message stringlengths 2 23.8k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 97 109k | cluster float64 0 0 | __index_level_0__ int64 194 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s of length n consisting of lowercase English letters.
For two given strings s and t, say S is the set of distinct characters of s and T is the set of distinct characters of t. The strings s and t are isomorphic if their lengths are equal and there is a one-to-one mapping (bijection) f between S and T for which f(si) = ti. Formally:
1. f(si) = ti for any index i,
2. for any character <image> there is exactly one character <image> that f(x) = y,
3. for any character <image> there is exactly one character <image> that f(x) = y.
For example, the strings "aababc" and "bbcbcz" are isomorphic. Also the strings "aaaww" and "wwwaa" are isomorphic. The following pairs of strings are not isomorphic: "aab" and "bbb", "test" and "best".
You have to handle m queries characterized by three integers x, y, len (1 ≤ x, y ≤ n - len + 1). For each query check if two substrings s[x... x + len - 1] and s[y... y + len - 1] are isomorphic.
Input
The first line contains two space-separated integers n and m (1 ≤ n ≤ 2·105, 1 ≤ m ≤ 2·105) — the length of the string s and the number of queries.
The second line contains string s consisting of n lowercase English letters.
The following m lines contain a single query on each line: xi, yi and leni (1 ≤ xi, yi ≤ n, 1 ≤ leni ≤ n - max(xi, yi) + 1) — the description of the pair of the substrings to check.
Output
For each query in a separate line print "YES" if substrings s[xi... xi + leni - 1] and s[yi... yi + leni - 1] are isomorphic and "NO" otherwise.
Example
Input
7 4
abacaba
1 1 1
1 4 2
2 1 3
2 4 3
Output
YES
YES
NO
YES
Note
The queries in the example are following:
1. substrings "a" and "a" are isomorphic: f(a) = a;
2. substrings "ab" and "ca" are isomorphic: f(a) = c, f(b) = a;
3. substrings "bac" and "aba" are not isomorphic since f(b) and f(c) must be equal to a at same time;
4. substrings "bac" and "cab" are isomorphic: f(b) = c, f(a) = a, f(c) = b.
Submitted Solution:
```
import sys
import os
def isomorphic(a,b):
sa = sorted(a)
sb = sorted(b)
fa = dict()
for ca,cb in zip(sa,sb):
if ca in fa.keys():
db = fa[ca]
if (db != cb):
return False
else:
if (cb in fa.values()):
return False
else:
fa[ca] = cb
return True
(n,m) = map(int, input().split())
s = input()
for idx in range(0,m):
(x,y,len) = map(int, input().split())
a = s[x-1:x-1+len]
b = s[y-1:y-1+len]
if isomorphic(a,b):
print("YES")
else:
print("NO")
``` | instruction | 0 | 83,138 | 0 | 166,276 |
No | output | 1 | 83,138 | 0 | 166,277 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s of length n consisting of lowercase English letters.
For two given strings s and t, say S is the set of distinct characters of s and T is the set of distinct characters of t. The strings s and t are isomorphic if their lengths are equal and there is a one-to-one mapping (bijection) f between S and T for which f(si) = ti. Formally:
1. f(si) = ti for any index i,
2. for any character <image> there is exactly one character <image> that f(x) = y,
3. for any character <image> there is exactly one character <image> that f(x) = y.
For example, the strings "aababc" and "bbcbcz" are isomorphic. Also the strings "aaaww" and "wwwaa" are isomorphic. The following pairs of strings are not isomorphic: "aab" and "bbb", "test" and "best".
You have to handle m queries characterized by three integers x, y, len (1 ≤ x, y ≤ n - len + 1). For each query check if two substrings s[x... x + len - 1] and s[y... y + len - 1] are isomorphic.
Input
The first line contains two space-separated integers n and m (1 ≤ n ≤ 2·105, 1 ≤ m ≤ 2·105) — the length of the string s and the number of queries.
The second line contains string s consisting of n lowercase English letters.
The following m lines contain a single query on each line: xi, yi and leni (1 ≤ xi, yi ≤ n, 1 ≤ leni ≤ n - max(xi, yi) + 1) — the description of the pair of the substrings to check.
Output
For each query in a separate line print "YES" if substrings s[xi... xi + leni - 1] and s[yi... yi + leni - 1] are isomorphic and "NO" otherwise.
Example
Input
7 4
abacaba
1 1 1
1 4 2
2 1 3
2 4 3
Output
YES
YES
NO
YES
Note
The queries in the example are following:
1. substrings "a" and "a" are isomorphic: f(a) = a;
2. substrings "ab" and "ca" are isomorphic: f(a) = c, f(b) = a;
3. substrings "bac" and "aba" are not isomorphic since f(b) and f(c) must be equal to a at same time;
4. substrings "bac" and "cab" are isomorphic: f(b) = c, f(a) = a, f(c) = b.
Submitted Solution:
```
import os, sys, math
def main():
n,m = [int(x) for x in input().split()]
s = input()
for i in range(m):
xi,yi,li = [int(x) for x in input().split()]
cond = isomorphic(s,xi,yi,li) and isomorphic(s,yi,xi,li)
if cond:
print("YES")
else:
print("NO")
def isomorphic(s,xi,yi,li):
d = {}
try:
for i in range(li):
if not (s[xi+i] in d):
d[s[xi+i]] = s[yi+i]
else:
if d[s[xi+i]] == s[yi+i]:
continue
else:
return False
return True
except IndexError:
return True
def debug(*args):
if 'DEBUG' in os.environ:
print(*args)
if __name__ == '__main__':
main()
``` | instruction | 0 | 83,139 | 0 | 166,278 |
No | output | 1 | 83,139 | 0 | 166,279 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337 | instruction | 0 | 83,456 | 0 | 166,912 |
Tags: combinatorics, constructive algorithms, math, strings
Correct Solution:
```
for _ in range(int(input())):
n = int(input())
t1 = 0
while (t1 * (t1 + 1)) // 2 <= n:
t1 += 1
n -= (t1 * (t1 - 1)) // 2
print('133' + '7' * n + (t1 - 2) * '3' + '7')
``` | output | 1 | 83,456 | 0 | 166,913 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337 | instruction | 0 | 83,457 | 0 | 166,914 |
Tags: combinatorics, constructive algorithms, math, strings
Correct Solution:
```
import bisect
ans=[-1]
n=0
while ans[-1]<=1000000000:
ans.append(n*(n+1)//2 )
#print(ans[-1])
n+=1
ans.pop(0)
#print(ans[:10])
for _ in range(int(input())):
n=int(input())
s="1"
lol=bisect.bisect(ans,n)
s+="3"*(lol)
# print(s)
bacha=(n-ans[lol-1])
s=list(s)
s.pop()
s.pop()
s.append("1"*bacha)
s.append("337")
print(("".join(s)))
``` | output | 1 | 83,457 | 0 | 166,915 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337 | instruction | 0 | 83,458 | 0 | 166,916 |
Tags: combinatorics, constructive algorithms, math, strings
Correct Solution:
```
from bisect import bisect
tri = []
i = 1
while (i*(i+1))//2 <= 10**9:
tri.append((i*(i+1))//2)
i += 1
q = int(input())
for _ in range(q):
n = int(input())
a = []
i = bisect(tri, n)
while tri[i-1] < n:
a.append(i+1)
n -= tri[i-1]
i = bisect(tri, n)
a.append(i+1)
a.reverse()
g = [a[0]]
for i in range(len(a)-1):
g.append(a[i+1]-a[i])
ans = "7"
for x in g:
ans += "3"*x
ans += "1"
print(ans[::-1])
``` | output | 1 | 83,458 | 0 | 166,917 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337 | instruction | 0 | 83,459 | 0 | 166,918 |
Tags: combinatorics, constructive algorithms, math, strings
Correct Solution:
```
from math import floor
t=int(input())
for i2 in range(t):
n=int(input())
if n<20:
print("133"+"7"*n)
continue
x=floor((n*2)**(1/2))-1
ma,ans=x,[0]*100000
n-=x*(x-1)//2
while n>5:
x=floor((n*2)**(1/2))-1
n-=x*(x-1)//2
ans[x]+=1
ans[2]+=n
print("1",end="")
for i in range(1,ma+1):
print("3",end="")
print("1"*ans[ma-i],end="")
print("7")
``` | output | 1 | 83,459 | 0 | 166,919 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337 | instruction | 0 | 83,460 | 0 | 166,920 |
Tags: combinatorics, constructive algorithms, math, strings
Correct Solution:
```
# ------------------- fast io --------------------
import os
import sys
from io import BytesIO, IOBase
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")
# ------------------- fast io --------------------
from math import gcd, ceil
def prod(a, mod=10**9+7):
ans = 1
for each in a:
ans = (ans * each) % mod
return ans
def lcm(a, b): return a * b // gcd(a, b)
def binary(x, length=16):
y = bin(x)[2:]
return y if len(y) >= length else "0" * (length - len(y)) + y
for _ in range(int(input()) if True else 1):
n = int(input())
#n, k = map(int, input().split())
#a, b = map(int, input().split())
#c, d = map(int, input().split())
#a = list(map(int, input().split()))
#b = list(map(int, input().split()))
if n <= 6:
print("1"*n + "337")
continue
# 1337
# 111111... 33 777777.....
# 1 * x + 3 * y + 7 * z
# x*y*(y-1)*z = 2*n
# 1*choose(y,2)*1
y = 4
while True:
total = (y*(y-1)) // 2
# 1 33 7 33 7
if (n - total) + y + 2 <= 10**5:
print("1" + "3"*2 + "7"*(n-total) + "3"*(y-2)+"7")
break
else:
y += 1
``` | output | 1 | 83,460 | 0 | 166,921 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337 | instruction | 0 | 83,461 | 0 | 166,922 |
Tags: combinatorics, constructive algorithms, math, strings
Correct Solution:
```
import sys
import math
from collections import defaultdict,deque
import heapq
mod=998244353
def get(n):
y=int(math.sqrt(1+8*n))
z=(1+y)//2
return z
t = int(sys.stdin.readline())
for _ in range(t):
n=int(sys.stdin.readline())
rem=n
newn=get(n)
rem=n-newn*(newn-1)//2
ans=[1]
ans.append(3)
ans.append(3)
for i in range(rem):
ans.append(7)
for i in range(newn-2):
ans.append(3)
ans.append(7)
print(''.join(str(x) for x in ans))
``` | output | 1 | 83,461 | 0 | 166,923 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337 | instruction | 0 | 83,462 | 0 | 166,924 |
Tags: combinatorics, constructive algorithms, math, strings
Correct Solution:
```
import bisect
arr = [0, 0] + [i * (i-1) // 2 for i in range(2, 100000)]
for t in range(int(input())):
n = int(input())
if n <= 10:
print("1" + "33" + "7"*n)
continue
i = bisect.bisect_right(arr, n) - 1
k = arr[i]
ans = "1" + "33" + ("7"*(n-k)) + ("3"*(i-2)) + "7"
print(ans)
``` | output | 1 | 83,462 | 0 | 166,925 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337 | instruction | 0 | 83,463 | 0 | 166,926 |
Tags: combinatorics, constructive algorithms, math, strings
Correct Solution:
```
q=int(input())
for k in range(q):
n=int(input())
i=0
while i*(i-1)/2<=n:
i+=1
b=i-1
a=n-b*(b-1)//2
print('133'+'7'*a+'3'*(b-2)+'7')
``` | output | 1 | 83,463 | 0 | 166,927 |
Evaluate the correctness of the submitted Python 2 solution to the coding contest problem. Provide a "Yes" or "No" response.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337
Submitted Solution:
```
from sys import stdin, stdout
from collections import Counter, defaultdict
from itertools import permutations, combinations
raw_input = stdin.readline
pr = stdout.write
def in_arr():
return map(int,raw_input().split())
def pr_num(n):
stdout.write(str(n)+'\n')
def pr_arr(arr):
for i in arr:
stdout.write(str(i)+' ')
stdout.write('\n')
range = xrange # not for python 3.0+
for t in range(int(raw_input())):
n=int(raw_input())
i=1
while (i*(i-1))/2<=n:
i+=1
i-=1
temp=(i*(i-1))/2
n-=temp
ans='1'+('3'*(i-2))
ans+='1'*n
ans+='33'
ans+='7\n'
pr(ans)
``` | instruction | 0 | 83,464 | 0 | 166,928 |
Yes | output | 1 | 83,464 | 0 | 166,929 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337
Submitted Solution:
```
from collections import deque
def read_int():
return int(input())
def read_ints():
return map(int, input().split(' '))
t = read_int()
for case_num in range(t):
n = read_int()
a = 1
i = 1
q = deque()
while n >= a:
n -= a
if a > 1:
q.appendleft('13')
while a >= 50000 and n >= a:
n -= a
q.appendleft('1')
i += 1
a += i
ans = ''.join(list(q)) + '1' * (n + 1) + '337'
print(ans)
``` | instruction | 0 | 83,465 | 0 | 166,930 |
Yes | output | 1 | 83,465 | 0 | 166,931 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337
Submitted Solution:
```
import math
t=int(input())
for _ in range(t):
n=int(input())
p="3"
print(1,end="")
b=[]
while(1):
x=math.sqrt(n*2)
x=int(x)
if(x*(x+1)<=n*2):
y=x
else:
y=x-1
b.append(y+1)
n-=(y*(y+1))//2
if(n==0):
break
for i in range(0,len(b)-1):
b[i]=b[i]-b[i+1]
b.reverse()
for i in b:
print(i*p+"7",end="")
print()
``` | instruction | 0 | 83,466 | 0 | 166,932 |
Yes | output | 1 | 83,466 | 0 | 166,933 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337
Submitted Solution:
```
# TAIWAN NUMBER ONE!!!!!!!!!!!!!!!!!!!
# TAIWAN NUMBER ONE!!!!!!!!!!!!!!!!!!!
# TAIWAN NUMBER ONE!!!!!!!!!!!!!!!!!!!
from sys import stdin, stdout
from itertools import accumulate
T = int(input())
#s = input()
#N,M,K,Q = [int(x) for x in stdin.readline().split()]
#arr = [int(x) for x in stdin.readline().split()]
check = [0]*45000
s = 0
for i in range(1,45001):
s += i
check[i-1] = s
for i in range(T):
N = int(input())
if N in check:
idx = check.index(N)
idx += 2
print('1','3'*idx,'7',sep='',end='\n')
else:
# find largest number < N in check
target = max(num for num in check if num < N)
three = check.index(target)
d = N - target
print('1','3'*2,'7'*d,'3'*(three),'7',sep='',end='\n')
``` | instruction | 0 | 83,467 | 0 | 166,934 |
Yes | output | 1 | 83,467 | 0 | 166,935 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337
Submitted Solution:
```
from sys import stdin
t = int(stdin.readline())
for case in range(t):
n = int(stdin.readline())
c = 0
out = [1,3]
num = 1
adder = 2
while c < n:
out.append(3)
c += num
num += 1
#print(c)
if c > n:
out[0], out[1] = out[1], out[0]
c -= num-1
out.pop()
out.pop()
out += [1]*(n-c)
out += [3,3]
out += [7]
print(''.join([str(x) for x in out]))
``` | instruction | 0 | 83,468 | 0 | 166,936 |
Yes | output | 1 | 83,468 | 0 | 166,937 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337
Submitted Solution:
```
t=int(input())
for i in range(t):
c2=0
c3=0
x=int(input())
f=1
while f:
if x%2==0:
x=x//2
c2+=1
continue
elif x%3==0:
x=x//3
c3+=1
continue
f=0
print("1"*c2+"13"+"3"*c3+"37")
``` | instruction | 0 | 83,469 | 0 | 166,938 |
No | output | 1 | 83,469 | 0 | 166,939 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337
Submitted Solution:
```
import math
t=int(input())
l1=[]
for i in range(t):
n=int(input())
r1=0
r1=2+int((-3+int(math.sqrt(9+8*(n-1))))/2)
c1="1"+("3"*r1)+"7"
l1.append(c1)
for i in range(t):
print(l1[i])
``` | instruction | 0 | 83,470 | 0 | 166,940 |
No | output | 1 | 83,470 | 0 | 166,941 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337
Submitted Solution:
```
t = int(input())
while t:
n = int(input())
import math
c3 = int(math.sqrt(n*2))
while c3*(c3-1) <= 2*n:
c3 += 1
c3 -= 1
need = n-(c3-1)*c3//2
ans = [1] + [3]*(c3-2) + [1]*need +[3,3] +[7]
print("".join(str(ans)))
t -= 1
``` | instruction | 0 | 83,471 | 0 | 166,942 |
No | output | 1 | 83,471 | 0 | 166,943 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
You are given an integer n.
You have to find a sequence s consisting of digits \{1, 3, 7\} such that it has exactly n subsequences equal to 1337.
For example, sequence 337133377 has 6 subsequences equal to 1337:
1. 337\underline{1}3\underline{3}\underline{3}7\underline{7} (you can remove the second and fifth characters);
2. 337\underline{1}\underline{3}3\underline{3}7\underline{7} (you can remove the third and fifth characters);
3. 337\underline{1}\underline{3}\underline{3}37\underline{7} (you can remove the fourth and fifth characters);
4. 337\underline{1}3\underline{3}\underline{3}\underline{7}7 (you can remove the second and sixth characters);
5. 337\underline{1}\underline{3}3\underline{3}\underline{7}7 (you can remove the third and sixth characters);
6. 337\underline{1}\underline{3}\underline{3}3\underline{7}7 (you can remove the fourth and sixth characters).
Note that the length of the sequence s must not exceed 10^5.
You have to answer t independent queries.
Input
The first line contains one integer t (1 ≤ t ≤ 10) — the number of queries.
Next t lines contains a description of queries: the i-th line contains one integer n_i (1 ≤ n_i ≤ 10^9).
Output
For the i-th query print one string s_i (1 ≤ |s_i| ≤ 10^5) consisting of digits \{1, 3, 7\}. String s_i must have exactly n_i subsequences 1337. If there are multiple such strings, print any of them.
Example
Input
2
6
1
Output
113337
1337
Submitted Solution:
```
X = int(input())
n = 0
while (n + 1) * (n + 2) // 2 <= X:
n += 1
n -= 1
m = X - (n + 1) * (n + 2) // 2
# assert (n + 2) * (n + 1) // 2 + m == X, "incorrect"
# assert 1 + n + 2 + m + 1< 1e5, "too large"
print ("133" + "7" * m + "3" * n + "7")
``` | instruction | 0 | 83,472 | 0 | 166,944 |
No | output | 1 | 83,472 | 0 | 166,945 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Homer has two friends Alice and Bob. Both of them are string fans.
One day, Alice and Bob decide to play a game on a string s = s_1 s_2 ... s_n of length n consisting of lowercase English letters. They move in turns alternatively and Alice makes the first move.
In a move, a player must choose an index i (1 ≤ i ≤ n) that has not been chosen before, and change s_i to any other lowercase English letter c that c ≠ s_i.
When all indices have been chosen, the game ends.
The goal of Alice is to make the final string lexicographically as small as possible, while the goal of Bob is to make the final string lexicographically as large as possible. Both of them are game experts, so they always play games optimally. Homer is not a game expert, so he wonders what the final string will be.
A string a is lexicographically smaller than a string b if and only if one of the following holds:
* a is a prefix of b, but a ≠ b;
* in the first position where a and b differ, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b.
Input
Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 1000) — the number of test cases. Description of the test cases follows.
The only line of each test case contains a single string s (1 ≤ |s| ≤ 50) consisting of lowercase English letters.
Output
For each test case, print the final string in a single line.
Example
Input
3
a
bbbb
az
Output
b
azaz
by
Note
In the first test case: Alice makes the first move and must change the only letter to a different one, so she changes it to 'b'.
In the second test case: Alice changes the first letter to 'a', then Bob changes the second letter to 'z', Alice changes the third letter to 'a' and then Bob changes the fourth letter to 'z'.
In the third test case: Alice changes the first letter to 'b', and then Bob changes the second letter to 'y'. | instruction | 0 | 83,610 | 0 | 167,220 |
Tags: games, greedy, strings
Correct Solution:
```
t = int(input())
for _ in range(t):
n = input()
b=""
for i in range(len(n)):
if i%2==0:
if n[i]=='a':
b+='b'
else:
b+='a'
else:
if n[i]=='z':
b+='y'
else:
b+='z'
print(b)
``` | output | 1 | 83,610 | 0 | 167,221 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Homer has two friends Alice and Bob. Both of them are string fans.
One day, Alice and Bob decide to play a game on a string s = s_1 s_2 ... s_n of length n consisting of lowercase English letters. They move in turns alternatively and Alice makes the first move.
In a move, a player must choose an index i (1 ≤ i ≤ n) that has not been chosen before, and change s_i to any other lowercase English letter c that c ≠ s_i.
When all indices have been chosen, the game ends.
The goal of Alice is to make the final string lexicographically as small as possible, while the goal of Bob is to make the final string lexicographically as large as possible. Both of them are game experts, so they always play games optimally. Homer is not a game expert, so he wonders what the final string will be.
A string a is lexicographically smaller than a string b if and only if one of the following holds:
* a is a prefix of b, but a ≠ b;
* in the first position where a and b differ, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b.
Input
Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 1000) — the number of test cases. Description of the test cases follows.
The only line of each test case contains a single string s (1 ≤ |s| ≤ 50) consisting of lowercase English letters.
Output
For each test case, print the final string in a single line.
Example
Input
3
a
bbbb
az
Output
b
azaz
by
Note
In the first test case: Alice makes the first move and must change the only letter to a different one, so she changes it to 'b'.
In the second test case: Alice changes the first letter to 'a', then Bob changes the second letter to 'z', Alice changes the third letter to 'a' and then Bob changes the fourth letter to 'z'.
In the third test case: Alice changes the first letter to 'b', and then Bob changes the second letter to 'y'. | instruction | 0 | 83,613 | 0 | 167,226 |
Tags: games, greedy, strings
Correct Solution:
```
from sys import stdin
input=lambda : stdin.readline().strip()
lin=lambda :list(map(int,input().split()))
iin=lambda :int(input())
main=lambda :map(int,input().split())
from math import ceil,sqrt,factorial,log
from collections import deque
from bisect import bisect_left
def gcd(a,b):
a,b=max(a,b),min(a,b)
while a%b!=0:
a,b=b,a%b
return b
mod=998244353
def solve(we):
s=list(input())
for i in range(len(s)):
if i%2==0:
if s[i]=='a':
s[i]='b'
else:
s[i]='a'
else:
if s[i]=='z':
s[i]='y'
else:
s[i]='z'
for i in s:
print(i,end='')
print()
qwe=1
qwe=iin()
for _ in range(qwe):
solve(_+1)
``` | output | 1 | 83,613 | 0 | 167,227 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Homer has two friends Alice and Bob. Both of them are string fans.
One day, Alice and Bob decide to play a game on a string s = s_1 s_2 ... s_n of length n consisting of lowercase English letters. They move in turns alternatively and Alice makes the first move.
In a move, a player must choose an index i (1 ≤ i ≤ n) that has not been chosen before, and change s_i to any other lowercase English letter c that c ≠ s_i.
When all indices have been chosen, the game ends.
The goal of Alice is to make the final string lexicographically as small as possible, while the goal of Bob is to make the final string lexicographically as large as possible. Both of them are game experts, so they always play games optimally. Homer is not a game expert, so he wonders what the final string will be.
A string a is lexicographically smaller than a string b if and only if one of the following holds:
* a is a prefix of b, but a ≠ b;
* in the first position where a and b differ, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b.
Input
Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 1000) — the number of test cases. Description of the test cases follows.
The only line of each test case contains a single string s (1 ≤ |s| ≤ 50) consisting of lowercase English letters.
Output
For each test case, print the final string in a single line.
Example
Input
3
a
bbbb
az
Output
b
azaz
by
Note
In the first test case: Alice makes the first move and must change the only letter to a different one, so she changes it to 'b'.
In the second test case: Alice changes the first letter to 'a', then Bob changes the second letter to 'z', Alice changes the third letter to 'a' and then Bob changes the fourth letter to 'z'.
In the third test case: Alice changes the first letter to 'b', and then Bob changes the second letter to 'y'. | instruction | 0 | 83,614 | 0 | 167,228 |
Tags: games, greedy, strings
Correct Solution:
```
import math
import sys
from collections import Counter
from typing import List
input = sys.stdin.readline
############ ---- Input Functions ---- ############
def inp():
return (int(input()))
def instr():
return (str(input()))
def inlt():
return (list(map(int, input().split())))
def insr():
s = input()
return (list(map(int, list(s[:len(s) - 1]))))
# def insr():
# s = input()
# return list(s[:len(s) - 1])
def invr():
return (map(int, input().split()))
def main():
t = inp()
for _ in range(t):
s = instr()[:-1]
r = []
alice = True
for c in s:
if alice:
if c == 'a':
r.append('b')
else:
r.append('a')
else:
if c == 'z':
r.append('y')
else:
r.append('z')
alice = not alice
print(''.join(r))
if __name__ == '__main__':
main()
``` | output | 1 | 83,614 | 0 | 167,229 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Homer has two friends Alice and Bob. Both of them are string fans.
One day, Alice and Bob decide to play a game on a string s = s_1 s_2 ... s_n of length n consisting of lowercase English letters. They move in turns alternatively and Alice makes the first move.
In a move, a player must choose an index i (1 ≤ i ≤ n) that has not been chosen before, and change s_i to any other lowercase English letter c that c ≠ s_i.
When all indices have been chosen, the game ends.
The goal of Alice is to make the final string lexicographically as small as possible, while the goal of Bob is to make the final string lexicographically as large as possible. Both of them are game experts, so they always play games optimally. Homer is not a game expert, so he wonders what the final string will be.
A string a is lexicographically smaller than a string b if and only if one of the following holds:
* a is a prefix of b, but a ≠ b;
* in the first position where a and b differ, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b.
Input
Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 1000) — the number of test cases. Description of the test cases follows.
The only line of each test case contains a single string s (1 ≤ |s| ≤ 50) consisting of lowercase English letters.
Output
For each test case, print the final string in a single line.
Example
Input
3
a
bbbb
az
Output
b
azaz
by
Note
In the first test case: Alice makes the first move and must change the only letter to a different one, so she changes it to 'b'.
In the second test case: Alice changes the first letter to 'a', then Bob changes the second letter to 'z', Alice changes the third letter to 'a' and then Bob changes the fourth letter to 'z'.
In the third test case: Alice changes the first letter to 'b', and then Bob changes the second letter to 'y'.
Submitted Solution:
```
for _ in range(int(input())):
s = str(input())
ans = str()
for i in range(len(s)):
if i % 2 == 0:
ans += ('a' if s[i] != 'a' else 'b')
else:
ans += ('z' if s[i] != 'z' else 'y')
print(ans)
``` | instruction | 0 | 83,617 | 0 | 167,234 |
Yes | output | 1 | 83,617 | 0 | 167,235 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Homer has two friends Alice and Bob. Both of them are string fans.
One day, Alice and Bob decide to play a game on a string s = s_1 s_2 ... s_n of length n consisting of lowercase English letters. They move in turns alternatively and Alice makes the first move.
In a move, a player must choose an index i (1 ≤ i ≤ n) that has not been chosen before, and change s_i to any other lowercase English letter c that c ≠ s_i.
When all indices have been chosen, the game ends.
The goal of Alice is to make the final string lexicographically as small as possible, while the goal of Bob is to make the final string lexicographically as large as possible. Both of them are game experts, so they always play games optimally. Homer is not a game expert, so he wonders what the final string will be.
A string a is lexicographically smaller than a string b if and only if one of the following holds:
* a is a prefix of b, but a ≠ b;
* in the first position where a and b differ, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b.
Input
Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 1000) — the number of test cases. Description of the test cases follows.
The only line of each test case contains a single string s (1 ≤ |s| ≤ 50) consisting of lowercase English letters.
Output
For each test case, print the final string in a single line.
Example
Input
3
a
bbbb
az
Output
b
azaz
by
Note
In the first test case: Alice makes the first move and must change the only letter to a different one, so she changes it to 'b'.
In the second test case: Alice changes the first letter to 'a', then Bob changes the second letter to 'z', Alice changes the third letter to 'a' and then Bob changes the fourth letter to 'z'.
In the third test case: Alice changes the first letter to 'b', and then Bob changes the second letter to 'y'.
Submitted Solution:
```
t = int(input())
for _ in range(t):
s1 = input()
res = ''
for i in range(len(s1)):
if i % 2 == 0:
if s1[i] != 'a':
res += 'a'
else:
res += 'b'
else:
if s1[i] != 'z':
res += 'z'
else:
res += 'y'
print(res)
``` | instruction | 0 | 83,618 | 0 | 167,236 |
Yes | output | 1 | 83,618 | 0 | 167,237 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Homer has two friends Alice and Bob. Both of them are string fans.
One day, Alice and Bob decide to play a game on a string s = s_1 s_2 ... s_n of length n consisting of lowercase English letters. They move in turns alternatively and Alice makes the first move.
In a move, a player must choose an index i (1 ≤ i ≤ n) that has not been chosen before, and change s_i to any other lowercase English letter c that c ≠ s_i.
When all indices have been chosen, the game ends.
The goal of Alice is to make the final string lexicographically as small as possible, while the goal of Bob is to make the final string lexicographically as large as possible. Both of them are game experts, so they always play games optimally. Homer is not a game expert, so he wonders what the final string will be.
A string a is lexicographically smaller than a string b if and only if one of the following holds:
* a is a prefix of b, but a ≠ b;
* in the first position where a and b differ, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b.
Input
Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 1000) — the number of test cases. Description of the test cases follows.
The only line of each test case contains a single string s (1 ≤ |s| ≤ 50) consisting of lowercase English letters.
Output
For each test case, print the final string in a single line.
Example
Input
3
a
bbbb
az
Output
b
azaz
by
Note
In the first test case: Alice makes the first move and must change the only letter to a different one, so she changes it to 'b'.
In the second test case: Alice changes the first letter to 'a', then Bob changes the second letter to 'z', Alice changes the third letter to 'a' and then Bob changes the fourth letter to 'z'.
In the third test case: Alice changes the first letter to 'b', and then Bob changes the second letter to 'y'.
Submitted Solution:
```
import sys
import math
from math import inf, gcd
from functools import *
from itertools import *
from collections import *
from typing import *
sys.setrecursionlimit(10**7)
ti = int(input())
for ii in range(ti):
s = list(input())
for i, j in enumerate(s):
if i % 2 == 0:
s[i] = 'b' if j == 'a' else 'a'
else:
s[i] = 'z' if j != 'z' else 'y'
print(''.join(s))
``` | instruction | 0 | 83,620 | 0 | 167,240 |
Yes | output | 1 | 83,620 | 0 | 167,241 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Homer has two friends Alice and Bob. Both of them are string fans.
One day, Alice and Bob decide to play a game on a string s = s_1 s_2 ... s_n of length n consisting of lowercase English letters. They move in turns alternatively and Alice makes the first move.
In a move, a player must choose an index i (1 ≤ i ≤ n) that has not been chosen before, and change s_i to any other lowercase English letter c that c ≠ s_i.
When all indices have been chosen, the game ends.
The goal of Alice is to make the final string lexicographically as small as possible, while the goal of Bob is to make the final string lexicographically as large as possible. Both of them are game experts, so they always play games optimally. Homer is not a game expert, so he wonders what the final string will be.
A string a is lexicographically smaller than a string b if and only if one of the following holds:
* a is a prefix of b, but a ≠ b;
* in the first position where a and b differ, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b.
Input
Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 1000) — the number of test cases. Description of the test cases follows.
The only line of each test case contains a single string s (1 ≤ |s| ≤ 50) consisting of lowercase English letters.
Output
For each test case, print the final string in a single line.
Example
Input
3
a
bbbb
az
Output
b
azaz
by
Note
In the first test case: Alice makes the first move and must change the only letter to a different one, so she changes it to 'b'.
In the second test case: Alice changes the first letter to 'a', then Bob changes the second letter to 'z', Alice changes the third letter to 'a' and then Bob changes the fourth letter to 'z'.
In the third test case: Alice changes the first letter to 'b', and then Bob changes the second letter to 'y'.
Submitted Solution:
```
t = int(input())
while t > 0:
s = str(input())
for i in range(len(s)):
if i % 2 == 0 and s[i] != 'a':
s = s.replace(s[i],'a',1)
elif i % 2 == 0 and s[i] == 'a':
s = s.replace(s[i],'b',1)
elif i % 2 == 1 and s[i] != 'z':
s = s.replace(s[i],'z',1)
elif i % 2 == 1 and s[i] == 'z':
s = s.replace(s[i],'y',1)
print(s)
t = t-1
``` | instruction | 0 | 83,624 | 0 | 167,248 |
No | output | 1 | 83,624 | 0 | 167,249 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz | instruction | 0 | 83,625 | 0 | 167,250 |
Tags: brute force, data structures, dp, greedy, strings
Correct Solution:
```
import sys
input = sys.stdin.readline
def maxthestring3():
for _ in range(int(input())):
s = input().rstrip()
lastpos = {v:i for i,v in enumerate(s)}
queue = []
his = set()
for i in range(len(s)):
nowl = s[i]
if nowl not in his:
if queue:
while queue[-1] < nowl and lastpos[queue[-1]] > i:
his.discard(queue.pop())
if not queue:
break
queue.append(nowl)
his.add(nowl)
else:
queue.append(nowl)
his.add(nowl)
print(''.join(queue))
maxthestring3()
``` | output | 1 | 83,625 | 0 | 167,251 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz | instruction | 0 | 83,626 | 0 | 167,252 |
Tags: brute force, data structures, dp, greedy, strings
Correct Solution:
```
# ------------------- fast io --------------------
import os
import sys
from io import BytesIO, IOBase
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")
# ------------------- fast io --------------------
from math import gcd, ceil
def prod(a, mod=10**9+7):
ans = 1
for each in a:
ans = (ans * each) % mod
return ans
def lcm(a, b): return a * b // gcd(a, b)
def binary(x, length=16):
y = bin(x)[2:]
return y if len(y) >= length else "0" * (length - len(y)) + y
from collections import deque
for _ in range(int(input()) if True else 1):
#n = int(input())
#n, k = map(int, input().split())
#a, b = map(int, input().split())
#c, d = map(int, input().split())
#a = list(map(int, input().split()))
#b = list(map(int, input().split()))
s = [ord(c)-97 for c in input()]
last = [-1]*26
first = [deque() for i in range(26)]
lasts = []
for i in range(len(s)-1, -1, -1):
if last[s[i]] == -1:
last[s[i]] = i
lasts += [i]
for i in range(len(s)):
first[s[i]] += [i]
ans = []
used = set()
cur = 0
while lasts:
mx = min(lasts)
for i in range(25, -1, -1):
if not first[i] or i in used:continue
if first[i][0] <= mx:
ans.append(chr(97+i))
used.add(i)
lasts.remove(last[i])
c2 = first[i][0] + 1
for j in range(cur, first[i][0]+1):
first[s[j]].popleft()
cur = c2
break
print(*ans,sep='')
``` | output | 1 | 83,626 | 0 | 167,253 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz | instruction | 0 | 83,627 | 0 | 167,254 |
Tags: brute force, data structures, dp, greedy, strings
Correct Solution:
```
for _ in range(int(input())):
ans = ""
s = input()
# print(s)
occ = {}
for c in s:
if c not in occ:
occ[c] = 0
occ[c] += 1
remove = set()
prev_i = -1
for i in range(len(s)):
# print(f'Curr {i=}, {prev_i=}, {s[i]=}, {remove=}')
occ[s[i]] -= 1
if s[i] in remove:
# print("skipped")
continue
if prev_i == -1 or s[i] > s[prev_i]:
prev_i = i
if occ[s[i]] == 0:
order = sorted(set(s[prev_i:i]), reverse=True)
# print(s[prev_i:i])
# print(order)
order_i = 0
for j in range(prev_i, i):
while order_i < len(order) and order[order_i] in remove:
order_i += 1
if order_i < len(order) and order[order_i] == s[j] and s[j] >= s[i] and s[j] not in remove:
ans += s[j]
# print(f"=== Added (for) {s[j]} {s[j:i]}")
remove.add(s[j])
prev_i = j
order = sorted(set(s[prev_i:i]), reverse=True)
order_i = 0
if s[i] not in remove:
ans += s[i]
# print(f"=== Adding (if) {s[i]}")
remove.add(s[i])
prev_i = i
print(ans)
# print("zyxwvutsrqpnmlhdokjifcbgae")
# print("wjrqiotyesdfhgknbv")
# print()
``` | output | 1 | 83,627 | 0 | 167,255 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz | instruction | 0 | 83,628 | 0 | 167,256 |
Tags: brute force, data structures, dp, greedy, strings
Correct Solution:
```
#Code by Sounak, IIESTS
#------------------------------warmup----------------------------
import os
import sys
import math
from io import BytesIO, IOBase
from fractions import Fraction
import collections
from itertools import permutations
from collections import defaultdict
from collections import deque
import threading
#sys.setrecursionlimit(300000)
#threading.stack_size(10**8)
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")
#-------------------------------------------------------------------------
#mod = 9223372036854775807
class SegmentTree:
def __init__(self, data, default=0, func=lambda a, b: max(a,b)):
"""initialize the segment tree with data"""
self._default = default
self._func = func
self._len = len(data)
self._size = _size = 1 << (self._len - 1).bit_length()
self.data = [default] * (2 * _size)
self.data[_size:_size + self._len] = data
for i in reversed(range(_size)):
self.data[i] = func(self.data[i + i], self.data[i + i + 1])
def __delitem__(self, idx):
self[idx] = self._default
def __getitem__(self, idx):
return self.data[idx + self._size]
def __setitem__(self, idx, value):
idx += self._size
self.data[idx] = value
idx >>= 1
while idx:
self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
idx >>= 1
def __len__(self):
return self._len
def query(self, start, stop):
if start == stop:
return self.__getitem__(start)
stop += 1
start += self._size
stop += self._size
res = self._default
while start < stop:
if start & 1:
res = self._func(res, self.data[start])
start += 1
if stop & 1:
stop -= 1
res = self._func(res, self.data[stop])
start >>= 1
stop >>= 1
return res
def __repr__(self):
return "SegmentTree({0})".format(self.data)
class SegmentTree1:
def __init__(self, data, default=10**6, func=lambda a, b: min(a,b)):
"""initialize the segment tree with data"""
self._default = default
self._func = func
self._len = len(data)
self._size = _size = 1 << (self._len - 1).bit_length()
self.data = [default] * (2 * _size)
self.data[_size:_size + self._len] = data
for i in reversed(range(_size)):
self.data[i] = func(self.data[i + i], self.data[i + i + 1])
def __delitem__(self, idx):
self[idx] = self._default
def __getitem__(self, idx):
return self.data[idx + self._size]
def __setitem__(self, idx, value):
idx += self._size
self.data[idx] = value
idx >>= 1
while idx:
self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
idx >>= 1
def __len__(self):
return self._len
def query(self, start, stop):
if start == stop:
return self.__getitem__(start)
stop += 1
start += self._size
stop += self._size
res = self._default
while start < stop:
if start & 1:
res = self._func(res, self.data[start])
start += 1
if stop & 1:
stop -= 1
res = self._func(res, self.data[stop])
start >>= 1
stop >>= 1
return res
def __repr__(self):
return "SegmentTree({0})".format(self.data)
MOD=10**9+7
class Factorial:
def __init__(self, MOD):
self.MOD = MOD
self.factorials = [1, 1]
self.invModulos = [0, 1]
self.invFactorial_ = [1, 1]
def calc(self, n):
if n <= -1:
print("Invalid argument to calculate n!")
print("n must be non-negative value. But the argument was " + str(n))
exit()
if n < len(self.factorials):
return self.factorials[n]
nextArr = [0] * (n + 1 - len(self.factorials))
initialI = len(self.factorials)
prev = self.factorials[-1]
m = self.MOD
for i in range(initialI, n + 1):
prev = nextArr[i - initialI] = prev * i % m
self.factorials += nextArr
return self.factorials[n]
def inv(self, n):
if n <= -1:
print("Invalid argument to calculate n^(-1)")
print("n must be non-negative value. But the argument was " + str(n))
exit()
p = self.MOD
pi = n % p
if pi < len(self.invModulos):
return self.invModulos[pi]
nextArr = [0] * (n + 1 - len(self.invModulos))
initialI = len(self.invModulos)
for i in range(initialI, min(p, n + 1)):
next = -self.invModulos[p % i] * (p // i) % p
self.invModulos.append(next)
return self.invModulos[pi]
def invFactorial(self, n):
if n <= -1:
print("Invalid argument to calculate (n^(-1))!")
print("n must be non-negative value. But the argument was " + str(n))
exit()
if n < len(self.invFactorial_):
return self.invFactorial_[n]
self.inv(n) # To make sure already calculated n^-1
nextArr = [0] * (n + 1 - len(self.invFactorial_))
initialI = len(self.invFactorial_)
prev = self.invFactorial_[-1]
p = self.MOD
for i in range(initialI, n + 1):
prev = nextArr[i - initialI] = (prev * self.invModulos[i % p]) % p
self.invFactorial_ += nextArr
return self.invFactorial_[n]
class Combination:
def __init__(self, MOD):
self.MOD = MOD
self.factorial = Factorial(MOD)
def ncr(self, n, k):
if k < 0 or n < k:
return 0
k = min(k, n - k)
f = self.factorial
return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD
mod=10**9+7
omod=998244353
#-------------------------------------------------------------------------
prime = [True for i in range(10)]
pp=[0]*10
def SieveOfEratosthenes(n=10):
p = 2
c=0
while (p * p <= n):
if (prime[p] == True):
c+=1
for i in range(p, n+1, p):
pp[i]+=1
prime[i] = False
p += 1
#---------------------------------Binary Search------------------------------------------
def binarySearch(arr, n, key):
left = 0
right = n-1
mid = 0
res=0
while (left <= right):
mid = (right + left)//2
if (arr[mid][0] > key):
right = mid-1
else:
res=mid
left = mid + 1
return res
#---------------------------------running code------------------------------------------
for i in range(int(input())):
s = input()
n = len(s)
res = []
used = set()
last = {c:i for i,c in enumerate(s)}
for i in range(n):
if s[i] not in used:
while res and res[-1] < s[i] and i < last[res[-1]]:
used.remove(res.pop())
res.append(s[i])
used.add(s[i])
print("".join(res))
``` | output | 1 | 83,628 | 0 | 167,257 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz | instruction | 0 | 83,629 | 0 | 167,258 |
Tags: brute force, data structures, dp, greedy, strings
Correct Solution:
```
t = int(input())
for test in range(1, t + 1):
s = list(input())
# start = time.time()
store = [0 for _ in range(len(s))]
curr = 0
visited = set()
last_seen = {}
for idx, ch in enumerate(s[::-1]):
if ch not in visited:
curr+=1
visited.add(ch)
store[-idx-1] = curr
if ch not in last_seen:
last_seen[ch] = len(s)-1-idx
# print(curr, store)
res = []
sel_idx = 0
visited = set()
while curr > 0:
choose = None
choose_idx = None
for idx in range(sel_idx, len(s)):
item = store[idx]
if item == curr and (s[idx] not in visited):
if choose is None or s[idx] > choose:
choose = s[idx]
choose_idx = idx
res.append(choose)
visited.add(choose)
sel_idx = choose_idx+1
new_store = []
curr -= 1
for idx, item in enumerate(store):
if idx <= last_seen[choose]:
new_store.append(item-1)
else:
new_store.append(item)
store = new_store
# print(res, curr, store)
# print(''.join(res))
# print(time.time()-start)
print(''.join(res))
# print(time.time()-start)
``` | output | 1 | 83,629 | 0 | 167,259 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz | instruction | 0 | 83,630 | 0 | 167,260 |
Tags: brute force, data structures, dp, greedy, strings
Correct Solution:
```
t = int(input())
for _ in range(t):
S = input()
l = [[] for i in range(26)]
for i in range(len(S)):
l[ord(S[i])-ord("a")].append(i)
last = [10**10]*26
for i in range(26):
if l[i]:
l[i] = l[i][::-1]
last[i] = l[i][0]
ans = ""
now = -1
while True:
nex = 10**10
ind = -1
for i in range(26):
if nex > last[i]:
nex = last[i]
ind = i
nex = min(nex,last[i])
if ind == -1:
break
for i in range(26)[::-1]:
if last[i] == 10**10:
continue
while l[i] and l[i][-1] <= now:
l[i].pop()
if l[i] and l[i][-1] <= nex:
ans += chr(ord("a")+i)
now = l[i][-1]
last[i] = 10**10
break
print(ans)
``` | output | 1 | 83,630 | 0 | 167,261 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz | instruction | 0 | 83,631 | 0 | 167,262 |
Tags: brute force, data structures, dp, greedy, strings
Correct Solution:
```
t = int(input())
for _ in range(t):
S = input()
l = [[] for i in range(26)]
for i in range(len(S))[::-1]:
l[ord(S[i])-ord("a")].append(i)
ans = ""
now = -1
while True:
nex = 10**10
ind = -1
for i in range(26):
if l[i] and nex > l[i][0]:
nex = l[i][0]
ind = i
if ind == -1:
break
for i in range(26)[::-1]:
while l[i] and l[i][-1] <= now:
l[i].pop()
if l[i] and l[i][-1] <= nex:
ans += chr(ord("a")+i)
now = l[i][-1]
l[i] = []
break
print(ans)
``` | output | 1 | 83,631 | 0 | 167,263 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz | instruction | 0 | 83,632 | 0 | 167,264 |
Tags: brute force, data structures, dp, greedy, strings
Correct Solution:
```
from collections import Counter
def get_input():
l = [int(e) for e in input().split()]
return l
def possible_char(i, c, s):
n = len(s)
possiblities = set()
ctemp = c.copy()
while i<n and ctemp[s[i]] != 1:
if ctemp[s[i]]>0:
possiblities.add(s[i])
ctemp[s[i]] -= 1
i += 1
if i<n:
possiblities.add(s[i])
return possiblities
def main(s):
sol = []
n = len(s)
i = 0
c = Counter(s)
while i<n:
possiblities = possible_char(i, c, s)
if len(possiblities)==0:
break
nc = max(possiblities)
sol.append(nc)
while i<n and s[i] != nc:
c[s[i]] -= 1
i += 1
c[nc] = 0
i += 1
print("".join(sol))
if __name__ == "__main__":
t = get_input()[0]
for _ in range(t):
s = input()
main(s)
``` | output | 1 | 83,632 | 0 | 167,265 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz
Submitted Solution:
```
import sys
#input = sys.stdin.readline
for _ in range(int(input())):
#n=int(input())
s=input()
d={}
for i in s:
if i in d:
d[i]+=1
else:
d[i]=1
v=[False for i in range(26)]
temp=[]
for i in s:
d[i]-=1
if v[ord(i)-ord('a')]==True:
continue
while temp and temp[-1]<i and d[temp[-1]]>0:
now=temp.pop()
v[ord(now)-ord('a')]=False
v[ord(i)-ord('a')]=True
temp.append(i)
ans=''
for i in temp:
ans+=i
print(ans)
``` | instruction | 0 | 83,633 | 0 | 167,266 |
Yes | output | 1 | 83,633 | 0 | 167,267 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz
Submitted Solution:
```
from bisect import bisect_left as bl
from bisect import bisect_right as br
from heapq import heappush,heappop
import math
from collections import *
from functools import reduce,cmp_to_key,lru_cache
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
# import sys
# input = sys.stdin.readline
M = mod = 10**9 + 7
def factors(n):return sorted(set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))
def inv_mod(n):return pow(n, mod - 2, mod)
def li():return [int(i) for i in input().rstrip().split()]
def st():return str(input().rstrip())[2:-1]
def val():return int(input().rstrip())
def li2():return [str(i)[2:-1] for i in input().rstrip().split()]
def li3():return [int(i) for i in st()]
for _ in range(val()):
s = st()
stack = []
last = {}
for i in range(len(s)):
last[s[i]] = i
n = len(set(s))
# print(s)
ans = ''
for i in range(len(s)):
add = 1
if s[i] in ''.join(s[k] for k in stack):continue
for j in list(stack)[::-1]:
if s[j] > s[i]:continue
elif s[j] < s[i]:
if last[s[j]] < i:
if s[i] in ''.join(s[k] for k in stack):add = 0
break
else:stack.remove(j)
else:
stack.remove(j)
if add:stack.append(i)
if len(stack) == n:
# print(''.join(s[i] for i in stack))
ans = max(ans, ''.join(s[j] for j in stack))
# print(i, stack, len(stack), n)
print(ans)
``` | instruction | 0 | 83,634 | 0 | 167,268 |
Yes | output | 1 | 83,634 | 0 | 167,269 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz
Submitted Solution:
```
from collections import deque , Counter
for idx in range(int(input())):
s = input()
count = Counter(s)
check = {i: 0 for i in count.keys()}
stack = []
for i in range(len(s)):
count[s[i]] -= 1
if check[s[i]]: continue
while len(stack) and s[i] > stack[-1] and count[stack[-1]]:
x = stack.pop()
check[x] = 0
stack.append(s[i])
check[s[i]] = 1
print(''.join(stack))
``` | instruction | 0 | 83,635 | 0 | 167,270 |
Yes | output | 1 | 83,635 | 0 | 167,271 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz
Submitted Solution:
```
# Legends Always Come Up with Solution
# Author: Manvir Singh
import os
import sys
from io import BytesIO, IOBase
from collections import defaultdict,Counter
def main():
for _ in range(int(input())):
s=input().rstrip()
n,d=len(s),set(s)
ans,l,indd=[],len(d),0
while len(ans)<l:
z,a=0,set()
for i in range(n-1,indd-1,-1):
if s[i] not in a and s[i] in d:
z+=1
a.add(s[i])
if z==len(d):
ma=""
for j in range(indd,i+1,1):
if s[j] in d and ma<s[j]:
ma=s[j]
ind=j
ans.append(ma)
indd=ind
d.discard(ma)
break
print("".join(ans))
# 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()
``` | instruction | 0 | 83,636 | 0 | 167,272 |
Yes | output | 1 | 83,636 | 0 | 167,273 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz
Submitted Solution:
```
#!/usr/bin/env pypy3
from sys import stdin, stdout
def input(): return stdin.readline().strip()
def read_int_list(): return list(map(int, input().split()))
def read_int_tuple(): return tuple(map(int, input().split()))
def read_int(): return int(input())
from collections import defaultdict
### CODE HERE
ALPHABET = "abcdefghijklmnopqrstuvwxyz"[::-1]
def ans(S):
indexes = defaultdict(set)
for i, c in enumerate(S):
indexes[c].add(i)
assigned = defaultdict(lambda: None)
for c in ALPHABET:
if assigned[c] is not None: continue
if len(indexes[c]) > 0:
j = min(indexes[c])
# print(f"assigned {c} -> {j}")
assigned[c] = j
# check whether to sweep the front
for d in ALPHABET:
if assigned[d] is not None: continue
if d in S[j:]:
# print(f"sweep the front for {d}")
for i in range(j):
if S[i] == d:
if i in indexes[S[i]]: indexes[S[i]].remove(i)
ret = []
for c in ALPHABET:
if assigned[c] is not None:
ret += [(assigned[c], c)]
ret = sorted(ret)
ret = [c for _, c in ret]
ret = ''.join(ret)
assert(len(ret) == len(set(S)))
return ret
for _ in range(read_int()):
S = input()
print(ans(S))
``` | instruction | 0 | 83,637 | 0 | 167,274 |
No | output | 1 | 83,637 | 0 | 167,275 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz
Submitted Solution:
```
import sys
from sys import stdin
tt = int(stdin.readline())
alp = "abcdefghijklmnopqrstuvwxyz"
ANS = []
for loop in range(tt):
s = list(stdin.readline()[:-1])
n = len(s)
alis = []
adic = {}
use = [False] * n
for i in s:
if i not in adic:
adic[i] = True
alis.append(i)
alis.sort()
anum = len(alis)
l = -1
for i in range(anum):
nmax = None
ntype = 0
dic = {}
for j in range(n-1,l,-1):
if not adic[s[j]]:
continue
if s[j] not in dic:
dic[s[j]] = 1
ntype += 1
if ntype + i >= anum:
if nmax == None :
nmax = j
elif s[j] >= s[nmax]:
nmax = j
use[nmax] = True
l = nmax
adic[s[nmax]] = False
#print (use)
ans = []
for i in range(n):
if use[i]:
ans.append(s[i])
ANS.append("".join(ans))
``` | instruction | 0 | 83,638 | 0 | 167,276 |
No | output | 1 | 83,638 | 0 | 167,277 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz
Submitted Solution:
```
t=int(input())
for _ in range(t):
s=str(input())
n=len(s)
dict1={}
for i in range(n):
if ord(s[i]) in dict1.keys():
dict1[ord(s[i])]+=1
else:
dict1[ord(s[i])]=1
i=0
maxi=0
k=0
dict2={}
arr=[0]*n
while i<n:
while i<n and dict1[ord(s[i])]>1:
maxi=max(maxi,ord(s[i]))
i+=1
if i==n:
for j in range(k,i):
if ord(s[j])!=maxi and dict1[ord(s[j])]>1:
arr[j]=-1
dict1[ord(s[j])]=max(1,dict1[ord(s[j])]-1)
if dict1[maxi]>1:
dict2[maxi]=1
while k<n and (dict1[ord(s[k])]==1 or ord(s[k]) in dict2.keys()):
if ord(s[k]) in dict2.keys() and dict1[ord(s[k])]>1:
dict1[ord(s[k])]=max(1,dict1[ord(s[k])]-1)
arr[k]=-1
k+=1
i=k
else:
maxi=max(maxi,ord(s[i]))
p=0
for j in range(k,i):
if (ord(s[j])!=maxi and dict1[ord(s[j])]>1) or (ord(s[j])==maxi and dict1[ord(s[j])]>2 and p==1):
arr[j]=-1
dict1[ord(s[j])]=max(1,dict1[ord(s[j])]-1)
if (ord(s[j])==maxi and dict1[ord(s[j])]>2 and p==0):
p=1
if dict1[maxi]>1:
dict2[maxi]=1
while i<n and (dict1[ord(s[i])]==1 or ord(s[i]) in dict2.keys()):
if ord(s[i]) in dict2.keys():
dict1[ord(s[i])]=max(1,dict1[ord(s[i])]-1)
arr[i]=-1
i+=1
k=i
for i in range(n):
if arr[i]==0:
print(s[i],end="")
print("")
``` | instruction | 0 | 83,639 | 0 | 167,278 |
No | output | 1 | 83,639 | 0 | 167,279 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s, consisting of lowercase Latin letters. While there is at least one character in the string s that is repeated at least twice, you perform the following operation:
* you choose the index i (1 ≤ i ≤ |s|) such that the character at position i occurs at least two times in the string s, and delete the character at position i, that is, replace s with s_1 s_2 … s_{i-1} s_{i+1} s_{i+2} … s_n.
For example, if s="codeforces", then you can apply the following sequence of operations:
* i=6 ⇒ s="codefrces";
* i=1 ⇒ s="odefrces";
* i=7 ⇒ s="odefrcs";
Given a given string s, find the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
A string a of length n is lexicographically less than a string b of length m, if:
* there is an index i (1 ≤ i ≤ min(n, m)) such that the first i-1 characters of the strings a and b are the same, and the i-th character of the string a is less than i-th character of string b;
* or the first min(n, m) characters in the strings a and b are the same and n < m.
For example, the string a="aezakmi" is lexicographically less than the string b="aezus".
Input
The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.
Each test case is characterized by a string s, consisting of lowercase Latin letters (1 ≤ |s| ≤ 2 ⋅ 10^5).
It is guaranteed that the sum of the lengths of the strings in all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output the lexicographically maximum string that can be obtained after applying a certain sequence of operations after which all characters in the string become unique.
Example
Input
6
codeforces
aezakmi
abacaba
convexhull
swflldjgpaxs
myneeocktxpqjpz
Output
odfrces
ezakmi
cba
convexhul
wfldjgpaxs
myneocktxqjpz
Submitted Solution:
```
ty=input()
for i in range(0,int(ty)):
text=input()
te=""
ls=list(text)
fn=[]
def f(l):
copy=l.copy()
mxl=[]
mx=0
for i in range(0,len(l)):
for a in range(0,len(l)):
copy=l.copy()
if i!=a and (l[i]==l[a]):
copy.pop(a)
numbers = [ord(letter) - 96 for letter in copy]
for k in range(0,len(numbers)) :
numbers[k]*=5**(len(numbers)-k+1)
if sum(numbers)>mx:
mxl=copy.copy()
mx=sum(numbers)
if len(mxl)==0:
mxl=copy.copy()
return(mxl)
for i in range(0,len(ls)):
ls=f(l=ls)
if len(ls)!=0:
fn=ls.copy()
for i in fn :
te+=i
print(te)
``` | instruction | 0 | 83,640 | 0 | 167,280 |
No | output | 1 | 83,640 | 0 | 167,281 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Polycarpus analyzes a string called abracadabra. This string is constructed using the following algorithm:
* On the first step the string consists of a single character "a".
* On the k-th step Polycarpus concatenates two copies of the string obtained on the (k - 1)-th step, while inserting the k-th character of the alphabet between them. Polycarpus uses the alphabet that consists of lowercase Latin letters and digits (a total of 36 characters). The alphabet characters are numbered like this: the 1-st character is "a", the 2-nd — "b", ..., the 26-th — "z", the 27-th — "0", the 28-th — "1", ..., the 36-th — "9".
Let's have a closer look at the algorithm. On the second step Polycarpus will concatenate two strings "a" and insert the character "b" between them, resulting in "aba" string. The third step will transform it into "abacaba", and the fourth one - into "abacabadabacaba". Thus, the string constructed on the k-th step will consist of 2k - 1 characters.
Polycarpus wrote down the string he got after 30 steps of the given algorithm and chose two non-empty substrings of it. Your task is to find the length of the longest common substring of the two substrings selected by Polycarpus.
A substring s[i... j] (1 ≤ i ≤ j ≤ |s|) of string s = s1s2... s|s| is a string sisi + 1... sj. For example, substring s[2...4] of string s = "abacaba" equals "bac". The string is its own substring.
The longest common substring of two strings s and t is the longest string that is a substring of both s and t. For example, the longest common substring of "contest" and "systemtesting" is string "test". There can be several common substrings of maximum length.
Input
The input consists of a single line containing four integers l1, r1, l2, r2 (1 ≤ li ≤ ri ≤ 109, i = 1, 2). The numbers are separated by single spaces. li and ri give the indices of the first and the last characters of the i-th chosen substring, correspondingly (i = 1, 2). The characters of string abracadabra are numbered starting from 1.
Output
Print a single number — the length of the longest common substring of the given strings. If there are no common substrings, print 0.
Examples
Input
3 6 1 4
Output
2
Input
1 1 4 4
Output
0
Note
In the first sample the first substring is "acab", the second one is "abac". These two substrings have two longest common substrings "ac" and "ab", but we are only interested in their length — 2.
In the second sample the first substring is "a", the second one is "c". These two substrings don't have any common characters, so the length of their longest common substring is 0. | instruction | 0 | 83,657 | 0 | 167,314 |
Tags: divide and conquer
Correct Solution:
```
aaa =0
def f(l1,r1,l2,r2,top):
global aaa
if (l1>r1 or l2> r2):
return 0
if (top-1<=aaa) or (r1-l1+1<=aaa) or (r2-l2+1<=aaa):
return 0
if top==2:
return 1
if (l1>top):
l1 -=top
r1 -= top
if (l2>top):
l2-=top
r2-=top
#print(l1,r1,l2,r2,top)
if (l1==l2 and r1==r2):
return r1-l1+1
if (l1==0 and r1==top-1):
return r2-l2+1
if (l2==0 and r2==top-1):
return r1-l1+1
if ( (l1<= l2 and l2<= r1) or (l2<= l1 and l1<= r2)):
ans = min(r1,r2) -max(l1,l2) +1
else:
ans = 0
#print(ans)
top = top//2
ans = max(ans, f(l1,min(r1,top-1),l2,min(r2,top-1), top))
ans = max(ans, f(l1,min(r1,top-1),max(top+1,l2),r2, top))
ans = max(ans, f(max(l1,top+1),r1, l2,min(r2,top-1), top))
ans = max(ans, f(max(l1,top+1),r1, max(l2,top+1),r2, top))
aaa = max(aaa,ans)
return ans
a = input().split()
print(f(int(a[0]),int(a[1]),int(a[2]),int(a[3]),2**36))
# Made By Mostafa_Khaled
``` | output | 1 | 83,657 | 0 | 167,315 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Polycarpus analyzes a string called abracadabra. This string is constructed using the following algorithm:
* On the first step the string consists of a single character "a".
* On the k-th step Polycarpus concatenates two copies of the string obtained on the (k - 1)-th step, while inserting the k-th character of the alphabet between them. Polycarpus uses the alphabet that consists of lowercase Latin letters and digits (a total of 36 characters). The alphabet characters are numbered like this: the 1-st character is "a", the 2-nd — "b", ..., the 26-th — "z", the 27-th — "0", the 28-th — "1", ..., the 36-th — "9".
Let's have a closer look at the algorithm. On the second step Polycarpus will concatenate two strings "a" and insert the character "b" between them, resulting in "aba" string. The third step will transform it into "abacaba", and the fourth one - into "abacabadabacaba". Thus, the string constructed on the k-th step will consist of 2k - 1 characters.
Polycarpus wrote down the string he got after 30 steps of the given algorithm and chose two non-empty substrings of it. Your task is to find the length of the longest common substring of the two substrings selected by Polycarpus.
A substring s[i... j] (1 ≤ i ≤ j ≤ |s|) of string s = s1s2... s|s| is a string sisi + 1... sj. For example, substring s[2...4] of string s = "abacaba" equals "bac". The string is its own substring.
The longest common substring of two strings s and t is the longest string that is a substring of both s and t. For example, the longest common substring of "contest" and "systemtesting" is string "test". There can be several common substrings of maximum length.
Input
The input consists of a single line containing four integers l1, r1, l2, r2 (1 ≤ li ≤ ri ≤ 109, i = 1, 2). The numbers are separated by single spaces. li and ri give the indices of the first and the last characters of the i-th chosen substring, correspondingly (i = 1, 2). The characters of string abracadabra are numbered starting from 1.
Output
Print a single number — the length of the longest common substring of the given strings. If there are no common substrings, print 0.
Examples
Input
3 6 1 4
Output
2
Input
1 1 4 4
Output
0
Note
In the first sample the first substring is "acab", the second one is "abac". These two substrings have two longest common substrings "ac" and "ab", but we are only interested in their length — 2.
In the second sample the first substring is "a", the second one is "c". These two substrings don't have any common characters, so the length of their longest common substring is 0. | instruction | 0 | 83,658 | 0 | 167,316 |
Tags: divide and conquer
Correct Solution:
```
def solve(x,l1,r1,l2,r2):
if x==0:return 1
if l1>x:
l1-=x+1
r1-=x+1
if l2>x:
l2-=x+1
r2-=x+1
ans=max(0,min(r1,r2)-max(l1,l2)+1)
if l1<=x and x<=r1 and l2<=x and x<=r2:
if l1==0 or r1==x*2:
ans=max(ans,max(x-l2,r2-x))
elif l2==0 or r2==x*2:
ans=max(ans,max(x-l1,r1-x))
else:
if l1<=x-1 and r2>=x+1:
ans=max(ans,solve(x//2,l1,x-1,0,r2-x-1))
if l2<=x-1 and r1>=x+1:
ans=max(ans,solve(x//2,l2,x-1,0,r1-x-1))
elif l1<=x and x<=r1:
if l1==0 or r1==x*2:
ans=max(ans,r2-l2+1)
else:
if l1<=x-1:
ans=max(ans,solve(x//2,l1,x-1,l2,r2))
if r1>=x+1:
ans=max(ans,solve(x//2,0,r1-x-1,l2,r2))
elif l2<=x and x<=r2:
if l2==0 or r2==x*2:
ans=max(ans,r1-l1+1)
else:
if l2<=x-1:
ans=max(ans,solve(x//2,l2,x-1,l1,r1))
if r2>=x+1:
ans=max(ans,solve(x//2,0,r2-x-1,l1,r1))
else:
ans=max(ans,solve(x//2,l1,r1,l2,r2))
return ans
l1,r1,l2,r2=map(int,input().split())
print(solve((1<<36)-1,l1-1,r1-1,l2-1,r2-1))
``` | output | 1 | 83,658 | 0 | 167,317 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Polycarpus analyzes a string called abracadabra. This string is constructed using the following algorithm:
* On the first step the string consists of a single character "a".
* On the k-th step Polycarpus concatenates two copies of the string obtained on the (k - 1)-th step, while inserting the k-th character of the alphabet between them. Polycarpus uses the alphabet that consists of lowercase Latin letters and digits (a total of 36 characters). The alphabet characters are numbered like this: the 1-st character is "a", the 2-nd — "b", ..., the 26-th — "z", the 27-th — "0", the 28-th — "1", ..., the 36-th — "9".
Let's have a closer look at the algorithm. On the second step Polycarpus will concatenate two strings "a" and insert the character "b" between them, resulting in "aba" string. The third step will transform it into "abacaba", and the fourth one - into "abacabadabacaba". Thus, the string constructed on the k-th step will consist of 2k - 1 characters.
Polycarpus wrote down the string he got after 30 steps of the given algorithm and chose two non-empty substrings of it. Your task is to find the length of the longest common substring of the two substrings selected by Polycarpus.
A substring s[i... j] (1 ≤ i ≤ j ≤ |s|) of string s = s1s2... s|s| is a string sisi + 1... sj. For example, substring s[2...4] of string s = "abacaba" equals "bac". The string is its own substring.
The longest common substring of two strings s and t is the longest string that is a substring of both s and t. For example, the longest common substring of "contest" and "systemtesting" is string "test". There can be several common substrings of maximum length.
Input
The input consists of a single line containing four integers l1, r1, l2, r2 (1 ≤ li ≤ ri ≤ 109, i = 1, 2). The numbers are separated by single spaces. li and ri give the indices of the first and the last characters of the i-th chosen substring, correspondingly (i = 1, 2). The characters of string abracadabra are numbered starting from 1.
Output
Print a single number — the length of the longest common substring of the given strings. If there are no common substrings, print 0.
Examples
Input
3 6 1 4
Output
2
Input
1 1 4 4
Output
0
Note
In the first sample the first substring is "acab", the second one is "abac". These two substrings have two longest common substrings "ac" and "ab", but we are only interested in their length — 2.
In the second sample the first substring is "a", the second one is "c". These two substrings don't have any common characters, so the length of their longest common substring is 0. | instruction | 0 | 83,659 | 0 | 167,318 |
Tags: divide and conquer
Correct Solution:
```
aaa =0
def f(l1,r1,l2,r2,top):
global aaa
if (l1>r1 or l2> r2):
return 0
if (top-1<=aaa) or (r1-l1+1<=aaa) or (r2-l2+1<=aaa):
return 0
if top==2:
return 1
if (l1>top):
l1 -=top
r1 -= top
if (l2>top):
l2-=top
r2-=top
#print(l1,r1,l2,r2,top)
if (l1==l2 and r1==r2):
return r1-l1+1
if (l1==0 and r1==top-1):
return r2-l2+1
if (l2==0 and r2==top-1):
return r1-l1+1
if ( (l1<= l2 and l2<= r1) or (l2<= l1 and l1<= r2)):
ans = min(r1,r2) -max(l1,l2) +1
else:
ans = 0
#print(ans)
top = top//2
ans = max(ans, f(l1,min(r1,top-1),l2,min(r2,top-1), top))
ans = max(ans, f(l1,min(r1,top-1),max(top+1,l2),r2, top))
ans = max(ans, f(max(l1,top+1),r1, l2,min(r2,top-1), top))
ans = max(ans, f(max(l1,top+1),r1, max(l2,top+1),r2, top))
aaa = max(aaa,ans)
return ans
a = input().split()
print(f(int(a[0]),int(a[1]),int(a[2]),int(a[3]),2**36))
``` | output | 1 | 83,659 | 0 | 167,319 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Polycarpus analyzes a string called abracadabra. This string is constructed using the following algorithm:
* On the first step the string consists of a single character "a".
* On the k-th step Polycarpus concatenates two copies of the string obtained on the (k - 1)-th step, while inserting the k-th character of the alphabet between them. Polycarpus uses the alphabet that consists of lowercase Latin letters and digits (a total of 36 characters). The alphabet characters are numbered like this: the 1-st character is "a", the 2-nd — "b", ..., the 26-th — "z", the 27-th — "0", the 28-th — "1", ..., the 36-th — "9".
Let's have a closer look at the algorithm. On the second step Polycarpus will concatenate two strings "a" and insert the character "b" between them, resulting in "aba" string. The third step will transform it into "abacaba", and the fourth one - into "abacabadabacaba". Thus, the string constructed on the k-th step will consist of 2k - 1 characters.
Polycarpus wrote down the string he got after 30 steps of the given algorithm and chose two non-empty substrings of it. Your task is to find the length of the longest common substring of the two substrings selected by Polycarpus.
A substring s[i... j] (1 ≤ i ≤ j ≤ |s|) of string s = s1s2... s|s| is a string sisi + 1... sj. For example, substring s[2...4] of string s = "abacaba" equals "bac". The string is its own substring.
The longest common substring of two strings s and t is the longest string that is a substring of both s and t. For example, the longest common substring of "contest" and "systemtesting" is string "test". There can be several common substrings of maximum length.
Input
The input consists of a single line containing four integers l1, r1, l2, r2 (1 ≤ li ≤ ri ≤ 109, i = 1, 2). The numbers are separated by single spaces. li and ri give the indices of the first and the last characters of the i-th chosen substring, correspondingly (i = 1, 2). The characters of string abracadabra are numbered starting from 1.
Output
Print a single number — the length of the longest common substring of the given strings. If there are no common substrings, print 0.
Examples
Input
3 6 1 4
Output
2
Input
1 1 4 4
Output
0
Note
In the first sample the first substring is "acab", the second one is "abac". These two substrings have two longest common substrings "ac" and "ab", but we are only interested in their length — 2.
In the second sample the first substring is "a", the second one is "c". These two substrings don't have any common characters, so the length of their longest common substring is 0.
Submitted Solution:
```
def solve(x,l1,r1,l2,r2):
if x==0:return 1
if l1>x:
l1-=x+1
r1-=x+1
if l2>x:
l2-=x+1
r2-=x+1
ans=max(0,min(r1,r2)-max(l1,l2)+1)
if l1<=x and x<=r1 and l2<=x and x<=r2:
if l1==0 or r1==x*2:
ans=max(ans,max(x-12,r2-x))
elif l2==0 or r2==x*2:
ans=max(ans,max(x-11,r1-x))
else:
if l1<=x-1 and r2>=x+1:
ans=max(ans,solve(x//2,l1,x-1,0,r2-x-1))
if l2<=x-1 and r1>=x+1:
ans=max(ans,solve(x//2,l2,x-1,0,r1-x-1))
elif l1<=x and x<=r1:
if l1==0 or r1==x*2:
ans=max(ans,r2-l2+1)
else:
if l1<=x-1:
ans=max(ans,solve(x//2,l1,x-1,l2,r2))
if r1>=x+1:
ans=max(ans,solve(x//2,0,r1-x-1,l2,r2))
elif l2<=x and x<=r2:
if l2==0 or r2==x*2:
ans=max(ans,r1-l1+1)
else:
if l2<=x-1:
ans=max(ans,solve(x//2,l2,x-1,l1,r1))
if r2>=x+1:
ans=max(ans,solve(x//2,0,r2-x-1,l1,r1))
else:
ans=max(ans,solve(x//2,l1,r1,l2,r2))
return ans
l1,r1,l2,r2=map(int,input().split())
print(solve((1<<36)-1,l1-1,r1-1,l2-1,r2-1))
``` | instruction | 0 | 83,660 | 0 | 167,320 |
No | output | 1 | 83,660 | 0 | 167,321 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Polycarpus analyzes a string called abracadabra. This string is constructed using the following algorithm:
* On the first step the string consists of a single character "a".
* On the k-th step Polycarpus concatenates two copies of the string obtained on the (k - 1)-th step, while inserting the k-th character of the alphabet between them. Polycarpus uses the alphabet that consists of lowercase Latin letters and digits (a total of 36 characters). The alphabet characters are numbered like this: the 1-st character is "a", the 2-nd — "b", ..., the 26-th — "z", the 27-th — "0", the 28-th — "1", ..., the 36-th — "9".
Let's have a closer look at the algorithm. On the second step Polycarpus will concatenate two strings "a" and insert the character "b" between them, resulting in "aba" string. The third step will transform it into "abacaba", and the fourth one - into "abacabadabacaba". Thus, the string constructed on the k-th step will consist of 2k - 1 characters.
Polycarpus wrote down the string he got after 30 steps of the given algorithm and chose two non-empty substrings of it. Your task is to find the length of the longest common substring of the two substrings selected by Polycarpus.
A substring s[i... j] (1 ≤ i ≤ j ≤ |s|) of string s = s1s2... s|s| is a string sisi + 1... sj. For example, substring s[2...4] of string s = "abacaba" equals "bac". The string is its own substring.
The longest common substring of two strings s and t is the longest string that is a substring of both s and t. For example, the longest common substring of "contest" and "systemtesting" is string "test". There can be several common substrings of maximum length.
Input
The input consists of a single line containing four integers l1, r1, l2, r2 (1 ≤ li ≤ ri ≤ 109, i = 1, 2). The numbers are separated by single spaces. li and ri give the indices of the first and the last characters of the i-th chosen substring, correspondingly (i = 1, 2). The characters of string abracadabra are numbered starting from 1.
Output
Print a single number — the length of the longest common substring of the given strings. If there are no common substrings, print 0.
Examples
Input
3 6 1 4
Output
2
Input
1 1 4 4
Output
0
Note
In the first sample the first substring is "acab", the second one is "abac". These two substrings have two longest common substrings "ac" and "ab", but we are only interested in their length — 2.
In the second sample the first substring is "a", the second one is "c". These two substrings don't have any common characters, so the length of their longest common substring is 0.
Submitted Solution:
```
def f(l1,r1,l2,r2,top):
if top==0:
return 0
if (l1>r1 or l2> r2):
return 0
if (l1>top):
l1 -=top
r1 -= top
if (l2>top):
l2-=top
r2-=top
#print(l1,r1,l2,r2,top)
if ( (l1<= l2 and l2<= r1) or (l2<= l1 and l1<= r2)):
ans = min(r1,r2) -max(l1,l2) +1
else:
ans = 0
#print(ans)
ans = max(ans, f(l1,min(r1,top-1),l2,min(r2,top-1), top//2))
ans = max(ans, f(l1,min(r1,top-1),max(top+1,l2),r2, top//2))
ans = max(ans, f(max(l1,top+1),r1, l2,min(r2,top-1), top//2))
ans = max(ans, f(max(l1,top+1),r1, max(l2,top+1),r2, top//2))
return ans
a = input().split()
print(f(int(a[0]),int(a[1]),int(a[2]),int(a[3]),2**30))
``` | instruction | 0 | 83,661 | 0 | 167,322 |
No | output | 1 | 83,661 | 0 | 167,323 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recall that string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly zero or all) characters. For example, for the string a="wowwo", the following strings are subsequences: "wowwo", "wowo", "oo", "wow", "", and others, but the following are not subsequences: "owoo", "owwwo", "ooo".
The wow factor of a string is the number of its subsequences equal to the word "wow". Bob wants to write a string that has a large wow factor. However, the "w" key on his keyboard is broken, so he types two "v"s instead.
Little did he realise that he may have introduced more "w"s than he thought. Consider for instance the string "ww". Bob would type it as "vvvv", but this string actually contains three occurrences of "w":
* "vvvv"
* "vvvv"
* "vvvv"
For example, the wow factor of the word "vvvovvv" equals to four because there are four wows:
* "vvvovvv"
* "vvvovvv"
* "vvvovvv"
* "vvvovvv"
Note that the subsequence "vvvovvv" does not count towards the wow factor, as the "v"s have to be consecutive.
For a given string s, compute and output its wow factor. Note that it is not guaranteed that it is possible to get s from another string replacing "w" with "vv". For example, s can be equal to "vov".
Input
The input contains a single non-empty string s, consisting only of characters "v" and "o". The length of s is at most 10^6.
Output
Output a single integer, the wow factor of s.
Examples
Input
vvvovvv
Output
4
Input
vvovooovovvovoovoovvvvovovvvov
Output
100
Note
The first example is explained in the legend. | instruction | 0 | 84,289 | 0 | 168,578 |
Tags: dp, strings
Correct Solution:
```
from sys import stdin, stdout
import math,sys,heapq
from itertools import permutations, combinations
from collections import defaultdict,deque,OrderedDict
from os import path
import random
import bisect as bi
def yes():print('YES')
def no():print('NO')
if (path.exists('input.txt')):
#------------------Sublime--------------------------------------#
sys.stdin=open('input.txt','r');sys.stdout=open('output.txt','w');
def I():return (int(input()))
def In():return(map(int,input().split()))
else:
#------------------PYPY FAst I/o--------------------------------#
def I():return (int(stdin.readline()))
def In():return(map(int,stdin.readline().split()))
#sys.setrecursionlimit(1500)
def dict(a):
d={}
for x in a:
if d.get(x,-1)!=-1:
d[x]+=1
else:
d[x]=1
return d
def find_gt(a, x):
'Find leftmost value greater than x'
i = bi.bisect_left(a, x)
if i != len(a):
return i
else:
return -1
def main():
try:
s=input()
n=len(s)
nov,noo=0,0
dpo,dpv=[],[]
t=s[0]
q=0
if s[0]=='v':
pos=0
else:
pos=-1
if s[0]=='v':
nov=1
total=0
for i in range(1,n-1):
if s[i]=='v':
if s[i+1]=='o' and s[i-1]=='o':
continue
else:
if noo>0 :
if len(dpv):
dpo.append(noo)
noo=0
nov+=1
else:
noo+=1
if nov>1:
dpv.append(nov-1)
total+=(nov-1)
nov=0
if nov:
if s[-1]=='v':
dpv.append(nov)
total+=nov
else:
dpv.append(nov-1)
total+=(nov-1)
# print(dpv)
# print(dpo)
ans=0
for i in range(len(dpv)-1):
total-=dpv[i]
if i>0:
dpv[i]+=dpv[i-1]
ans+=(dpo[i]*dpv[i]*(total))
print(ans)
except:
pass
M = 998244353
P = 1000000007
if __name__ == '__main__':
#for _ in range(I()):main()
for _ in range(1):main()
``` | output | 1 | 84,289 | 0 | 168,579 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recall that string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly zero or all) characters. For example, for the string a="wowwo", the following strings are subsequences: "wowwo", "wowo", "oo", "wow", "", and others, but the following are not subsequences: "owoo", "owwwo", "ooo".
The wow factor of a string is the number of its subsequences equal to the word "wow". Bob wants to write a string that has a large wow factor. However, the "w" key on his keyboard is broken, so he types two "v"s instead.
Little did he realise that he may have introduced more "w"s than he thought. Consider for instance the string "ww". Bob would type it as "vvvv", but this string actually contains three occurrences of "w":
* "vvvv"
* "vvvv"
* "vvvv"
For example, the wow factor of the word "vvvovvv" equals to four because there are four wows:
* "vvvovvv"
* "vvvovvv"
* "vvvovvv"
* "vvvovvv"
Note that the subsequence "vvvovvv" does not count towards the wow factor, as the "v"s have to be consecutive.
For a given string s, compute and output its wow factor. Note that it is not guaranteed that it is possible to get s from another string replacing "w" with "vv". For example, s can be equal to "vov".
Input
The input contains a single non-empty string s, consisting only of characters "v" and "o". The length of s is at most 10^6.
Output
Output a single integer, the wow factor of s.
Examples
Input
vvvovvv
Output
4
Input
vvovooovovvovoovoovvvvovovvvov
Output
100
Note
The first example is explained in the legend. | instruction | 0 | 84,290 | 0 | 168,580 |
Tags: dp, strings
Correct Solution:
```
a = input()
d = []
l = 0
p = len(a)
for x in range(p):
if x == p-1 and a[x] == "o":
d.append(0)
if a[x] == "v":
l += 1
else:
d.append(l)
l = 0
d.append(l)
n = 0
dp = []
for x in range(len(d)):
if d[x] > 0:
n += d[x]-1
dp.append(n)
h = len(dp)
s = 0
for x in range(h):
s += (dp[x])*(dp[-1]-dp[x])
print(s)
``` | output | 1 | 84,290 | 0 | 168,581 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recall that string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly zero or all) characters. For example, for the string a="wowwo", the following strings are subsequences: "wowwo", "wowo", "oo", "wow", "", and others, but the following are not subsequences: "owoo", "owwwo", "ooo".
The wow factor of a string is the number of its subsequences equal to the word "wow". Bob wants to write a string that has a large wow factor. However, the "w" key on his keyboard is broken, so he types two "v"s instead.
Little did he realise that he may have introduced more "w"s than he thought. Consider for instance the string "ww". Bob would type it as "vvvv", but this string actually contains three occurrences of "w":
* "vvvv"
* "vvvv"
* "vvvv"
For example, the wow factor of the word "vvvovvv" equals to four because there are four wows:
* "vvvovvv"
* "vvvovvv"
* "vvvovvv"
* "vvvovvv"
Note that the subsequence "vvvovvv" does not count towards the wow factor, as the "v"s have to be consecutive.
For a given string s, compute and output its wow factor. Note that it is not guaranteed that it is possible to get s from another string replacing "w" with "vv". For example, s can be equal to "vov".
Input
The input contains a single non-empty string s, consisting only of characters "v" and "o". The length of s is at most 10^6.
Output
Output a single integer, the wow factor of s.
Examples
Input
vvvovvv
Output
4
Input
vvovooovovvovoovoovvvvovovvvov
Output
100
Note
The first example is explained in the legend. | instruction | 0 | 84,291 | 0 | 168,582 |
Tags: dp, strings
Correct Solution:
```
a=input()
res=''
if(len(a)<3):
print(0)
exit()
for i in range(len(a)-1):
if(a[i]=='v' and a[i+1]=='v'):
res+='w'
elif(a[i]=='v' and a[i+1]=='o'):
continue
else:
res+='o'
s=0
a=[]
for i in range(len(res)):
if(res[i]=='w'):
s+=1
t=0
rs=0
for i in range(len(res)):
if(res[i]=='o'):
rs+=t*(s-t)
else:
t+=1
print(rs)
``` | output | 1 | 84,291 | 0 | 168,583 |
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