部分列 = [..., L[-1]]、更新後の最長増加部分列 = [..., L[-1], a]
LIS.append(a)
else:
LIS[bisect_left(LIS, a)] = a # 最長ではない増加部分列の最後の要素を小さい値に更新。これにより、a > LIS[-1] を満たす可能性が増える。
print(len(LIS))
``` | instruction | 0 | 7,513 | 12 | 15,026 |
Yes | output | 1 | 7,513 | 12 | 15,027 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1
Submitted Solution:
```
import bisect
def LIS():
L.append(a[0])
length[0] = 1
for i in range(n-1):
if L[-1]<a[i+1]:
L.append(a[i+1])
length[i+1] = length[i]+1
else:
L[bisect.bisect_left(L,a[i+1])] = a[i+1]
length[i+1] = length[i]
return length[-1]
n = int(input())
a = [int(input()) for _ in range(n)]
L = []
length = [None]*n
print(LIS())
``` | instruction | 0 | 7,514 | 12 | 15,028 |
Yes | output | 1 | 7,514 | 12 | 15,029 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1
Submitted Solution:
```
#最長増加部分列問題 (LIS)
import bisect
N = int(input())
seq = [0] * N
for i in range(N):
seq[i] = int(input())
LIS = [seq[0]]
#print(LIS)
for i in range(len(seq)):
if seq[i] > LIS[-1]:
LIS.append(seq[i])
else:
LIS[bisect.bisect_left(LIS, seq[i])] = seq[i]
#print(LIS)
#print(LIS)
print(len(LIS))
``` | instruction | 0 | 7,515 | 12 | 15,030 |
Yes | output | 1 | 7,515 | 12 | 15,031 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1
Submitted Solution:
```
from bisect import bisect_left
n=int(input())
a=[int(input()) for _ in range(n)]
dp=[float('inf') for _ in range(n)]
l=[]
l.append(a[0])
dp[0]=a[0]
for i in a[1:]:
if l[-1]<i:
l.append(i)
dp[len(l)-1]=i
else:
x=bisect_left(l,i)
dp[x]=i
l[x]=i
print(len(l))
``` | instruction | 0 | 7,516 | 12 | 15,032 |
Yes | output | 1 | 7,516 | 12 | 15,033 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1
Submitted Solution:
```
n = int(input())
in_list = []
for i in range(n):
in_list.append(list(map(int, input().split())))
matrices = [["0" for _ in range(n)] for _ in range(n)]
for i in range(n):
inp = in_list[i]
u = inp[0]
k = inp[1]
for j in range(k):
m = inp[j+2]
matrices[i][m-1] = "1"
for i in range(n):
print(" ".join(matrices[i]))
``` | instruction | 0 | 7,518 | 12 | 15,036 |
No | output | 1 | 7,518 | 12 | 15,037 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This problem is given in two editions, which differ exclusively in the constraints on the number n.
You are given an array of integers a[1], a[2], ..., a[n]. A block is a sequence of contiguous (consecutive) elements a[l], a[l+1], ..., a[r] (1 ≤ l ≤ r ≤ n). Thus, a block is defined by a pair of indices (l, r).
Find a set of blocks (l_1, r_1), (l_2, r_2), ..., (l_k, r_k) such that:
* They do not intersect (i.e. they are disjoint). Formally, for each pair of blocks (l_i, r_i) and (l_j, r_j) where i ≠ j either r_i < l_j or r_j < l_i.
* For each block the sum of its elements is the same. Formally, $$$a[l_1]+a[l_1+1]+...+a[r_1]=a[l_2]+a[l_2+1]+...+a[r_2]= ... = a[l_k]+a[l_k+1]+...+a[r_k].$$$
* The number of the blocks in the set is maximum. Formally, there does not exist a set of blocks (l_1', r_1'), (l_2', r_2'), ..., (l_{k'}', r_{k'}') satisfying the above two requirements with k' > k.
<image> The picture corresponds to the first example. Blue boxes illustrate blocks.
Write a program to find such a set of blocks.
Input
The first line contains integer n (1 ≤ n ≤ 1500) — the length of the given array. The second line contains the sequence of elements a[1], a[2], ..., a[n] (-10^5 ≤ a_i ≤ 10^5).
Output
In the first line print the integer k (1 ≤ k ≤ n). The following k lines should contain blocks, one per line. In each line print a pair of indices l_i, r_i (1 ≤ l_i ≤ r_i ≤ n) — the bounds of the i-th block. You can print blocks in any order. If there are multiple answers, print any of them.
Examples
Input
7
4 1 2 2 1 5 3
Output
3
7 7
2 3
4 5
Input
11
-5 -4 -3 -2 -1 0 1 2 3 4 5
Output
2
3 4
1 1
Input
4
1 1 1 1
Output
4
4 4
1 1
2 2
3 3 | instruction | 0 | 7,614 | 12 | 15,228 |
Tags: data structures, greedy
Correct Solution:
```
"""
#If FastIO not needed, used this and don't forget to strip
#import sys, math
#input = sys.stdin.readline
"""
import os
import sys
from io import BytesIO, IOBase
import heapq as h
from bisect import bisect_left, bisect_right
from types import GeneratorType
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
import os
self.os = os
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 = self.os.read(self._fd, max(self.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 = self.os.read(self._fd, max(self.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:
self.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")
from collections import defaultdict as dd, deque as dq
import math, string
def getInts():
return [int(s) for s in input().split()]
def getInt():
return int(input())
def getStrs():
return [s for s in input().split()]
def getStr():
return input()
def listStr():
return list(input())
MOD = 10**9+7
"""
we can use prefix sums to calculate every possible subarray - there are at most 1275 of these
For each possible value we can greedily take the first index to finish?
"""
def solve():
N = getInt()
A = getInts()
P, curr = [0], 0
for a in A:
curr += a
P.append(curr)
D = dd(list)
for L in range(N):
for R in range(L+1,N+1):
D[P[R]-P[L]].append((R,L))
best = 0
best_key = -10**9
best_arr = []
for key, arr in D.items():
D[key].sort(reverse=True)
tmp = []
while D[key]:
R, L = D[key].pop()
if not tmp or L >= prev_R:
tmp.append((L,R))
prev_R = R
if len(tmp) > best:
best = len(tmp)
best_key = key
best_arr = tmp[:]
print(best)
for L, R in best_arr:
print(L+1,R)
return
#for _ in range(getInt()):
solve()
``` | output | 1 | 7,614 | 12 | 15,229 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This problem is given in two editions, which differ exclusively in the constraints on the number n.
You are given an array of integers a[1], a[2], ..., a[n]. A block is a sequence of contiguous (consecutive) elements a[l], a[l+1], ..., a[r] (1 ≤ l ≤ r ≤ n). Thus, a block is defined by a pair of indices (l, r).
Find a set of blocks (l_1, r_1), (l_2, r_2), ..., (l_k, r_k) such that:
* They do not intersect (i.e. they are disjoint). Formally, for each pair of blocks (l_i, r_i) and (l_j, r_j) where i ≠ j either r_i < l_j or r_j < l_i.
* For each block the sum of its elements is the same. Formally, $$$a[l_1]+a[l_1+1]+...+a[r_1]=a[l_2]+a[l_2+1]+...+a[r_2]= ... = a[l_k]+a[l_k+1]+...+a[r_k].$$$
* The number of the blocks in the set is maximum. Formally, there does not exist a set of blocks (l_1', r_1'), (l_2', r_2'), ..., (l_{k'}', r_{k'}') satisfying the above two requirements with k' > k.
<image> The picture corresponds to the first example. Blue boxes illustrate blocks.
Write a program to find such a set of blocks.
Input
The first line contains integer n (1 ≤ n ≤ 1500) — the length of the given array. The second line contains the sequence of elements a[1], a[2], ..., a[n] (-10^5 ≤ a_i ≤ 10^5).
Output
In the first line print the integer k (1 ≤ k ≤ n). The following k lines should contain blocks, one per line. In each line print a pair of indices l_i, r_i (1 ≤ l_i ≤ r_i ≤ n) — the bounds of the i-th block. You can print blocks in any order. If there are multiple answers, print any of them.
Examples
Input
7
4 1 2 2 1 5 3
Output
3
7 7
2 3
4 5
Input
11
-5 -4 -3 -2 -1 0 1 2 3 4 5
Output
2
3 4
1 1
Input
4
1 1 1 1
Output
4
4 4
1 1
2 2
3 3 | instruction | 0 | 7,615 | 12 | 15,230 |
Tags: data structures, greedy
Correct Solution:
```
from collections import defaultdict
def main():
n = int(input())
values = list(map(int, input().split(' ')))
# print(values)
ans = defaultdict(list)
for i in range(n):
s = 0
# print("---------- i = {} ----------".format(i))
for j in range(i, -1, -1):
s += values[j]
# print("i = {}; j = {} s = {}".format(i, j, s))
# print("ans = {}; (i + 1) = {}".format(i + 1, ans[s][-1]))
# if (i + 1) not in ans[s][-1]:
ans[s].append((j + 1, i + 1))
# print(ans)
answer = dict()
max = 0
for key in ans:
# print("key = {} ; ans[key] = {}".format(key, ans[key], len(ans[key])))
sum_pairs = ans[key]
non_overlap_pairs = [sum_pairs[0]]
previous_pair_second_value = sum_pairs[0][1]
for each_pair in sum_pairs[1:]:
# print("each_pair = {}".format(each_pair))
if previous_pair_second_value < each_pair[0]:
# print(each_pair)
non_overlap_pairs.append(each_pair)
previous_pair_second_value = each_pair[1]
# else:
# print("Found overlapping pair for key = {}".format(each_pair))
# ans[key] = non_overlap_pairs
if len(non_overlap_pairs) > max:
max = len(non_overlap_pairs)
answer = {max: non_overlap_pairs}
# print(list(answer.keys())[0])
for key in answer.keys():
print(key)
for value in answer[key]:
print(str(value[0]) + ' ' + str(value[1]))
if __name__=="__main__":
main()
``` | output | 1 | 7,615 | 12 | 15,231 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This problem is given in two editions, which differ exclusively in the constraints on the number n.
You are given an array of integers a[1], a[2], ..., a[n]. A block is a sequence of contiguous (consecutive) elements a[l], a[l+1], ..., a[r] (1 ≤ l ≤ r ≤ n). Thus, a block is defined by a pair of indices (l, r).
Find a set of blocks (l_1, r_1), (l_2, r_2), ..., (l_k, r_k) such that:
* They do not intersect (i.e. they are disjoint). Formally, for each pair of blocks (l_i, r_i) and (l_j, r_j) where i ≠ j either r_i < l_j or r_j < l_i.
* For each block the sum of its elements is the same. Formally, $$$a[l_1]+a[l_1+1]+...+a[r_1]=a[l_2]+a[l_2+1]+...+a[r_2]= ... = a[l_k]+a[l_k+1]+...+a[r_k].$$$
* The number of the blocks in the set is maximum. Formally, there does not exist a set of blocks (l_1', r_1'), (l_2', r_2'), ..., (l_{k'}', r_{k'}') satisfying the above two requirements with k' > k.
<image> The picture corresponds to the first example. Blue boxes illustrate blocks.
Write a program to find such a set of blocks.
Input
The first line contains integer n (1 ≤ n ≤ 1500) — the length of the given array. The second line contains the sequence of elements a[1], a[2], ..., a[n] (-10^5 ≤ a_i ≤ 10^5).
Output
In the first line print the integer k (1 ≤ k ≤ n). The following k lines should contain blocks, one per line. In each line print a pair of indices l_i, r_i (1 ≤ l_i ≤ r_i ≤ n) — the bounds of the i-th block. You can print blocks in any order. If there are multiple answers, print any of them.
Examples
Input
7
4 1 2 2 1 5 3
Output
3
7 7
2 3
4 5
Input
11
-5 -4 -3 -2 -1 0 1 2 3 4 5
Output
2
3 4
1 1
Input
4
1 1 1 1
Output
4
4 4
1 1
2 2
3 3 | instruction | 0 | 7,616 | 12 | 15,232 |
Tags: data structures, greedy
Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
if n == 1:
print(1)
print('1 1')
else:
d = [[]]*(n-1)
d[0] = a
for i in range(1,n-1):
d[i] = [d[i-1][j]+a[j+i] for j in range(0,n-i)]
d2 = {}
for i,d_ in enumerate(d):
for j,x in enumerate(d_):
if x in d2:
d2[x].append([j+1,j+i+1])
else:
d2[x]=[[j+1,j+i+1]]
list_keys = list(d2.keys())
#res = 0
ma = 0
for key in list_keys:
d2[key].sort(key=lambda x:x[1])
after = -1
cnt = 0
tmp = []
for y,z in d2[key]:
if y > after:
cnt += 1
after = z
tmp.append([y,z])
if cnt > ma:
ma = cnt
res = tmp
# for j in range(len(d2[key])):
# after = -1
# cnt = 0
# tmp = []
# for y,z in d2[key][j:]:
# if y > after:
# cnt += 1
# after = z
# tmp.append([y,z])
# if cnt > ma:
# ma = cnt
# res = tmp
print(len(res))
for x in res:
print(*x)
``` | output | 1 | 7,616 | 12 | 15,233 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This problem is given in two editions, which differ exclusively in the constraints on the number n.
You are given an array of integers a[1], a[2], ..., a[n]. A block is a sequence of contiguous (consecutive) elements a[l], a[l+1], ..., a[r] (1 ≤ l ≤ r ≤ n). Thus, a block is defined by a pair of indices (l, r).
Find a set of blocks (l_1, r_1), (l_2, r_2), ..., (l_k, r_k) such that:
* They do not intersect (i.e. they are disjoint). Formally, for each pair of blocks (l_i, r_i) and (l_j, r_j) where i ≠ j either r_i < l_j or r_j < l_i.
* For each block the sum of its elements is the same. Formally, $$$a[l_1]+a[l_1+1]+...+a[r_1]=a[l_2]+a[l_2+1]+...+a[r_2]= ... = a[l_k]+a[l_k+1]+...+a[r_k].$$$
* The number of the blocks in the set is maximum. Formally, there does not exist a set of blocks (l_1', r_1'), (l_2', r_2'), ..., (l_{k'}', r_{k'}') satisfying the above two requirements with k' > k.
<image> The picture corresponds to the first example. Blue boxes illustrate blocks.
Write a program to find such a set of blocks.
Input
The first line contains integer n (1 ≤ n ≤ 1500) — the length of the given array. The second line contains the sequence of elements a[1], a[2], ..., a[n] (-10^5 ≤ a_i ≤ 10^5).
Output
In the first line print the integer k (1 ≤ k ≤ n). The following k lines should contain blocks, one per line. In each line print a pair of indices l_i, r_i (1 ≤ l_i ≤ r_i ≤ n) — the bounds of the i-th block. You can print blocks in any order. If there are multiple answers, print any of them.
Examples
Input
7
4 1 2 2 1 5 3
Output
3
7 7
2 3
4 5
Input
11
-5 -4 -3 -2 -1 0 1 2 3 4 5
Output
2
3 4
1 1
Input
4
1 1 1 1
Output
4
4 4
1 1
2 2
3 3 | instruction | 0 | 7,617 | 12 | 15,234 |
Tags: data structures, greedy
Correct Solution:
```
n=int(input())
ans=[]
l=[int(i) for i in input().split()]
from collections import defaultdict
d=defaultdict(list)
for i in range(n):
sm=0
for j in range(i,n):
sm+=l[j]
d[sm].append([i,j])
for sm in d:
z=d[sm]
#print(z)
z.sort(key=lambda x:x[1])#activity selection
t=[z[0]]
#print(t)
#print(t[-1])
for i in z:
#print(i[0])
if i[0]<=t[-1][1]:
continue
t.append(i)
if len(t)>len(ans):
ans=t
print(len(ans))
for i in range(len(ans)):
print(ans[i][0]+1,ans[i][1]+1)
``` | output | 1 | 7,617 | 12 | 15,235 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This problem is given in two editions, which differ exclusively in the constraints on the number n.
You are given an array of integers a[1], a[2], ..., a[n]. A block is a sequence of contiguous (consecutive) elements a[l], a[l+1], ..., a[r] (1 ≤ l ≤ r ≤ n). Thus, a block is defined by a pair of indices (l, r).
Find a set of blocks (l_1, r_1), (l_2, r_2), ..., (l_k, r_k) such that:
* They do not intersect (i.e. they are disjoint). Formally, for each pair of blocks (l_i, r_i) and (l_j, r_j) where i ≠ j either r_i < l_j or r_j < l_i.
* For each block the sum of its elements is the same. Formally, $$$a[l_1]+a[l_1+1]+...+a[r_1]=a[l_2]+a[l_2+1]+...+a[r_2]= ... = a[l_k]+a[l_k+1]+...+a[r_k].$$$
* The number of the blocks in the set is maximum. Formally, there does not exist a set of blocks (l_1', r_1'), (l_2', r_2'), ..., (l_{k'}', r_{k'}') satisfying the above two requirements with k' > k.
<image> The picture corresponds to the first example. Blue boxes illustrate blocks.
Write a program to find such a set of blocks.
Input
The first line contains integer n (1 ≤ n ≤ 1500) — the length of the given array. The second line contains the sequence of elements a[1], a[2], ..., a[n] (-10^5 ≤ a_i ≤ 10^5).
Output
In the first line print the integer k (1 ≤ k ≤ n). The following k lines should contain blocks, one per line. In each line print a pair of indices l_i, r_i (1 ≤ l_i ≤ r_i ≤ n) — the bounds of the i-th block. You can print blocks in any order. If there are multiple answers, print any of them.
Examples
Input
7
4 1 2 2 1 5 3
Output
3
7 7
2 3
4 5
Input
11
-5 -4 -3 -2 -1 0 1 2 3 4 5
Output
2
3 4
1 1
Input
4
1 1 1 1
Output
4
4 4
1 1
2 2
3 3 | instruction | 0 | 7,618 | 12 | 15,236 |
Tags: data structures, greedy
Correct Solution:
```
# Legends Always Come Up with Solution
# Author: Manvir Singh
import os
import sys
from io import BytesIO, IOBase
from collections import defaultdict
def main():
n=int(input())
a=list(map(int,input().split()))
b,ma,ans=defaultdict(list),0,[]
for i in range(n):
su=0
for j in range(i,n):
su+=a[j]
b[su].append((i,j))
for i in b:
z,c=b[i],0
for j in range(len(z)-1):
if z[j+1][0]<=z[j][1]:
if z[j][1]<=z[j+1][1]:
z[j+1]=z[j]
z[j]=[]
else:
c+=1
c+=(z[-1]!=[])
if ma<c:
ma,ans=c,z
print(ma)
for i in ans:
if i!=[]:
print(i[0]+1,i[1]+1)
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
if __name__ == "__main__":
main()
``` | output | 1 | 7,618 | 12 | 15,237 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This problem is given in two editions, which differ exclusively in the constraints on the number n.
You are given an array of integers a[1], a[2], ..., a[n]. A block is a sequence of contiguous (consecutive) elements a[l], a[l+1], ..., a[r] (1 ≤ l ≤ r ≤ n). Thus, a block is defined by a pair of indices (l, r).
Find a set of blocks (l_1, r_1), (l_2, r_2), ..., (l_k, r_k) such that:
* They do not intersect (i.e. they are disjoint). Formally, for each pair of blocks (l_i, r_i) and (l_j, r_j) where i ≠ j either r_i < l_j or r_j < l_i.
* For each block the sum of its elements is the same. Formally, $$$a[l_1]+a[l_1+1]+...+a[r_1]=a[l_2]+a[l_2+1]+...+a[r_2]= ... = a[l_k]+a[l_k+1]+...+a[r_k].$$$
* The number of the blocks in the set is maximum. Formally, there does not exist a set of blocks (l_1', r_1'), (l_2', r_2'), ..., (l_{k'}', r_{k'}') satisfying the above two requirements with k' > k.
<image> The picture corresponds to the first example. Blue boxes illustrate blocks.
Write a program to find such a set of blocks.
Input
The first line contains integer n (1 ≤ n ≤ 1500) — the length of the given array. The second line contains the sequence of elements a[1], a[2], ..., a[n] (-10^5 ≤ a_i ≤ 10^5).
Output
In the first line print the integer k (1 ≤ k ≤ n). The following k lines should contain blocks, one per line. In each line print a pair of indices l_i, r_i (1 ≤ l_i ≤ r_i ≤ n) — the bounds of the i-th block. You can print blocks in any order. If there are multiple answers, print any of them.
Examples
Input
7
4 1 2 2 1 5 3
Output
3
7 7
2 3
4 5
Input
11
-5 -4 -3 -2 -1 0 1 2 3 4 5
Output
2
3 4
1 1
Input
4
1 1 1 1
Output
4
4 4
1 1
2 2
3 3 | instruction | 0 | 7,619 | 12 | 15,238 |
Tags: data structures, greedy
Correct Solution:
```
# Legends Always Come Up with Solution
# Author: Manvir Singh
import os
import sys
from io import BytesIO, IOBase
from collections import defaultdict
def main():
n=int(input())
a=list(map(int,input().split()))
b=defaultdict(list)
for i in range(n):
su=0
for j in range(i,n):
su+=a[j]
b[su].append((i,j))
ma,ans=0,set()
for i in b:
z,c=b[i],set()
for j in range(len(z)-1):
if z[j+1][0]<=z[j][1]:
if z[j][1]<=z[j+1][1]:
z[j+1]=z[j]
z[j]=[]
else:
c.add(z[j])
if z[-1]:
c.add(z[-1])
if ma<len(c):
ma=len(c)
ans=c
print(ma)
for i in ans:
print(i[0]+1,i[1]+1)
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
if __name__ == "__main__":
main()
``` | output | 1 | 7,619 | 12 | 15,239 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This problem is given in two editions, which differ exclusively in the constraints on the number n.
You are given an array of integers a[1], a[2], ..., a[n]. A block is a sequence of contiguous (consecutive) elements a[l], a[l+1], ..., a[r] (1 ≤ l ≤ r ≤ n). Thus, a block is defined by a pair of indices (l, r).
Find a set of blocks (l_1, r_1), (l_2, r_2), ..., (l_k, r_k) such that:
* They do not intersect (i.e. they are disjoint). Formally, for each pair of blocks (l_i, r_i) and (l_j, r_j) where i ≠ j either r_i < l_j or r_j < l_i.
* For each block the sum of its elements is the same. Formally, $$$a[l_1]+a[l_1+1]+...+a[r_1]=a[l_2]+a[l_2+1]+...+a[r_2]= ... = a[l_k]+a[l_k+1]+...+a[r_k].$$$
* The number of the blocks in the set is maximum. Formally, there does not exist a set of blocks (l_1', r_1'), (l_2', r_2'), ..., (l_{k'}', r_{k'}') satisfying the above two requirements with k' > k.
<image> The picture corresponds to the first example. Blue boxes illustrate blocks.
Write a program to find such a set of blocks.
Input
The first line contains integer n (1 ≤ n ≤ 1500) — the length of the given array. The second line contains the sequence of elements a[1], a[2], ..., a[n] (-10^5 ≤ a_i ≤ 10^5).
Output
In the first line print the integer k (1 ≤ k ≤ n). The following k lines should contain blocks, one per line. In each line print a pair of indices l_i, r_i (1 ≤ l_i ≤ r_i ≤ n) — the bounds of the i-th block. You can print blocks in any order. If there are multiple answers, print any of them.
Examples
Input
7
4 1 2 2 1 5 3
Output
3
7 7
2 3
4 5
Input
11
-5 -4 -3 -2 -1 0 1 2 3 4 5
Output
2
3 4
1 1
Input
4
1 1 1 1
Output
4
4 4
1 1
2 2
3 3 | instruction | 0 | 7,620 | 12 | 15,240 |
Tags: data structures, greedy
Correct Solution:
```
# Legends Always Come Up with Solution
# Author: Manvir Singh
import os
import sys
from io import BytesIO, IOBase
from collections import defaultdict
def main():
n=int(input())
a=list(map(int,input().split()))
b=defaultdict(list)
for i in range(n):
su=0
for j in range(i,n):
su+=a[j]
b[su].append([i,j])
ma,ans=0,set()
for i in b:
z,c=b[i],set()
for j in range(len(z)-1):
if z[j+1][0]<=z[j][1]:
if z[j][1]<=z[j+1][1]:
z[j+1]=z[j]
z[j]=[]
for j in range(len(z)):
if z[j]:
c.add(tuple(z[j]))
if ma<len(c):
ma=len(c)
ans=c
print(ma)
for i in ans:
print(i[0]+1,i[1]+1)
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
if __name__ == "__main__":
main()
``` | output | 1 | 7,620 | 12 | 15,241 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This problem is given in two editions, which differ exclusively in the constraints on the number n.
You are given an array of integers a[1], a[2], ..., a[n]. A block is a sequence of contiguous (consecutive) elements a[l], a[l+1], ..., a[r] (1 ≤ l ≤ r ≤ n). Thus, a block is defined by a pair of indices (l, r).
Find a set of blocks (l_1, r_1), (l_2, r_2), ..., (l_k, r_k) such that:
* They do not intersect (i.e. they are disjoint). Formally, for each pair of blocks (l_i, r_i) and (l_j, r_j) where i ≠ j either r_i < l_j or r_j < l_i.
* For each block the sum of its elements is the same. Formally, $$$a[l_1]+a[l_1+1]+...+a[r_1]=a[l_2]+a[l_2+1]+...+a[r_2]= ... = a[l_k]+a[l_k+1]+...+a[r_k].$$$
* The number of the blocks in the set is maximum. Formally, there does not exist a set of blocks (l_1', r_1'), (l_2', r_2'), ..., (l_{k'}', r_{k'}') satisfying the above two requirements with k' > k.
<image> The picture corresponds to the first example. Blue boxes illustrate blocks.
Write a program to find such a set of blocks.
Input
The first line contains integer n (1 ≤ n ≤ 1500) — the length of the given array. The second line contains the sequence of elements a[1], a[2], ..., a[n] (-10^5 ≤ a_i ≤ 10^5).
Output
In the first line print the integer k (1 ≤ k ≤ n). The following k lines should contain blocks, one per line. In each line print a pair of indices l_i, r_i (1 ≤ l_i ≤ r_i ≤ n) — the bounds of the i-th block. You can print blocks in any order. If there are multiple answers, print any of them.
Examples
Input
7
4 1 2 2 1 5 3
Output
3
7 7
2 3
4 5
Input
11
-5 -4 -3 -2 -1 0 1 2 3 4 5
Output
2
3 4
1 1
Input
4
1 1 1 1
Output
4
4 4
1 1
2 2
3 3 | instruction | 0 | 7,621 | 12 | 15,242 |
Tags: data structures, greedy
Correct Solution:
```
import sys
from collections import defaultdict
import math
n=int(sys.stdin.readline())
arr=list(map(int,sys.stdin.readline().split()))
dp=defaultdict(list)
for i in range(n):
s=0
for j in range(i,n):
s+=arr[j]
dp[s].append([j,i])
ans=0
#print(dp,'dp')
rem=[]
for s in dp:
dp[s].sort()
m=len(dp[s])
lastj=-1
count=0
temp=[]
for k in range(m):
j,i=dp[s][k]
if i>lastj:
temp.append([i,j])
count+=1
lastj=j
#ans=max(ans,count)
if ans<count:
ans=count
#print(temp,'temp')
rem=[a for a in temp]
print(ans)
for i in range(ans):
print(rem[i][0]+1,rem[i][1]+1)
``` | output | 1 | 7,621 | 12 | 15,243 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This problem is given in two editions, which differ exclusively in the constraints on the number n.
You are given an array of integers a[1], a[2], ..., a[n]. A block is a sequence of contiguous (consecutive) elements a[l], a[l+1], ..., a[r] (1 ≤ l ≤ r ≤ n). Thus, a block is defined by a pair of indices (l, r).
Find a set of blocks (l_1, r_1), (l_2, r_2), ..., (l_k, r_k) such that:
* They do not intersect (i.e. they are disjoint). Formally, for each pair of blocks (l_i, r_i) and (l_j, r_j) where i ≠ j either r_i < l_j or r_j < l_i.
* For each block the sum of its elements is the same. Formally, $$$a[l_1]+a[l_1+1]+...+a[r_1]=a[l_2]+a[l_2+1]+...+a[r_2]= ... = a[l_k]+a[l_k+1]+...+a[r_k].$$$
* The number of the blocks in the set is maximum. Formally, there does not exist a set of blocks (l_1', r_1'), (l_2', r_2'), ..., (l_{k'}', r_{k'}') satisfying the above two requirements with k' > k.
<image> The picture corresponds to the first example. Blue boxes illustrate blocks.
Write a program to find such a set of blocks.
Input
The first line contains integer n (1 ≤ n ≤ 1500) — the length of the given array. The second line contains the sequence of elements a[1], a[2], ..., a[n] (-10^5 ≤ a_i ≤ 10^5).
Output
In the first line print the integer k (1 ≤ k ≤ n). The following k lines should contain blocks, one per line. In each line print a pair of indices l_i, r_i (1 ≤ l_i ≤ r_i ≤ n) — the bounds of the i-th block. You can print blocks in any order. If there are multiple answers, print any of them.
Examples
Input
7
4 1 2 2 1 5 3
Output
3
7 7
2 3
4 5
Input
11
-5 -4 -3 -2 -1 0 1 2 3 4 5
Output
2
3 4
1 1
Input
4
1 1 1 1
Output
4
4 4
1 1
2 2
3 3
Submitted Solution:
```
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# @oj: codeforces
# @id: hitwanyang
# @email: 296866643@qq.com
# @date: 2020/12/17 17:03
# @url: https://codeforc.es/contest/1141/problem/F2
import sys, os
from io import BytesIO, IOBase
import collections, itertools, bisect, heapq, math, string
from decimal import *
# region fastio
BUFSIZE = 8192
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------------------
## 注意嵌套括号!!!!!!
## 先有思路,再写代码,别着急!!!
## 先有朴素解法,不要有思维定式,试着换思路解决
## 精度 print("%.10f" % ans)
## sqrt:int(math.sqrt(n))+1
## 字符串拼接不要用+操作，会超时
## 二进制转换:bin(1)[2:].rjust(32,'0')
## array copy:cur=array[::]
## oeis:example 1, 3, _, 1260, _, _, _, _, _, 12164510040883200
## sqrt:Decimal(x).sqrt()避免精度误差
## 无穷大表示:float('inf')
def main():
n = int(input())
a = list(map(int, input().split()))
res = []
prefix = list(itertools.accumulate(a))
d = collections.defaultdict(list)
for i in range(n):
for j in range(i, n):
if i == 0:
d[prefix[j]].append((i, j))
# res.append((i, j, prefix[j]))
else:
v = prefix[j] - prefix[i - 1]
d[v].append((i, j))
# res.append((i, j, prefix[j] - prefix[i - 1]))
ans = []
for k in d.keys():
v = d[k]
cnt = []
tmp = sorted(v,key=lambda x:(x[1],x[0]))
if len(tmp) == 1:
cnt.append((tmp[0][0] + 1, tmp[0][1] + 1))
else:
pre = tmp[0]
# 贪心求不相交区间的最大个数
cnt.append((pre[0] + 1, pre[1] + 1))
for i in range(1, len(tmp)):
cur = tmp[i]
if cur[0] > pre[1]:
cnt.append((cur[0] + 1, cur[1] + 1))
pre = cur
if len(cnt) > len(ans):
ans = cnt
############## TLE code ##############
## 按区间右端点排序
# sr = sorted(res, key=lambda x: (x[2], x[1], x[0]))
# print(time.time() - start)
# l, r = 0, 0
# while r < len(sr):
# pre = sr[l]
# cnt = [(pre[0] + 1, pre[1] + 1)]
# while r < len(sr) and sr[l][2] == sr[r][2]:
# cur=sr[r]
# if cur[0] > pre[1]:
# cnt.append((cur[0] + 1, cur[1] + 1))
# pre = cur
# r += 1
# l = r
# if len(cnt) > len(ans):
# ans = cnt
# print (time.time()-start)
print(len(ans))
for a in ans:
print(a[0], a[1])
if __name__ == "__main__":
main()
``` | instruction | 0 | 7,622 | 12 | 15,244 |
Yes | output | 1 | 7,622 | 12 | 15,245 |
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