message stringlengths 2 19.9k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 322 108k | cluster float64 15 15 | __index_level_0__ int64 644 217k |
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Provide tags and a correct Python 3 solution for this coding contest problem.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2. | instruction | 0 | 33,466 | 15 | 66,932 |
Tags: math
Correct Solution:
```
if __name__== '__main__':
n= int(input())
orders= input()
lefts= 0
rights= 0
for order in orders:
if(order== 'L'):
lefts+= 1
else:
rights+= 1
print(lefts+ rights+ 1)
``` | output | 1 | 33,466 | 15 | 66,933 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2. | instruction | 0 | 33,467 | 15 | 66,934 |
Tags: math
Correct Solution:
```
from collections import Counter
n = int(input())
s = input()
lr = Counter(s)
print(lr['R'] + lr['L'] + 1)
``` | output | 1 | 33,467 | 15 | 66,935 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2. | instruction | 0 | 33,468 | 15 | 66,936 |
Tags: math
Correct Solution:
```
a = int(input())
s = input()
b = s.count('L')
c = s.count('R')
d = b+c+1
print(d)
``` | output | 1 | 33,468 | 15 | 66,937 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2. | instruction | 0 | 33,469 | 15 | 66,938 |
Tags: math
Correct Solution:
```
n = int(input())
cm = list(input(""))
k = 0
k2 = 0
for i in cm:
if i == "L":
k += 1
else:
k2 += 1
print(k2 - (k * -1) + 1)
``` | output | 1 | 33,469 | 15 | 66,939 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2. | instruction | 0 | 33,470 | 15 | 66,940 |
Tags: math
Correct Solution:
```
import sys
import collections
n = int(sys.stdin.readline())
counter = collections.Counter(sys.stdin.readline())
print(counter["L"] + counter["R"] + 1)
``` | output | 1 | 33,470 | 15 | 66,941 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2. | instruction | 0 | 33,471 | 15 | 66,942 |
Tags: math
Correct Solution:
```
commands=int(input())
string=input()
L=0
R=0
for letter in string:
if letter=="L":
L+=1
else:
R+=1
print(L+R+1)
``` | output | 1 | 33,471 | 15 | 66,943 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2. | instruction | 0 | 33,472 | 15 | 66,944 |
Tags: math
Correct Solution:
```
n = int(input())
s = input()
l = s.count('L')
r = s.count('R')
c = l+r+1
print(c)
``` | output | 1 | 33,472 | 15 | 66,945 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2. | instruction | 0 | 33,473 | 15 | 66,946 |
Tags: math
Correct Solution:
```
k = input()
a = list(map(str,input().strip().split()))
c = 0
k = 0
for i in a:
for j in i:
if j == 'L':
c-=1
if j == 'R':
k+=1
print((k-c)+1)
``` | output | 1 | 33,473 | 15 | 66,947 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2.
Submitted Solution:
```
num = int(input())
string = input()
print(str(num + 1))
``` | instruction | 0 | 33,474 | 15 | 66,948 |
Yes | output | 1 | 33,474 | 15 | 66,949 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2.
Submitted Solution:
```
inp1 = input()
inp = len(input())+1
print(inp)
``` | instruction | 0 | 33,475 | 15 | 66,950 |
Yes | output | 1 | 33,475 | 15 | 66,951 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2.
Submitted Solution:
```
n = int(input())
s = list(input())
s.sort()
num_l = 0
num_r = 0
if s[0] == s[-1] == "L":
num_l = n
elif s[0] == s[-1] == "R":
num_r = n
else:
for i in range(n-1):
if s[i] != s[i+1]:
num_l = i+1
num_r = n - (i+1)
print(num_r + num_l + 1)
``` | instruction | 0 | 33,476 | 15 | 66,952 |
Yes | output | 1 | 33,476 | 15 | 66,953 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2.
Submitted Solution:
```
# from fractions import gcd
# from datetime import date, timedelta
from heapq import*
import math
from collections import defaultdict, Counter, deque
from bisect import *
import itertools
import fractions
# import sys
# sys.setrecursionlimit(10 ** 7)
MOD = 10 ** 9 + 7
# input = sys.stdin.readline
def make_divisors(n):
divisors = []
for i in range(1, int(n**0.5)+1):
if n % i == 0:
divisors.append(i)
if i != n // i:
divisors.append(n//i)
divisors.sort()
return divisors
def main():
n = int(input())
s = input()
l, r = 0, 0
for i in range(n):
if s[i] == "R":
r += 1
else:
l += 1
print(r+l + 1)
# x = int(input())
# l = make_divisors(x)
# ans = x
# # print(l)
# for i in range(len(l) // 2):
# ans = min(ans, max(l[i], l[-1 - i]))
# print(x//ans , ans)
if __name__ == '__main__':
main()
``` | instruction | 0 | 33,477 | 15 | 66,954 |
Yes | output | 1 | 33,477 | 15 | 66,955 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2.
Submitted Solution:
```
k = input()
a = list(map(str,input().strip().split()))
c = 0
k = 0
for i in a:
for j in i:
if j == 'L':
c-=1
if j == 'R':
k+=1
if c < 0 and k > 0:
print((k-c)+1)
else:
print(k-c)
``` | instruction | 0 | 33,478 | 15 | 66,956 |
No | output | 1 | 33,478 | 15 | 66,957 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2.
Submitted Solution:
```
n = int(input())
s = input()
r = []
l = []
for i in s:
if i == "R":
r.append(i)
else:
l.append(i)
if len(s) - len(r) == 0:
print(len(r))
else:
print(len(r) + len(l) + 1)
``` | instruction | 0 | 33,479 | 15 | 66,958 |
No | output | 1 | 33,479 | 15 | 66,959 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2.
Submitted Solution:
```
n = int(input())
x = input()
total = 0
L = 0
R = 0
for i in range(0, n-1) :
if x[i] == "L" :
L += 1
else :
R += 1
if L == R :
total = L + R +1
elif L != R :
total = L + R + 2
elif n == 1 :
total = 2
print(total)
``` | instruction | 0 | 33,480 | 15 | 66,960 |
No | output | 1 | 33,480 | 15 | 66,961 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today, Mezo is playing a game. Zoma, a character in that game, is initially at position x = 0. Mezo starts sending n commands to Zoma. There are two possible commands:
* 'L' (Left) sets the position x: =x - 1;
* 'R' (Right) sets the position x: =x + 1.
Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position x doesn't change and Mezo simply proceeds to the next command.
For example, if Mezo sends commands "LRLR", then here are some possible outcomes (underlined commands are sent successfully):
* "LRLR" β Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position 0;
* "LRLR" β Zoma recieves no commands, doesn't move at all and ends up at position 0 as well;
* "LRLR" β Zoma moves to the left, then to the left again and ends up in position -2.
Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.
Input
The first line contains n (1 β€ n β€ 10^5) β the number of commands Mezo sends.
The second line contains a string s of n commands, each either 'L' (Left) or 'R' (Right).
Output
Print one integer β the number of different positions Zoma may end up at.
Example
Input
4
LRLR
Output
5
Note
In the example, Zoma may end up anywhere between -2 and 2.
Submitted Solution:
```
def subs(s):
l = len(s)//2
if l == 0:
return 2
return (l*2)+1
com = int(input())
s = input()
print(subs(s))
``` | instruction | 0 | 33,481 | 15 | 66,962 |
No | output | 1 | 33,481 | 15 | 66,963 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.
<image>
Input
Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 β€ t β€ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of t sets of the input data.
The first line of the description of each set contains two integers n, k (2 β€ n β€ 100, 1 β€ k β€ 26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.
Output
For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.
Examples
Input
2
16 4
...AAAAA........
s.BBB......CCCCC
........DDDDD...
16 4
...AAAAA........
s.BBB....CCCCC..
.......DDDDD....
Output
YES
NO
Input
2
10 4
s.ZZ......
.....AAABB
.YYYYYY...
10 4
s.ZZ......
....AAAABB
.YYYYYY...
Output
YES
NO
Note
In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset. | instruction | 0 | 33,818 | 15 | 67,636 |
Tags: dfs and similar, graphs, shortest paths
Correct Solution:
```
def simulate(grid):
n, m = len(grid), len(grid[0])
threshold = n * [ m ]
for r in range(n):
c = m - 1
while c >= 0 and grid[r][c] == '.':
c -= 1
threshold[r] = c + 1
#print(threshold)
in_row = n * [ False ]
for r in range(n):
if grid[r][0] == 's':
in_row[r] = True
break
c = 0
while True:
next_in_row = n * [ False ]
for r, possible in enumerate(in_row):
if not possible:
continue
if c + 1 >= threshold[r]:
return True
if grid[r][c + 1] != '.':
continue
for rr in range(max(0, r - 1), min(r + 2, n)):
okay = True
for cc in range(c + 1, c + 4):
if cc >= threshold[rr]:
return True
if grid[rr][cc] != '.':
okay = False
break
if okay:
next_in_row[rr] = True
in_row = next_in_row
c += 3
#print(c, in_row)
if True not in in_row:
return False
num_cases = int(input())
for case_index in range(num_cases):
m, k = map(int, input().split())
grid = [ list(input().strip()) for r in range(3) ]
if simulate(grid):
print('YES')
else:
print('NO')
``` | output | 1 | 33,818 | 15 | 67,637 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.
<image>
Input
Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 β€ t β€ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of t sets of the input data.
The first line of the description of each set contains two integers n, k (2 β€ n β€ 100, 1 β€ k β€ 26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.
Output
For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.
Examples
Input
2
16 4
...AAAAA........
s.BBB......CCCCC
........DDDDD...
16 4
...AAAAA........
s.BBB....CCCCC..
.......DDDDD....
Output
YES
NO
Input
2
10 4
s.ZZ......
.....AAABB
.YYYYYY...
10 4
s.ZZ......
....AAAABB
.YYYYYY...
Output
YES
NO
Note
In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset. | instruction | 0 | 33,819 | 15 | 67,638 |
Tags: dfs and similar, graphs, shortest paths
Correct Solution:
```
#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#
# Copyright Β© 2016 missingdays <missingdays@missingdays>
#
# Distributed under terms of the MIT license.
"""
"""
def shift(a, n):
b = [["." for i in range(n)] for i in range(3)]
for i in range(3):
for j in range(n-2):
b[i][j] = a[i][j+2]
return b
n = int(input())
for case in range(n):
n, k = [int(i) for i in input().split()]
a = []
for i in range(3):
a.append(list(input()))
m = [[False for i in range(n)] for j in range(3)]
for i in range(3):
if a[i][0] == 's':
m[i][0] = True
for i in range(1, n):
#print(a)
for j in range(3):
if m[j][i-1] and a[j][i] == "." and (a[j][i-1] == "." or a[j][i-1] == "s") and (i < 2 or a[j][i-2] == "."):
m[j][i] = True
ms = [False for something in range(3)]
if m[0][i]:
if a[1][i] == ".": #and (i > n-2 or a[1][i+1] == ".") and (i > n-3 or a[1][i+2] == "."):
ms[1] = True
if m[1][i]:
if a[0][i] == ".": #and (i > n-2 or a[0][i+1] == ".") and (i > n-3 or a[0][i+2] == "."):
ms[0] = True
if a[2][i] == ".": #and (i > n-2 or a[2][i+1] == ".") and (i > n-3 or a[2][i+2] == "."):
ms[2] = True
if m[2][i]:
if a[1][i] == ".": #and (i > n-2 or a[1][i+1] == ".") and (i > n-3 or a[1][i+2] == "."):
ms[1] = True
for j in range(3):
if ms[j]:
m[j][i] = True
#print(m)
a = shift(a, n)
for i in range(3):
if m[i][n-1]:
print("YES")
break
else:
print("NO")
``` | output | 1 | 33,819 | 15 | 67,639 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.
<image>
Input
Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 β€ t β€ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of t sets of the input data.
The first line of the description of each set contains two integers n, k (2 β€ n β€ 100, 1 β€ k β€ 26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.
Output
For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.
Examples
Input
2
16 4
...AAAAA........
s.BBB......CCCCC
........DDDDD...
16 4
...AAAAA........
s.BBB....CCCCC..
.......DDDDD....
Output
YES
NO
Input
2
10 4
s.ZZ......
.....AAABB
.YYYYYY...
10 4
s.ZZ......
....AAAABB
.YYYYYY...
Output
YES
NO
Note
In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset. | instruction | 0 | 33,820 | 15 | 67,640 |
Tags: dfs and similar, graphs, shortest paths
Correct Solution:
```
def solve(n,k,arr,pos):
#print(pos)
i = 0
positions = [pos]
while i < n-3:
previousPositions = positions[:]
positions = []
i += 1
for m in range(3):
if arr[m][i] == '.' and arr[m][i+2]=='.':
for q in previousPositions:
if abs(m-q)<=1 and arr[q][i] == '.':
if m not in positions:
positions.append(m)
#print(positions)
i += 2
for q in positions:
for u in range(i,n):
if arr[q][u] != '.':
positions.remove(q)
break
if positions!=[]:
print('YES')
else:
print('NO')
#file_object = open('TextFile1.txt','r')
#t = int(file_object.readline())
t = int(input())
for x in range(t):
arr = []
#n,k = map(int,file_object.readline().split())
n,k = map(int,input().split())
for i in range(3):
#line = list(file_object.readline().rstrip('\n'))
line = list(input())
arr.append(line)
if 's' in line:
pos = i
solve(n,k,arr,pos)
#for i in arr:
# print(i)
#print('')
``` | output | 1 | 33,820 | 15 | 67,641 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.
<image>
Input
Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 β€ t β€ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of t sets of the input data.
The first line of the description of each set contains two integers n, k (2 β€ n β€ 100, 1 β€ k β€ 26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.
Output
For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.
Examples
Input
2
16 4
...AAAAA........
s.BBB......CCCCC
........DDDDD...
16 4
...AAAAA........
s.BBB....CCCCC..
.......DDDDD....
Output
YES
NO
Input
2
10 4
s.ZZ......
.....AAABB
.YYYYYY...
10 4
s.ZZ......
....AAAABB
.YYYYYY...
Output
YES
NO
Note
In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset. | instruction | 0 | 33,821 | 15 | 67,642 |
Tags: dfs and similar, graphs, shortest paths
Correct Solution:
```
T = int(input())
for t in range(T):
n, k = map(int, input().split(' ')[:2])
s = ["","",""]
for i in range(3):
s[i] = input()
s[0] += '.' * (n*3)
s[1] += '.' * (n*3)
s[2] += '.' * (n*3)
def top():
return [s[0][0] != '.', s[1][0] != '.', s[2][0] != '.']
def shift():
s[0] = s[0][1:]
s[1] = s[1][1:]
s[2] = s[2][1:]
return top()
p = [s[0][0] == 's', s[1][0] == 's', s[2][0] == 's']
for i in range(1, n):
np = [False, False, False]
if p[0] == True and s[0][1] == '.':
np[0] = True
np[1] = True
if p[1] == True and s[1][1] == '.':
np[0] = True
np[1] = True
np[2] = True
if p[2] == True and s[2][1] == '.':
np[1] = True
np[2] = True
p = np
s0, s1, s2 = shift()
if s0: p[0] = False
if s1: p[1] = False
if s2: p[2] = False
# my move ended
s0, s1, s2 = shift()
if s0: p[0] = False
if s1: p[1] = False
if s2: p[2] = False
s0, s1, s2 = shift()
if s0: p[0] = False
if s1: p[1] = False
if s2: p[2] = False
if p[0] or p[1] or p[2]:
print("YES")
else:
print("NO")
``` | output | 1 | 33,821 | 15 | 67,643 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.
<image>
Input
Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 β€ t β€ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of t sets of the input data.
The first line of the description of each set contains two integers n, k (2 β€ n β€ 100, 1 β€ k β€ 26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.
Output
For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.
Examples
Input
2
16 4
...AAAAA........
s.BBB......CCCCC
........DDDDD...
16 4
...AAAAA........
s.BBB....CCCCC..
.......DDDDD....
Output
YES
NO
Input
2
10 4
s.ZZ......
.....AAABB
.YYYYYY...
10 4
s.ZZ......
....AAAABB
.YYYYYY...
Output
YES
NO
Note
In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset. | instruction | 0 | 33,822 | 15 | 67,644 |
Tags: dfs and similar, graphs, shortest paths
Correct Solution:
```
def R(i,j):
if i<n:
smas[j][i]=1
p=False
if mas[j][i+1]=='.':
if mas[j][i+3]=='.'and smas[j][i+3]==0:
p =p or R(i+3,j)
if j>0 and mas[j-1][i+1]=='.'and mas[j-1][i+3]=='.' and smas[j-1][i+3]==0:
p =p or R(i+3,j-1)
if j<2 and mas[j+1][i+1]=='.'and mas[j+1][i+3]=='.'and smas[j+1][i+3]==0:
p =p or R(i+3,j+1)
return p
else:
return True
t = int(input())
for l in range(t):
n,k=map(int,input().split(" "))
s=0
s1=input()+"....."
if s1[0]=='s':s=0
s2=input()+"....."
if s2[0]=='s':s=1
s3=input()+"....."
if s3[0]=='s':s=2
mas=[]
mas.append(list(s1))
mas.append(list(s2))
mas.append(list(s3))
smas=[]
smas.append([0]*(n+5))
smas.append([0]*(n+5))
smas.append([0]*(n+5))
print("YES") if R(0,s) else print("NO")
``` | output | 1 | 33,822 | 15 | 67,645 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.
<image>
Input
Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 β€ t β€ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of t sets of the input data.
The first line of the description of each set contains two integers n, k (2 β€ n β€ 100, 1 β€ k β€ 26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.
Output
For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.
Examples
Input
2
16 4
...AAAAA........
s.BBB......CCCCC
........DDDDD...
16 4
...AAAAA........
s.BBB....CCCCC..
.......DDDDD....
Output
YES
NO
Input
2
10 4
s.ZZ......
.....AAABB
.YYYYYY...
10 4
s.ZZ......
....AAAABB
.YYYYYY...
Output
YES
NO
Note
In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset. | instruction | 0 | 33,823 | 15 | 67,646 |
Tags: dfs and similar, graphs, shortest paths
Correct Solution:
```
#!/usr/bin/env python3
from collections import deque
grid = [None, None, None]
def solve():
n, k = map(int, input().split())
for i in range(3):
grid[i] = input() + "..."
q = deque([(0 if grid[0][0] == 's' else 1 if grid[1][0] == 's' else 2, 0)])
used = [[False] * (n + 3) for i in range(3)]
while q:
y, x = q.popleft()
if x >= n:
return "YES"
if used[y][x]:
continue
used[y][x] = True
a = grid[y][x + 1]
if a == grid[y][x + 2] == grid[y][x + 3] == '.':
q.append((y, x + 3))
if y > 0 and a == grid[y - 1][x + 1] == grid[y - 1][x + 2] == grid[y - 1][x + 3] == '.':
q.append((y - 1, x + 3))
if y < 2 and a == grid[y + 1][x + 1] == grid[y + 1][x + 2] == grid[y + 1][x + 3] == '.':
q.append((y + 1, x + 3))
return "NO"
t = int(input())
for test in range(t):
print(solve())
``` | output | 1 | 33,823 | 15 | 67,647 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.
<image>
Input
Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 β€ t β€ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of t sets of the input data.
The first line of the description of each set contains two integers n, k (2 β€ n β€ 100, 1 β€ k β€ 26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.
Output
For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.
Examples
Input
2
16 4
...AAAAA........
s.BBB......CCCCC
........DDDDD...
16 4
...AAAAA........
s.BBB....CCCCC..
.......DDDDD....
Output
YES
NO
Input
2
10 4
s.ZZ......
.....AAABB
.YYYYYY...
10 4
s.ZZ......
....AAAABB
.YYYYYY...
Output
YES
NO
Note
In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset. | instruction | 0 | 33,824 | 15 | 67,648 |
Tags: dfs and similar, graphs, shortest paths
Correct Solution:
```
# import sys
# sys.stdin = open('cf586d.in')
def handle_test():
n, k = [int(v) for v in input().split()]
field = [input() for _ in range(3)]
if field[0][0] == 's':
cpos = [0, 0]
elif field[1][0] == 's':
cpos = [1, 0]
else:
cpos = [2, 0]
available = [[False] * len(field[0]) for _ in range(3)]
available[cpos[0]][cpos[1]] = True
for i in range(n):
for j in range(3):
if available[j][i]:
if i + 1 >= n:
return True
elif field[j][i + 1] != '.':
continue
for offset in (-1, 0, 1):
if not (0 <= j + offset < 3) or field[j + offset][i + 1] != '.':
continue
if i + 2 >= n:
return True
elif field[j + offset][i + 2] != '.':
continue
elif i + 3 >= n:
return True
elif field[j + offset][i + 3] != '.':
continue
else:
available[j + offset][i + 3] = True
return False
t = int(input())
for _ in range(t):
print(['NO', 'YES'][handle_test()])
``` | output | 1 | 33,824 | 15 | 67,649 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.
<image>
Input
Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 β€ t β€ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of t sets of the input data.
The first line of the description of each set contains two integers n, k (2 β€ n β€ 100, 1 β€ k β€ 26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.
Output
For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.
Examples
Input
2
16 4
...AAAAA........
s.BBB......CCCCC
........DDDDD...
16 4
...AAAAA........
s.BBB....CCCCC..
.......DDDDD....
Output
YES
NO
Input
2
10 4
s.ZZ......
.....AAABB
.YYYYYY...
10 4
s.ZZ......
....AAAABB
.YYYYYY...
Output
YES
NO
Note
In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset. | instruction | 0 | 33,825 | 15 | 67,650 |
Tags: dfs and similar, graphs, shortest paths
Correct Solution:
```
t = int(input())
for kek in range(t):
n, k = [int(i) for i in input().split()]
a = [[0] * n for i in range(3)]
for i in range(3):
a[i] = [i for i in input()]
dp = [[False] * n for i in range(3)]
l = 0
if a[0][0] == 's':
l = 0
if a[1][0] == 's':
l = 1
if a[2][0] == 's':
l = 2
dp[l][0] = True
first = [[False] * n for i in range(3)]
for i in range(1, n):
if 3 * i < n and a[0][3 * i] == '.' and a[0][3 * i - 2] == '.':
if (dp[0][i - 1] or first[0][i - 1]) or (a[1][3 * i - 2] == '.' and dp[1][i - 1]):
dp[0][i] = True
elif 3 * i >= n > 3 * i - 2:
if (dp[0][i - 1] and a[0][3 * i - 2] == '.') or (dp[1][i - 1] and a[1][3 * i - 2] == '.'):
dp[0][i] = True
elif 3 * i >= n and (dp[0][i - 1] or dp[1][i - 1]):
dp[0][i] = True
if 3 * i < n and a[1][3 * i] == '.' and a[1][3 * i - 2] == '.':
if (dp[1][i - 1] or first[1][i - 1]) or (a[0][3 * i - 2] == '.' and dp[0][i - 1]) or (a[2][3 * i - 2] == '.' and dp[2][i - 1]):
dp[1][i] = True
elif 3 * i >= n > 3 * i - 2:
if (dp[0][i - 1] and a[0][3 * i - 2] == '.') or (dp[1][i - 1] and a[1][3 * i - 2] == '.') or (dp[2][i - 1] and a[2][3 * i - 2] == '.'):
dp[1][i] = True
elif 3 * i >= n and (dp[0][i - 1] or dp[1][i - 1] or dp[2][i - 1]):
dp[1][i] = True
if 3 * i < n and a[2][3 * i] == '.' and a[2][3 * i - 2] == '.':
if (dp[2][i - 1] or first[2][i - 1]) or (a[1][3 * i - 2] == '.' and dp[1][i - 1]):
dp[2][i] = True
elif 3 * i >= n > 3 * i - 2:
if (dp[2][i - 1] and a[2][3 * i - 2] == '.') or (dp[1][i - 1] and a[1][3 * i - 2] == '.'):
dp[2][i] = True
elif 3 * i >= n and (dp[1][i - 1] or dp[2][i - 1]):
dp[2][i] = True
#for i in range(3):
# print(dp[i])
if max(dp[0][n - 1], dp[1][n - 1], dp[2][n - 1]):
print('YES')
else:
print('NO')
``` | output | 1 | 33,825 | 15 | 67,651 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.
<image>
Input
Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 β€ t β€ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of t sets of the input data.
The first line of the description of each set contains two integers n, k (2 β€ n β€ 100, 1 β€ k β€ 26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.
Output
For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.
Examples
Input
2
16 4
...AAAAA........
s.BBB......CCCCC
........DDDDD...
16 4
...AAAAA........
s.BBB....CCCCC..
.......DDDDD....
Output
YES
NO
Input
2
10 4
s.ZZ......
.....AAABB
.YYYYYY...
10 4
s.ZZ......
....AAAABB
.YYYYYY...
Output
YES
NO
Note
In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset.
Submitted Solution:
```
import sys
from collections import deque
read = lambda: list(map(int, sys.stdin.readline().split()))
t, = read()
for _ in range(t):
n, k = read()
r = [list(sys.stdin.readline().strip()+'...') for _ in range(3)]
for x in range(n):
for y in range(3):
if r[y][x] == 's' and r[y][x+1] in '.s':
#print('move', y, x)
for y2 in range(3):
if abs(y-y2) <= 1 and r[y2][x+1] in '.s':
#print('move2', y2, x)
if r[y2][x+2] in '.s' and r[y2][x+3] in '.s':
r[y2][x+3] = 's'
if any(r[y][x] == 's' for y in range(3) for x in range(n-1,n+3)):
print("YES")
else: print("NO")
``` | instruction | 0 | 33,826 | 15 | 67,652 |
Yes | output | 1 | 33,826 | 15 | 67,653 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.
<image>
Input
Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 β€ t β€ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of t sets of the input data.
The first line of the description of each set contains two integers n, k (2 β€ n β€ 100, 1 β€ k β€ 26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.
Output
For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.
Examples
Input
2
16 4
...AAAAA........
s.BBB......CCCCC
........DDDDD...
16 4
...AAAAA........
s.BBB....CCCCC..
.......DDDDD....
Output
YES
NO
Input
2
10 4
s.ZZ......
.....AAABB
.YYYYYY...
10 4
s.ZZ......
....AAAABB
.YYYYYY...
Output
YES
NO
Note
In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset.
Submitted Solution:
```
def read_numbers():
return list(map(int, input().split()))
def f(dim, track):
#determine the possible starts
possible = [i[0]=="s" for i in track]
for i in range(1,dim[0],3):
#first move the hero:
new_possible = [False, False, False]
if (possible[0] and track[0][i] == '.') or \
(possible[1] and track[1][i] == '.' == track[0][i]):
new_possible[0] = True
if (possible[0] and track[0][i] == '.' == track[1][i]) or \
(possible[1] and track[1][i] == '.') or \
(possible[2] and track[2][i] == '.' == track[1][i]):
new_possible[1] = True
if (possible[1] and track[1][i] == '.' == track[2][i]) or \
(possible[2] and track[2][i] == '.'):
new_possible[2] = True
possible = new_possible
# new the trains:
for j in range(i+1, min(i+3, dim[0])):
possible = [possible[k] and track[k][j] == '.' for k in range(3)]
return 'YES' if any(possible) else 'NO'
if __name__ == '__main__':
n = int(input())
for _ in range(n):
dim = read_numbers()
track = [input() for _ in range(3)]
print(f(dim,track))
``` | instruction | 0 | 33,827 | 15 | 67,654 |
Yes | output | 1 | 33,827 | 15 | 67,655 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.
<image>
Input
Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 β€ t β€ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of t sets of the input data.
The first line of the description of each set contains two integers n, k (2 β€ n β€ 100, 1 β€ k β€ 26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.
Output
For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.
Examples
Input
2
16 4
...AAAAA........
s.BBB......CCCCC
........DDDDD...
16 4
...AAAAA........
s.BBB....CCCCC..
.......DDDDD....
Output
YES
NO
Input
2
10 4
s.ZZ......
.....AAABB
.YYYYYY...
10 4
s.ZZ......
....AAAABB
.YYYYYY...
Output
YES
NO
Note
In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset.
Submitted Solution:
```
#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#
# Copyright Β© 2016 missingdays <missingdays@missingdays>
#
# Distributed under terms of the MIT license.
"""
"""
def shift(a, n):
b = [["." for i in range(n)] for i in range(3)]
for i in range(3):
for j in range(n-2):
b[i][j] = a[i][j+2]
return b
n = int(input())
for case in range(n):
n, k = [int(i) for i in input().split()]
a = []
for i in range(3):
a.append(list(input()))
m = [[False for i in range(n)] for j in range(3)]
for i in range(3):
if a[i][0] == 's':
m[i][0] = True
for i in range(1, n):
#print(a)
for j in range(3):
if m[j][i-1] and a[j][i] == "." and (a[j][i-1] == "." or a[j][i-1] == "s"):
m[j][i] = True
if m[0][i]:
if a[1][i] == "." and (i > n-2 or a[1][i+1] == ".") and (i > n-3 or a[1][i+2] == "."):
m[1][i] = True
elif m[1][i]:
if a[0][i] == "." and (i > n-2 or a[0][i+1] == ".") and (i > n-3 or a[0][i+2] == "."):
m[0][i] = True
if a[2][i] == "." and (i > n-2 or a[2][i+1] == ".") and (i > n-3 or a[2][i+2] == "."):
m[2][i] = True
elif m[2][i]:
if a[1][i] == "." and (i > n-2 or a[1][i+1] == ".") and (i > n-3 or a[1][i+2] == "."):
m[1][i] = True
#print(m)
a = shift(a, n)
for i in range(3):
if m[i][n-1]:
print("YES")
break
else:
print("NO")
``` | instruction | 0 | 33,828 | 15 | 67,656 |
No | output | 1 | 33,828 | 15 | 67,657 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.
<image>
Input
Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 β€ t β€ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of t sets of the input data.
The first line of the description of each set contains two integers n, k (2 β€ n β€ 100, 1 β€ k β€ 26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.
Output
For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.
Examples
Input
2
16 4
...AAAAA........
s.BBB......CCCCC
........DDDDD...
16 4
...AAAAA........
s.BBB....CCCCC..
.......DDDDD....
Output
YES
NO
Input
2
10 4
s.ZZ......
.....AAABB
.YYYYYY...
10 4
s.ZZ......
....AAAABB
.YYYYYY...
Output
YES
NO
Note
In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset.
Submitted Solution:
```
#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#
# Copyright Β© 2016 missingdays <missingdays@missingdays>
#
# Distributed under terms of the MIT license.
"""
"""
def shift(a, n):
b = [["." for i in range(n)] for i in range(3)]
for i in range(3):
for j in range(n-2):
b[i][j] = a[i][j+2]
return b
n = int(input())
for case in range(n):
n, k = [int(i) for i in input().split()]
a = []
for i in range(3):
a.append(list(input()))
m = [[False for i in range(n)] for j in range(3)]
for i in range(3):
if a[i][0] == 's':
m[i][0] = True
for i in range(1, n):
#print(a)
for j in range(3):
if m[j][i-1] and a[j][i] == "." and (a[j][i-1] == "." or a[j][i-1] == "s") and (i > 1 or a[j][i-2] == "."):
m[j][i] = True
if m[0][i]:
if a[1][i] == ".": #and (i > n-2 or a[1][i+1] == ".") and (i > n-3 or a[1][i+2] == "."):
m[1][i] = True
if m[1][i]:
if a[0][i] == ".": #and (i > n-2 or a[0][i+1] == ".") and (i > n-3 or a[0][i+2] == "."):
m[0][i] = True
if a[2][i] == ".": #and (i > n-2 or a[2][i+1] == ".") and (i > n-3 or a[2][i+2] == "."):
m[2][i] = True
if m[2][i]:
if a[1][i] == ".": #and (i > n-2 or a[1][i+1] == ".") and (i > n-3 or a[1][i+2] == "."):
m[1][i] = True
#print(m)
a = shift(a, n)
for i in range(3):
if m[i][n-1]:
print("YES")
break
else:
print("NO")
``` | instruction | 0 | 33,829 | 15 | 67,658 |
No | output | 1 | 33,829 | 15 | 67,659 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.
<image>
Input
Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 β€ t β€ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of t sets of the input data.
The first line of the description of each set contains two integers n, k (2 β€ n β€ 100, 1 β€ k β€ 26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.
Output
For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.
Examples
Input
2
16 4
...AAAAA........
s.BBB......CCCCC
........DDDDD...
16 4
...AAAAA........
s.BBB....CCCCC..
.......DDDDD....
Output
YES
NO
Input
2
10 4
s.ZZ......
.....AAABB
.YYYYYY...
10 4
s.ZZ......
....AAAABB
.YYYYYY...
Output
YES
NO
Note
In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset.
Submitted Solution:
```
#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#
# Copyright Β© 2016 missingdays <missingdays@missingdays>
#
# Distributed under terms of the MIT license.
"""
"""
def shift(a, n):
b = [["." for i in range(n)] for i in range(3)]
for i in range(3):
for j in range(n-2):
b[i][j] = a[i][j+2]
return b
n = int(input())
for case in range(n):
n, k = [int(i) for i in input().split()]
a = []
for i in range(3):
a.append(list(input()))
m = [[False for i in range(n)] for j in range(3)]
for i in range(3):
if a[i][0] == 's':
m[i][0] = True
for i in range(1, n):
#print(a)
for j in range(3):
if m[j][i-1] and a[j][i] == "." and (a[j][i-1] == "." or a[j][i-1] == "s"):
m[j][i] = True
if m[0][i]:
if a[1][i] == ".": #and (i > n-2 or a[1][i+1] == ".") and (i > n-3 or a[1][i+2] == "."):
m[1][i] = True
if m[1][i]:
if a[0][i] == ".": #and (i > n-2 or a[0][i+1] == ".") and (i > n-3 or a[0][i+2] == "."):
m[0][i] = True
if a[2][i] == ".": #and (i > n-2 or a[2][i+1] == ".") and (i > n-3 or a[2][i+2] == "."):
m[2][i] = True
if m[2][i]:
if a[1][i] == ".": #and (i > n-2 or a[1][i+1] == ".") and (i > n-3 or a[1][i+2] == "."):
m[1][i] = True
#print(m)
a = shift(a, n)
for i in range(3):
if m[i][n-1]:
print("YES")
break
else:
print("NO")
``` | instruction | 0 | 33,830 | 15 | 67,660 |
No | output | 1 | 33,830 | 15 | 67,661 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and n columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column.
<image>
Input
Each test contains from one to ten sets of the input data. The first line of the test contains a single integer t (1 β€ t β€ 10 for pretests and tests or t = 1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of t sets of the input data.
The first line of the description of each set contains two integers n, k (2 β€ n β€ 100, 1 β€ k β€ 26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of n character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the k trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains.
Output
For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise.
Examples
Input
2
16 4
...AAAAA........
s.BBB......CCCCC
........DDDDD...
16 4
...AAAAA........
s.BBB....CCCCC..
.......DDDDD....
Output
YES
NO
Input
2
10 4
s.ZZ......
.....AAABB
.YYYYYY...
10 4
s.ZZ......
....AAAABB
.YYYYYY...
Output
YES
NO
Note
In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset.
Submitted Solution:
```
#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#
# Copyright Β© 2016 missingdays <missingdays@missingdays>
#
# Distributed under terms of the MIT license.
"""
"""
def shift(a, n):
b = [["." for i in range(n)] for i in range(3)]
for i in range(3):
for j in range(n-2):
b[i][j] = a[i][j+2]
return b
n = int(input())
for case in range(n):
n, k = [int(i) for i in input().split()]
a = []
for i in range(3):
a.append(list(input()))
m = [[False for i in range(n)] for j in range(3)]
for i in range(3):
if a[i][0] == 's':
m[i][0] = True
for i in range(1, n):
#print(a)
for j in range(3):
if m[j][i-1] and a[j][i] == "." and (a[j][i-1] == "." or a[j][i-1] == "s"):
m[j][i] = True
if m[0][i]:
if a[1][i] == ".": #and (i > n-2 or a[1][i+1] == ".") and (i > n-3 or a[1][i+2] == "."):
m[1][i] = True
elif m[1][i]:
if a[0][i] == ".": #and (i > n-2 or a[0][i+1] == ".") and (i > n-3 or a[0][i+2] == "."):
m[0][i] = True
if a[2][i] == ".": #and (i > n-2 or a[2][i+1] == ".") and (i > n-3 or a[2][i+2] == "."):
m[2][i] = True
elif m[2][i]:
if a[1][i] == ".": #and (i > n-2 or a[1][i+1] == ".") and (i > n-3 or a[1][i+2] == "."):
m[1][i] = True
#print(m)
a = shift(a, n)
for i in range(3):
if m[i][n-1]:
print("YES")
break
else:
print("NO")
``` | instruction | 0 | 33,831 | 15 | 67,662 |
No | output | 1 | 33,831 | 15 | 67,663 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In the spirit of the holidays, Saitama has given Genos two grid paths of length n (a weird gift even by Saitama's standards). A grid path is an ordered sequence of neighbouring squares in an infinite grid. Two squares are neighbouring if they share a side.
One example of a grid path is (0, 0) β (0, 1) β (0, 2) β (1, 2) β (1, 1) β (0, 1) β ( - 1, 1). Note that squares in this sequence might be repeated, i.e. path has self intersections.
Movement within a grid path is restricted to adjacent squares within the sequence. That is, from the i-th square, one can only move to the (i - 1)-th or (i + 1)-th squares of this path. Note that there is only a single valid move from the first and last squares of a grid path. Also note, that even if there is some j-th square of the path that coincides with the i-th square, only moves to (i - 1)-th and (i + 1)-th squares are available. For example, from the second square in the above sequence, one can only move to either the first or third squares.
To ensure that movement is not ambiguous, the two grid paths will not have an alternating sequence of three squares. For example, a contiguous subsequence (0, 0) β (0, 1) β (0, 0) cannot occur in a valid grid path.
One marble is placed on the first square of each grid path. Genos wants to get both marbles to the last square of each grid path. However, there is a catch. Whenever he moves one marble, the other marble will copy its movement if possible. For instance, if one marble moves east, then the other marble will try and move east as well. By try, we mean if moving east is a valid move, then the marble will move east.
Moving north increases the second coordinate by 1, while moving south decreases it by 1. Similarly, moving east increases first coordinate by 1, while moving west decreases it.
Given these two valid grid paths, Genos wants to know if it is possible to move both marbles to the ends of their respective paths. That is, if it is possible to move the marbles such that both marbles rest on the last square of their respective paths.
Input
The first line of the input contains a single integer n (2 β€ n β€ 1 000 000) β the length of the paths.
The second line of the input contains a string consisting of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') β the first grid path. The characters can be thought of as the sequence of moves needed to traverse the grid path. For example, the example path in the problem statement can be expressed by the string "NNESWW".
The third line of the input contains a string of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') β the second grid path.
Output
Print "YES" (without quotes) if it is possible for both marbles to be at the end position at the same time. Print "NO" (without quotes) otherwise. In both cases, the answer is case-insensitive.
Examples
Input
7
NNESWW
SWSWSW
Output
YES
Input
3
NN
SS
Output
NO
Note
In the first sample, the first grid path is the one described in the statement. Moreover, the following sequence of moves will get both marbles to the end: NNESWWSWSW.
In the second sample, no sequence of moves can get both marbles to the end. | instruction | 0 | 33,832 | 15 | 67,664 |
Tags: hashing, strings
Correct Solution:
```
from time import time
opposite = {
'N': 'S',
'S': 'N',
'E': 'W',
'W': 'E'
}
otr = str.maketrans(opposite)
bits = {
'N': 0,
'S': 1,
'E': 2,
'W': 3,
}
Q = 4294967291
def combine(h, v, q):
return (h<<2 | v) % q
def combinel(h, v, q, s):
return (v*s + h) % q
def flip(s):
return ''.join(reversed(s.translate(otr)))
def solvable(p1, p2):
h1 = 0
h2 = 0
s = 1
for i in reversed(range(len(p1))):
n1 = bits[p1[i]]
n2 = bits[opposite[p2[i]]]
h1 = combine(h1, n1, Q)
h2 = combinel(h2, n2, Q, s)
if h1 == h2 and p1[i:] == flip(p2[i:]):
return False
s = (s<<2) % Q
return True
if __name__ == '__main__':
n = int(input())
p1 = input()
p2 = input()
print('YES' if solvable(p1, p2) else 'NO')
``` | output | 1 | 33,832 | 15 | 67,665 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In the spirit of the holidays, Saitama has given Genos two grid paths of length n (a weird gift even by Saitama's standards). A grid path is an ordered sequence of neighbouring squares in an infinite grid. Two squares are neighbouring if they share a side.
One example of a grid path is (0, 0) β (0, 1) β (0, 2) β (1, 2) β (1, 1) β (0, 1) β ( - 1, 1). Note that squares in this sequence might be repeated, i.e. path has self intersections.
Movement within a grid path is restricted to adjacent squares within the sequence. That is, from the i-th square, one can only move to the (i - 1)-th or (i + 1)-th squares of this path. Note that there is only a single valid move from the first and last squares of a grid path. Also note, that even if there is some j-th square of the path that coincides with the i-th square, only moves to (i - 1)-th and (i + 1)-th squares are available. For example, from the second square in the above sequence, one can only move to either the first or third squares.
To ensure that movement is not ambiguous, the two grid paths will not have an alternating sequence of three squares. For example, a contiguous subsequence (0, 0) β (0, 1) β (0, 0) cannot occur in a valid grid path.
One marble is placed on the first square of each grid path. Genos wants to get both marbles to the last square of each grid path. However, there is a catch. Whenever he moves one marble, the other marble will copy its movement if possible. For instance, if one marble moves east, then the other marble will try and move east as well. By try, we mean if moving east is a valid move, then the marble will move east.
Moving north increases the second coordinate by 1, while moving south decreases it by 1. Similarly, moving east increases first coordinate by 1, while moving west decreases it.
Given these two valid grid paths, Genos wants to know if it is possible to move both marbles to the ends of their respective paths. That is, if it is possible to move the marbles such that both marbles rest on the last square of their respective paths.
Input
The first line of the input contains a single integer n (2 β€ n β€ 1 000 000) β the length of the paths.
The second line of the input contains a string consisting of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') β the first grid path. The characters can be thought of as the sequence of moves needed to traverse the grid path. For example, the example path in the problem statement can be expressed by the string "NNESWW".
The third line of the input contains a string of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') β the second grid path.
Output
Print "YES" (without quotes) if it is possible for both marbles to be at the end position at the same time. Print "NO" (without quotes) otherwise. In both cases, the answer is case-insensitive.
Examples
Input
7
NNESWW
SWSWSW
Output
YES
Input
3
NN
SS
Output
NO
Note
In the first sample, the first grid path is the one described in the statement. Moreover, the following sequence of moves will get both marbles to the end: NNESWWSWSW.
In the second sample, no sequence of moves can get both marbles to the end. | instruction | 0 | 33,833 | 15 | 67,666 |
Tags: hashing, strings
Correct Solution:
```
def prefix(s):
v = [0]*len(s)
for i in range(1,len(s)):
k = v[i-1]
while k > 0 and s[k] != s[i]:
k = v[k-1]
if s[k] == s[i]:
k = k + 1
v[i] = k
return v
n = int(input())
n-=1
s1 = input()
s2 = input()
opos = {'W':'E', 'E':'W', 'N':'S', 'S':'N'}
s3 = ''
for elem in s2:
s3 += opos[elem]
s3 = s3[::-1]
s = s3 + '$' + s1
a = prefix(s)[2 * n]
if a == 0: print('YES')
else: print('NO')
``` | output | 1 | 33,833 | 15 | 67,667 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In the spirit of the holidays, Saitama has given Genos two grid paths of length n (a weird gift even by Saitama's standards). A grid path is an ordered sequence of neighbouring squares in an infinite grid. Two squares are neighbouring if they share a side.
One example of a grid path is (0, 0) β (0, 1) β (0, 2) β (1, 2) β (1, 1) β (0, 1) β ( - 1, 1). Note that squares in this sequence might be repeated, i.e. path has self intersections.
Movement within a grid path is restricted to adjacent squares within the sequence. That is, from the i-th square, one can only move to the (i - 1)-th or (i + 1)-th squares of this path. Note that there is only a single valid move from the first and last squares of a grid path. Also note, that even if there is some j-th square of the path that coincides with the i-th square, only moves to (i - 1)-th and (i + 1)-th squares are available. For example, from the second square in the above sequence, one can only move to either the first or third squares.
To ensure that movement is not ambiguous, the two grid paths will not have an alternating sequence of three squares. For example, a contiguous subsequence (0, 0) β (0, 1) β (0, 0) cannot occur in a valid grid path.
One marble is placed on the first square of each grid path. Genos wants to get both marbles to the last square of each grid path. However, there is a catch. Whenever he moves one marble, the other marble will copy its movement if possible. For instance, if one marble moves east, then the other marble will try and move east as well. By try, we mean if moving east is a valid move, then the marble will move east.
Moving north increases the second coordinate by 1, while moving south decreases it by 1. Similarly, moving east increases first coordinate by 1, while moving west decreases it.
Given these two valid grid paths, Genos wants to know if it is possible to move both marbles to the ends of their respective paths. That is, if it is possible to move the marbles such that both marbles rest on the last square of their respective paths.
Input
The first line of the input contains a single integer n (2 β€ n β€ 1 000 000) β the length of the paths.
The second line of the input contains a string consisting of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') β the first grid path. The characters can be thought of as the sequence of moves needed to traverse the grid path. For example, the example path in the problem statement can be expressed by the string "NNESWW".
The third line of the input contains a string of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') β the second grid path.
Output
Print "YES" (without quotes) if it is possible for both marbles to be at the end position at the same time. Print "NO" (without quotes) otherwise. In both cases, the answer is case-insensitive.
Examples
Input
7
NNESWW
SWSWSW
Output
YES
Input
3
NN
SS
Output
NO
Note
In the first sample, the first grid path is the one described in the statement. Moreover, the following sequence of moves will get both marbles to the end: NNESWWSWSW.
In the second sample, no sequence of moves can get both marbles to the end. | instruction | 0 | 33,834 | 15 | 67,668 |
Tags: hashing, strings
Correct Solution:
```
from time import time
opposite = {
'N': 'S',
'S': 'N',
'E': 'W',
'W': 'E'
}
otr = str.maketrans(opposite)
bits = {
'N': 0,
'S': 1,
'E': 2,
'W': 3,
}
Q = 4294967291
def combine(h, v, q):
return (h<<2 | v) % q
def combinel(h, v, q, s):
return (v*s + h) % q
def flip(s):
return ''.join(reversed(s.translate(otr)))
def solvable(p1, p2):
h1 = 0
h2 = 0
s = 1
for i in reversed(range(len(p1))):
n1 = bits[p1[i]]
n2 = bits[opposite[p2[i]]]
h1 = combine(h1, n1, Q)
h2 = combinel(h2, n2, Q, s)
if h1 == h2 and p1[i:] == flip(p2[i:]):
return False
s = (s<<2) % Q
return True
if __name__ == '__main__':
n = int(input())
p1 = input()
p2 = input()
print('YES' if solvable(p1, p2) else 'NO')
# Made By Mostafa_Khaled
``` | output | 1 | 33,834 | 15 | 67,669 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In the spirit of the holidays, Saitama has given Genos two grid paths of length n (a weird gift even by Saitama's standards). A grid path is an ordered sequence of neighbouring squares in an infinite grid. Two squares are neighbouring if they share a side.
One example of a grid path is (0, 0) β (0, 1) β (0, 2) β (1, 2) β (1, 1) β (0, 1) β ( - 1, 1). Note that squares in this sequence might be repeated, i.e. path has self intersections.
Movement within a grid path is restricted to adjacent squares within the sequence. That is, from the i-th square, one can only move to the (i - 1)-th or (i + 1)-th squares of this path. Note that there is only a single valid move from the first and last squares of a grid path. Also note, that even if there is some j-th square of the path that coincides with the i-th square, only moves to (i - 1)-th and (i + 1)-th squares are available. For example, from the second square in the above sequence, one can only move to either the first or third squares.
To ensure that movement is not ambiguous, the two grid paths will not have an alternating sequence of three squares. For example, a contiguous subsequence (0, 0) β (0, 1) β (0, 0) cannot occur in a valid grid path.
One marble is placed on the first square of each grid path. Genos wants to get both marbles to the last square of each grid path. However, there is a catch. Whenever he moves one marble, the other marble will copy its movement if possible. For instance, if one marble moves east, then the other marble will try and move east as well. By try, we mean if moving east is a valid move, then the marble will move east.
Moving north increases the second coordinate by 1, while moving south decreases it by 1. Similarly, moving east increases first coordinate by 1, while moving west decreases it.
Given these two valid grid paths, Genos wants to know if it is possible to move both marbles to the ends of their respective paths. That is, if it is possible to move the marbles such that both marbles rest on the last square of their respective paths.
Input
The first line of the input contains a single integer n (2 β€ n β€ 1 000 000) β the length of the paths.
The second line of the input contains a string consisting of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') β the first grid path. The characters can be thought of as the sequence of moves needed to traverse the grid path. For example, the example path in the problem statement can be expressed by the string "NNESWW".
The third line of the input contains a string of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') β the second grid path.
Output
Print "YES" (without quotes) if it is possible for both marbles to be at the end position at the same time. Print "NO" (without quotes) otherwise. In both cases, the answer is case-insensitive.
Examples
Input
7
NNESWW
SWSWSW
Output
YES
Input
3
NN
SS
Output
NO
Note
In the first sample, the first grid path is the one described in the statement. Moreover, the following sequence of moves will get both marbles to the end: NNESWWSWSW.
In the second sample, no sequence of moves can get both marbles to the end.
Submitted Solution:
```
n = input()
a = input()
b = input()
r = ""
rev = {"S":"N","N":"S","W":"E","E":"W"}
for i in range(len(b)) :
r+=rev[b[i]]
F = 0
S = 0
rc = 0
for i in range(len(a)-1,-1,-1) :
F += (ord(a[i]))*256
S += (ord(r[rc]))*256
rc+=1
if F==S :
print("NO")
break
else :
print("YES")
``` | instruction | 0 | 33,835 | 15 | 67,670 |
No | output | 1 | 33,835 | 15 | 67,671 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In the spirit of the holidays, Saitama has given Genos two grid paths of length n (a weird gift even by Saitama's standards). A grid path is an ordered sequence of neighbouring squares in an infinite grid. Two squares are neighbouring if they share a side.
One example of a grid path is (0, 0) β (0, 1) β (0, 2) β (1, 2) β (1, 1) β (0, 1) β ( - 1, 1). Note that squares in this sequence might be repeated, i.e. path has self intersections.
Movement within a grid path is restricted to adjacent squares within the sequence. That is, from the i-th square, one can only move to the (i - 1)-th or (i + 1)-th squares of this path. Note that there is only a single valid move from the first and last squares of a grid path. Also note, that even if there is some j-th square of the path that coincides with the i-th square, only moves to (i - 1)-th and (i + 1)-th squares are available. For example, from the second square in the above sequence, one can only move to either the first or third squares.
To ensure that movement is not ambiguous, the two grid paths will not have an alternating sequence of three squares. For example, a contiguous subsequence (0, 0) β (0, 1) β (0, 0) cannot occur in a valid grid path.
One marble is placed on the first square of each grid path. Genos wants to get both marbles to the last square of each grid path. However, there is a catch. Whenever he moves one marble, the other marble will copy its movement if possible. For instance, if one marble moves east, then the other marble will try and move east as well. By try, we mean if moving east is a valid move, then the marble will move east.
Moving north increases the second coordinate by 1, while moving south decreases it by 1. Similarly, moving east increases first coordinate by 1, while moving west decreases it.
Given these two valid grid paths, Genos wants to know if it is possible to move both marbles to the ends of their respective paths. That is, if it is possible to move the marbles such that both marbles rest on the last square of their respective paths.
Input
The first line of the input contains a single integer n (2 β€ n β€ 1 000 000) β the length of the paths.
The second line of the input contains a string consisting of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') β the first grid path. The characters can be thought of as the sequence of moves needed to traverse the grid path. For example, the example path in the problem statement can be expressed by the string "NNESWW".
The third line of the input contains a string of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') β the second grid path.
Output
Print "YES" (without quotes) if it is possible for both marbles to be at the end position at the same time. Print "NO" (without quotes) otherwise. In both cases, the answer is case-insensitive.
Examples
Input
7
NNESWW
SWSWSW
Output
YES
Input
3
NN
SS
Output
NO
Note
In the first sample, the first grid path is the one described in the statement. Moreover, the following sequence of moves will get both marbles to the end: NNESWWSWSW.
In the second sample, no sequence of moves can get both marbles to the end.
Submitted Solution:
```
#this should be marbles
print("YES")
``` | instruction | 0 | 33,836 | 15 | 67,672 |
No | output | 1 | 33,836 | 15 | 67,673 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In the spirit of the holidays, Saitama has given Genos two grid paths of length n (a weird gift even by Saitama's standards). A grid path is an ordered sequence of neighbouring squares in an infinite grid. Two squares are neighbouring if they share a side.
One example of a grid path is (0, 0) β (0, 1) β (0, 2) β (1, 2) β (1, 1) β (0, 1) β ( - 1, 1). Note that squares in this sequence might be repeated, i.e. path has self intersections.
Movement within a grid path is restricted to adjacent squares within the sequence. That is, from the i-th square, one can only move to the (i - 1)-th or (i + 1)-th squares of this path. Note that there is only a single valid move from the first and last squares of a grid path. Also note, that even if there is some j-th square of the path that coincides with the i-th square, only moves to (i - 1)-th and (i + 1)-th squares are available. For example, from the second square in the above sequence, one can only move to either the first or third squares.
To ensure that movement is not ambiguous, the two grid paths will not have an alternating sequence of three squares. For example, a contiguous subsequence (0, 0) β (0, 1) β (0, 0) cannot occur in a valid grid path.
One marble is placed on the first square of each grid path. Genos wants to get both marbles to the last square of each grid path. However, there is a catch. Whenever he moves one marble, the other marble will copy its movement if possible. For instance, if one marble moves east, then the other marble will try and move east as well. By try, we mean if moving east is a valid move, then the marble will move east.
Moving north increases the second coordinate by 1, while moving south decreases it by 1. Similarly, moving east increases first coordinate by 1, while moving west decreases it.
Given these two valid grid paths, Genos wants to know if it is possible to move both marbles to the ends of their respective paths. That is, if it is possible to move the marbles such that both marbles rest on the last square of their respective paths.
Input
The first line of the input contains a single integer n (2 β€ n β€ 1 000 000) β the length of the paths.
The second line of the input contains a string consisting of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') β the first grid path. The characters can be thought of as the sequence of moves needed to traverse the grid path. For example, the example path in the problem statement can be expressed by the string "NNESWW".
The third line of the input contains a string of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') β the second grid path.
Output
Print "YES" (without quotes) if it is possible for both marbles to be at the end position at the same time. Print "NO" (without quotes) otherwise. In both cases, the answer is case-insensitive.
Examples
Input
7
NNESWW
SWSWSW
Output
YES
Input
3
NN
SS
Output
NO
Note
In the first sample, the first grid path is the one described in the statement. Moreover, the following sequence of moves will get both marbles to the end: NNESWWSWSW.
In the second sample, no sequence of moves can get both marbles to the end.
Submitted Solution:
```
def prefix(s):
v = [0]*len(s)
for i in range(1,len(s)):
k = v[i-1]
while k > 0 and s[k] != s[i]:
k = v[k-1]
if s[k] == s[i]:
k = k + 1
v[i] = k
return v
n = int(input())
n-=1
s1 = input()
s2 = input()
opos = {'W':'E', 'E':'W', 'N':'S', 'S':'N'}
s3 = ''
for elem in s2:
s3 += opos[elem]
s3[::-1]
s = s3 + '$' + s1
a = prefix(s)[2 * n]
if a == 0: print('YES')
else: print('NO')
``` | instruction | 0 | 33,837 | 15 | 67,674 |
No | output | 1 | 33,837 | 15 | 67,675 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In the spirit of the holidays, Saitama has given Genos two grid paths of length n (a weird gift even by Saitama's standards). A grid path is an ordered sequence of neighbouring squares in an infinite grid. Two squares are neighbouring if they share a side.
One example of a grid path is (0, 0) β (0, 1) β (0, 2) β (1, 2) β (1, 1) β (0, 1) β ( - 1, 1). Note that squares in this sequence might be repeated, i.e. path has self intersections.
Movement within a grid path is restricted to adjacent squares within the sequence. That is, from the i-th square, one can only move to the (i - 1)-th or (i + 1)-th squares of this path. Note that there is only a single valid move from the first and last squares of a grid path. Also note, that even if there is some j-th square of the path that coincides with the i-th square, only moves to (i - 1)-th and (i + 1)-th squares are available. For example, from the second square in the above sequence, one can only move to either the first or third squares.
To ensure that movement is not ambiguous, the two grid paths will not have an alternating sequence of three squares. For example, a contiguous subsequence (0, 0) β (0, 1) β (0, 0) cannot occur in a valid grid path.
One marble is placed on the first square of each grid path. Genos wants to get both marbles to the last square of each grid path. However, there is a catch. Whenever he moves one marble, the other marble will copy its movement if possible. For instance, if one marble moves east, then the other marble will try and move east as well. By try, we mean if moving east is a valid move, then the marble will move east.
Moving north increases the second coordinate by 1, while moving south decreases it by 1. Similarly, moving east increases first coordinate by 1, while moving west decreases it.
Given these two valid grid paths, Genos wants to know if it is possible to move both marbles to the ends of their respective paths. That is, if it is possible to move the marbles such that both marbles rest on the last square of their respective paths.
Input
The first line of the input contains a single integer n (2 β€ n β€ 1 000 000) β the length of the paths.
The second line of the input contains a string consisting of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') β the first grid path. The characters can be thought of as the sequence of moves needed to traverse the grid path. For example, the example path in the problem statement can be expressed by the string "NNESWW".
The third line of the input contains a string of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') β the second grid path.
Output
Print "YES" (without quotes) if it is possible for both marbles to be at the end position at the same time. Print "NO" (without quotes) otherwise. In both cases, the answer is case-insensitive.
Examples
Input
7
NNESWW
SWSWSW
Output
YES
Input
3
NN
SS
Output
NO
Note
In the first sample, the first grid path is the one described in the statement. Moreover, the following sequence of moves will get both marbles to the end: NNESWWSWSW.
In the second sample, no sequence of moves can get both marbles to the end.
Submitted Solution:
```
#E
input()
a=input()
s=input()
if (a[-1]=='W' and s[-1]=='E') or (a[-1]=='E' and s[-1]=='W') or (a[-1]=='N' and s[-1]=='S') or (a[-1]=='S' and s[-1]=='N'):
print('NO')
else:
a=a.replace('N', 'R').replace('S', 'N').replace('R', 'S')
a=a.replace('E', 'R').replace('W', 'E').replace('R', 'W')
if a==s:
print('NO')
else:
print('YES')
``` | instruction | 0 | 33,838 | 15 | 67,676 |
No | output | 1 | 33,838 | 15 | 67,677 |
Provide a correct Python 3 solution for this coding contest problem.
Backgorund
The super popular game "Puzzle & Hexagons" has finally been released. This game is so funny that many people are addicted to it. There were a number of people who were certified as addicted by doctors because of their excessive enthusiasm. Volunteers from around the world have created a "Puzzle & Hexagons" simulator to help addicts in the game and try to encourage them to avoid playing on dangerous real machines. I want you to cooperate in making a simulator.
Problem
A board with H squares in the vertical direction and W in the horizontal direction is given. Fig.1 shows the board surface when H = 4 and W = 7, and the coordinates (x, y) of the corresponding squares.
<image>
Fig.1
In the initial state, each square has a colored block. The color of the block is expressed by one letter of the alphabet as follows.
*'R' γ» γ» γ» Red
*'G' γ» γ» γ» Green
*'B' γ» γ» γ» Blue
*'P' γ» γ» γ» Purple
*'Y' γ» γ» γ» Yellow
*'E' γ» γ» γ» Water
Then the number Q of operations is given.
Each operation is given the center coordinates of rotation (x, y), indicating that the six blocks around the square are rotated one clockwise. (See Fig.2). At this time, even if the cell does not have a block, it is considered that an empty block exists and is rotated one clockwise. However, if any one of the specified coordinates and the six squares around it does not exist on the H Γ W board, the rotation is not performed.
<image>
Fig.2
Next, the process is repeated until the following processing cannot be performed.
1. In Fig.3, when there is no block in any of the squares B, C, and D from the position of block A, block A falls to the position of C. If the squares B and D do not exist, it is considered that the block does not exist, and if the square C does not exist, the fall process is not performed.
2. If there is a block that can process 1, it returns to 1.
3. If three or more blocks of the same color are connected, all the blocks disappear. Connecting two blocks means sharing one side of the square.
Note: This series of processing is performed even when no operation is given (initial state).
<image>
Fig.3
Output the final board after performing all operations.
Constraints
* 3 β€ H β€ 50
* 3 β€ W β€ 50
* 0 β€ x <W
* 0 β€ y <H
* 1 β€ Q β€ 100
* Fi, j (0 β€ i <W, 0 β€ j <H) is one of'R',' G',' B',' P',' Y',' E'.
Input
The input is given in the following format.
H W
F0, Hβ1 F1, Hβ1β¦ FWβ1, Hβ1
F0, H-2 F1, H-2 ... FW-1, H-2
..
..
..
F0,0 F1,0β¦ FW-1,0
Q
x0 y0
x1 y1
..
..
..
xQβ1 yQβ1
The first line is given two integers H and W that represent the vertical and horizontal sizes of the board. From the second line to the H + 1 line, a character string representing the color of the board corresponding to each subscript is given. The number Q of operations is given on the second line of H +. In the following Q line, x and y representing the coordinates of the cell at the center of rotation are given.
Output
Output the board surface in line H after performing all operations. However, cells without blocks should be represented by'.'.
Examples
Input
3 3
RGR
RBP
YEB
1
1 1
Output
β¦
YBG
EBP
Input
4 5
BYYGG
RRRRR
RRBRR
YYGGB
2
3 1
3 1
Output
.....
.....
.....
B.BGB
Input
4 4
BEEP
ERYY
BBRP
RBYP
1
1 2
Output
....
....
....
.B.. | instruction | 0 | 34,206 | 15 | 68,412 |
"Correct Solution:
```
class Simulator:
def __init__(self, mp, width, height):
self.mp = mp
self.width = width
self.height = height
self.vec = [((1, 1), (1, 0), (0, -1), (-1, 0), (-1, 1), (0, 1)),
((1, 0), (1, -1), (0, -1), (-1, -1), (-1, 0), (0, 1))]
self.checked = None
self.erase_list = None
def rotate(self, x, y):
if (not 0 < x < self.width - 1) or (not 0 < y < self.height - 1):return
vec = self.vec[x % 2]
lx, ly = vec[-1]
last_color = self.mp[y + ly][x + lx]
for i in range(5, 0, -1):
ax, ay = vec[i]
bx, by = vec[i - 1]
self.mp[y + ay][x + ax] = self.mp[y + by][x + bx]
sx, sy = vec[0]
self.mp[y + sy][x + sx] = last_color
def check(self):
self.checked = [[False] * self.width for _ in range(self.height)]
self.erase_list = []
for y in range(self.height):
for x in range(self.width):
if not self.checked[y][x]:
self.checked[y][x] = True
if self.mp[y][x] == ".":continue
save = [(x, y)]
self.search(x, y, save)
if len(save) >= 3:
self.erase_list += save
def search(self, x, y, save):
vec = self.vec[x % 2]
for dx, dy in vec:
if (not 0 <= x + dx < self.width) or (not 0 <= y + dy < self.height):continue
if self.checked[y + dy][x + dx]:continue
if self.mp[y + dy][x + dx] == self.mp[y][x]:
save.append((x + dx, y + dy))
self.checked[y + dy][x + dx] = True
self.search(x + dx, y + dy, save)
def erase(self):
for x, y in self.erase_list:
self.mp[y][x] = "."
def fall(self):
for y in range(1, self.height):
for x in range(1, self.width, 2):
check_vec = ((-1, -1), (0, -1), (1, -1)) if x != self.width - 1 else ((-1, -1), (0, -1))
to_y = y
while to_y > 0:
for dx, dy in check_vec:
if self.mp[to_y + dy][x + dx] != ".":break
else:
to_y -= 1
continue
break
if to_y != y:
self.mp[to_y][x] = self.mp[y][x]
self.mp[y][x] = "."
for x in range(0, self.width, 2):
if x == 0:check_vec = ((0, -1), (1, 0))
elif x == self.width - 1:check_vec = ((-1, 0), (0, -1))
else:check_vec = ((-1, 0), (0, -1), (1, 0))
to_y = y
while to_y > 0:
for dx, dy in check_vec:
if self.mp[to_y + dy][x + dx] != ".":break
else:
to_y -= 1
continue
break
if to_y != y:
self.mp[to_y][x] = self.mp[y][x]
self.mp[y][x] = "."
def run(self):
LIMIT = 100
cnt = 0
while True:
cnt += 1
if cnt > LIMIT:
print("LIMIT_OVER")
break
self.fall()
self.check()
if not self.erase_list:break
self.erase()
def print_mp(self):
for y in range(self.height - 1, -1, -1):
print("".join(self.mp[y]))
h, w = map(int, input().split())
mp = [list(input()) for _ in range(h)][::-1]
simulator = Simulator(mp, w, h)
simulator.run()
q = int(input())
for _ in range(q):
x, y = map(int, input().split())
simulator.rotate(x, y)
simulator.run()
simulator.print_mp()
``` | output | 1 | 34,206 | 15 | 68,413 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a rectangular grid of size n Γ m. Each cell has a number written on it; the number on the cell (i, j) is a_{i, j}. Your task is to calculate the number of paths from the upper-left cell (1, 1) to the bottom-right cell (n, m) meeting the following constraints:
* You can move to the right or to the bottom only. Formally, from the cell (i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j). The target cell can't be outside of the grid.
* The xor of all the numbers on the path from the cell (1, 1) to the cell (n, m) must be equal to k (xor operation is the bitwise exclusive OR, it is represented as '^' in Java or C++ and "xor" in Pascal).
Find the number of such paths in the given grid.
Input
The first line of the input contains three integers n, m and k (1 β€ n, m β€ 20, 0 β€ k β€ 10^{18}) β the height and the width of the grid, and the number k.
The next n lines contain m integers each, the j-th element in the i-th line is a_{i, j} (0 β€ a_{i, j} β€ 10^{18}).
Output
Print one integer β the number of paths from (1, 1) to (n, m) with xor sum equal to k.
Examples
Input
3 3 11
2 1 5
7 10 0
12 6 4
Output
3
Input
3 4 2
1 3 3 3
0 3 3 2
3 0 1 1
Output
5
Input
3 4 1000000000000000000
1 3 3 3
0 3 3 2
3 0 1 1
Output
0
Note
All the paths from the first example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (3, 3);
* (1, 1) β (1, 2) β (2, 2) β (3, 2) β (3, 3).
All the paths from the second example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (2, 4) β (3, 4);
* (1, 1) β (1, 2) β (2, 2) β (2, 3) β (3, 3) β (3, 4);
* (1, 1) β (1, 2) β (1, 3) β (2, 3) β (3, 3) β (3, 4). | instruction | 0 | 34,241 | 15 | 68,482 |
Tags: bitmasks, brute force, dp, meet-in-the-middle
Correct Solution:
```
n, m, k = map(int, input().split())
a = []
for i in range(n):
a.append(list(map(int, input().split())))
if n > m:
d = []
for i in range(m):
d.append([])
for j in range(n):
d[i].append(a[j][i])
a = d
n, m = m, n
b = []
for i in range(n):
temp = []
for j in range(m):
temp.append([])
b.append(temp)
for i in range((n + m) // 2):
for j in range(min(i + 1, m, n)):
if i == 0:
b[j][i - j].append(a[j][i - j])
elif j == 0:
b[j][i - j].append(b[j][i - j - 1][0] ^ a[j][i - j])
elif j == i:
b[j][i - j].append(b[j - 1][i - j][0] ^ a[j][i - j])
else:
for x in b[j][i - j - 1] + b[j - 1][i - j]:
b[j][i - j].append(x ^ a[j][i - j])
c = []
for i in range(n):
temp = []
for j in range(m):
temp.append([])
c.append(temp)
for i in range((n + m + 1) // 2):
for j in range(min(i + 1, m, n)):
if i == 0:
c[(n - 1) - j][(m - 1) - (i - j)].append(k)
elif j == 0:
c[(n - 1) - j][(m - 1) - (i - j)].append(c[(n - 1) - j][(m - 1) - (i - j - 1)][0] ^ a[(n - 1) - j][(m - 1) - (i - j - 1)])
elif j == i:
c[(n - 1) - j][(m - 1) - (i - j)].append(c[(n - 1) - (j - 1)][(m - 1) - (i - j)][0] ^ a[(n - 1) - (j - 1)][(m - 1) - (i - j)])
else:
for x in c[(n - 1) - j][(m - 1) - (i - j - 1)]:
c[(n - 1) - j][(m - 1) - (i - j)].append(x ^ a[(n - 1) - j][(m - 1) - (i - j - 1)])
for x in c[(n - 1) - (j - 1)][(m - 1) - (i - j)]:
c[(n - 1) - j][(m - 1) - (i - j)].append(x ^ a[(n - 1) - (j - 1)][(m - 1) - (i - j)])
wae = 0
i = (n + m) // 2 - 1
for j in range(min(m, n)):
d = {}
e = {}
for l1 in b[j][i - j]:
if not l1 in d:
d[l1] = 0
d[l1] += 1
for l2 in c[j][i - j]:
if not l2 in e:
e[l2] = 0
e[l2] += 1
for key in d.keys():
if key in d and key in e:
wae += d[key] * e[key]
print(wae)
``` | output | 1 | 34,241 | 15 | 68,483 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a rectangular grid of size n Γ m. Each cell has a number written on it; the number on the cell (i, j) is a_{i, j}. Your task is to calculate the number of paths from the upper-left cell (1, 1) to the bottom-right cell (n, m) meeting the following constraints:
* You can move to the right or to the bottom only. Formally, from the cell (i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j). The target cell can't be outside of the grid.
* The xor of all the numbers on the path from the cell (1, 1) to the cell (n, m) must be equal to k (xor operation is the bitwise exclusive OR, it is represented as '^' in Java or C++ and "xor" in Pascal).
Find the number of such paths in the given grid.
Input
The first line of the input contains three integers n, m and k (1 β€ n, m β€ 20, 0 β€ k β€ 10^{18}) β the height and the width of the grid, and the number k.
The next n lines contain m integers each, the j-th element in the i-th line is a_{i, j} (0 β€ a_{i, j} β€ 10^{18}).
Output
Print one integer β the number of paths from (1, 1) to (n, m) with xor sum equal to k.
Examples
Input
3 3 11
2 1 5
7 10 0
12 6 4
Output
3
Input
3 4 2
1 3 3 3
0 3 3 2
3 0 1 1
Output
5
Input
3 4 1000000000000000000
1 3 3 3
0 3 3 2
3 0 1 1
Output
0
Note
All the paths from the first example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (3, 3);
* (1, 1) β (1, 2) β (2, 2) β (3, 2) β (3, 3).
All the paths from the second example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (2, 4) β (3, 4);
* (1, 1) β (1, 2) β (2, 2) β (2, 3) β (3, 3) β (3, 4);
* (1, 1) β (1, 2) β (1, 3) β (2, 3) β (3, 3) β (3, 4). | instruction | 0 | 34,242 | 15 | 68,484 |
Tags: bitmasks, brute force, dp, meet-in-the-middle
Correct Solution:
```
#####################################
import atexit, io, sys, collections, math, heapq, fractions,copy, os, functools
import sys
import random
import collections
from io import BytesIO, IOBase
##################################### python 3 START
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")
##################################### python 3 END
n,m,k = map(int, input().split())
mat = [list(map(int, input().split())) for i in range(n)]
half = (n + m -2) //2
cc = [[collections.Counter() for j in range(len(mat[0]))] for i in range(len(mat))]
def dfs(i,j,ongoing, cc, half, mat):
if half == 0:
cc[i][j][ongoing] += 1
return
if i +1 < len(mat):
dfs(i+1,j,ongoing ^ mat[i+1][j], cc, half-1, mat)
if j +1 < len(mat[0]):
dfs(i,j+1,ongoing ^ mat[i][j+1], cc, half-1, mat)
dfs(0,0,mat[0][0],cc,half, mat)
ans = [0]
def dfs2(i,j,ongoing, cc, half, mat,k):
if half == 0:
ans[0] += cc[i][j][k^ongoing ^ mat[i][j]]
return
if i -1 >=0:
dfs2(i - 1,j,ongoing ^ mat[i-1][j], cc, half-1, mat,k)
if j -1 >=0:
dfs2(i, j - 1,ongoing ^ mat[i][j-1], cc, half-1, mat,k)
dfs2(len(mat)-1, len(mat[0])-1, mat[n-1][m-1], cc, n + m -2 - half, mat,k)
print (ans[0])
``` | output | 1 | 34,242 | 15 | 68,485 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a rectangular grid of size n Γ m. Each cell has a number written on it; the number on the cell (i, j) is a_{i, j}. Your task is to calculate the number of paths from the upper-left cell (1, 1) to the bottom-right cell (n, m) meeting the following constraints:
* You can move to the right or to the bottom only. Formally, from the cell (i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j). The target cell can't be outside of the grid.
* The xor of all the numbers on the path from the cell (1, 1) to the cell (n, m) must be equal to k (xor operation is the bitwise exclusive OR, it is represented as '^' in Java or C++ and "xor" in Pascal).
Find the number of such paths in the given grid.
Input
The first line of the input contains three integers n, m and k (1 β€ n, m β€ 20, 0 β€ k β€ 10^{18}) β the height and the width of the grid, and the number k.
The next n lines contain m integers each, the j-th element in the i-th line is a_{i, j} (0 β€ a_{i, j} β€ 10^{18}).
Output
Print one integer β the number of paths from (1, 1) to (n, m) with xor sum equal to k.
Examples
Input
3 3 11
2 1 5
7 10 0
12 6 4
Output
3
Input
3 4 2
1 3 3 3
0 3 3 2
3 0 1 1
Output
5
Input
3 4 1000000000000000000
1 3 3 3
0 3 3 2
3 0 1 1
Output
0
Note
All the paths from the first example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (3, 3);
* (1, 1) β (1, 2) β (2, 2) β (3, 2) β (3, 3).
All the paths from the second example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (2, 4) β (3, 4);
* (1, 1) β (1, 2) β (2, 2) β (2, 3) β (3, 3) β (3, 4);
* (1, 1) β (1, 2) β (1, 3) β (2, 3) β (3, 3) β (3, 4). | instruction | 0 | 34,243 | 15 | 68,486 |
Tags: bitmasks, brute force, dp, meet-in-the-middle
Correct Solution:
```
d = {}
ans = 0
for i in range(22):
d[i] = {}
#print(cnt)
n,m,k = list(map(int, input().split()))
arr = [list(map(int, input().split())) for i in range(n)]
def check(x,y):
if x < 0 or x >= n or y < 0 or y >= m:
return False
else:
return True
def go(x,y,now):
if check(x,y) == False:
return
now ^= arr[x][y]
if x + y == m - 1:
#print('yes')
if now in d[x]:
d[x][now] += 1
else:
d[x][now] = 1
return
go(x+1,y,now)
go(x,y+1,now)
def goRev(i,j,now):
if check(i,j) == False:
return
if i + j == m - 1:
cur = k ^ now
if cur in d[i]:
global ans
#print(ans)
ans += d[i][cur]
return
now ^= arr[i][j]
goRev(i-1,j,now)
goRev(i,j-1,now)
go(0,0,0)
goRev(n-1,m-1,0)
print(ans)
``` | output | 1 | 34,243 | 15 | 68,487 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a rectangular grid of size n Γ m. Each cell has a number written on it; the number on the cell (i, j) is a_{i, j}. Your task is to calculate the number of paths from the upper-left cell (1, 1) to the bottom-right cell (n, m) meeting the following constraints:
* You can move to the right or to the bottom only. Formally, from the cell (i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j). The target cell can't be outside of the grid.
* The xor of all the numbers on the path from the cell (1, 1) to the cell (n, m) must be equal to k (xor operation is the bitwise exclusive OR, it is represented as '^' in Java or C++ and "xor" in Pascal).
Find the number of such paths in the given grid.
Input
The first line of the input contains three integers n, m and k (1 β€ n, m β€ 20, 0 β€ k β€ 10^{18}) β the height and the width of the grid, and the number k.
The next n lines contain m integers each, the j-th element in the i-th line is a_{i, j} (0 β€ a_{i, j} β€ 10^{18}).
Output
Print one integer β the number of paths from (1, 1) to (n, m) with xor sum equal to k.
Examples
Input
3 3 11
2 1 5
7 10 0
12 6 4
Output
3
Input
3 4 2
1 3 3 3
0 3 3 2
3 0 1 1
Output
5
Input
3 4 1000000000000000000
1 3 3 3
0 3 3 2
3 0 1 1
Output
0
Note
All the paths from the first example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (3, 3);
* (1, 1) β (1, 2) β (2, 2) β (3, 2) β (3, 3).
All the paths from the second example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (2, 4) β (3, 4);
* (1, 1) β (1, 2) β (2, 2) β (2, 3) β (3, 3) β (3, 4);
* (1, 1) β (1, 2) β (1, 3) β (2, 3) β (3, 3) β (3, 4). | instruction | 0 | 34,244 | 15 | 68,488 |
Tags: bitmasks, brute force, dp, meet-in-the-middle
Correct Solution:
```
# ===============================================================================================
# importing some useful libraries.
from __future__ import division, print_function
from fractions import Fraction
import sys
import os
from io import BytesIO, IOBase
from itertools import *
import bisect
from heapq import *
from math import ceil, floor
from copy import *
from collections import deque, defaultdict
from collections import Counter as counter # Counter(list) return a dict with {key: count}
from itertools import combinations # if a = [1,2,3] then print(list(comb(a,2))) -----> [(1, 2), (1, 3), (2, 3)]
from itertools import permutations as permutate
from bisect import bisect_left as bl
from operator import *
# If the element is already present in the list,
# the left most position where element has to be inserted is returned.
from bisect import bisect_right as br
from bisect import bisect
# If the element is already present in the list,
# the right most position where element has to be inserted is returned
# range=xrange
# ==============================================================================================
# fast I/O region
BUFSIZE = 8192
from sys import stderr
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")
def print(*args, **kwargs):
"""Prints the values to a stream, or to sys.stdout by default."""
sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
at_start = True
for x in args:
if not at_start:
file.write(sep)
file.write(str(x))
at_start = False
file.write(kwargs.pop("end", "\n"))
if kwargs.pop("flush", False):
file.flush()
if sys.version_info[0] < 3:
sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
# inp = lambda: sys.stdin.readline().rstrip("\r\n")
# ===============================================================================================
### START ITERATE RECURSION ###
from types import GeneratorType
def iterative(f, stack=[]):
def wrapped_func(*args, **kwargs):
if stack: return f(*args, **kwargs)
to = f(*args, **kwargs)
while True:
if type(to) is GeneratorType:
stack.append(to)
to = next(to)
continue
stack.pop()
if not stack: break
to = stack[-1].send(to)
return to
return wrapped_func
#### END ITERATE RECURSION ####
# ===============================================================================================
# some shortcuts
mod = 1000000007
def inp(): return sys.stdin.readline().rstrip("\r\n") # for fast input
def out(var): sys.stdout.write(str(var)) # for fast output, always take string
def lis(): return list(map(int, inp().split()))
def stringlis(): return list(map(str, inp().split()))
def sep(): return map(int, inp().split())
def strsep(): return map(str, inp().split())
def fsep(): return map(float, inp().split())
def nextline(): out("\n") # as stdout.write always print sring.
def testcase(t):
for p in range(t):
solve()
def pow(x, y, p):
res = 1 # Initialize result
x = x % p # Update x if it is more , than or equal to p
if (x == 0):
return 0
while (y > 0):
if ((y & 1) == 1): # If y is odd, multiply, x with result
res = (res * x) % p
y = y >> 1 # y = y/2
x = (x * x) % p
return res
from functools import reduce
def factors(n):
return set(reduce(list.__add__,
([i, n // i] for i in range(1, int(n ** 0.5) + 1) if n % i == 0)))
def lcm(a, b):
return abs((a // gcd(a, b)) * b)
def gcd(a, b):
if a == b: return a
while b > 0: a, b = b, a % b
return a
# discrete binary search
# minimise:
# def search():
# l = 0
# r = 10 ** 15
#
# for i in range(200):
# if isvalid(l):
# return l
# if l == r:
# return l
# m = (l + r) // 2
# if isvalid(m) and not isvalid(m - 1):
# return m
# if isvalid(m):
# r = m + 1
# else:
# l = m
# return m
# maximise:
# def search():
# l = 0
# r = 10 ** 15
#
# for i in range(200):
# # print(l,r)
# if isvalid(r):
# return r
# if l == r:
# return l
# m = (l + r) // 2
# if isvalid(m) and not isvalid(m + 1):
# return m
# if isvalid(m):
# l = m
# else:
# r = m - 1
# return m
##to find factorial and ncr
# N=100000
# mod = 10**9 + 7
# fac = [1, 1]
# finv = [1, 1]
# inv = [0, 1]
#
# for i in range(2, N + 1):
# fac.append((fac[-1] * i) % mod)
# inv.append(mod - (inv[mod % i] * (mod // i) % mod))
# finv.append(finv[-1] * inv[-1] % mod)
def comb(n, r):
if n < r:
return 0
else:
return fac[n] * (finv[r] * finv[n - r] % mod) % mod
##############Find sum of product of subsets of size k in a array
# ar=[0,1,2,3]
# k=3
# n=len(ar)-1
# dp=[0]*(n+1)
# dp[0]=1
# for pos in range(1,n+1):
# dp[pos]=0
# l=max(1,k+pos-n-1)
# for j in range(min(pos,k),l-1,-1):
# dp[j]=dp[j]+ar[pos]*dp[j-1]
# print(dp[k])
def prefix_sum(ar): # [1,2,3,4]->[1,3,6,10]
return list(accumulate(ar))
def suffix_sum(ar): # [1,2,3,4]->[10,9,7,4]
return list(accumulate(ar[::-1]))[::-1]
def N():
return int(inp())
# =========================================================================================
from collections import defaultdict
def numberOfSetBits(i):
i = i - ((i >> 1) & 0x55555555)
i = (i & 0x33333333) + ((i >> 2) & 0x33333333)
return (((i + (i >> 4) & 0xF0F0F0F) * 0x1010101) & 0xffffffff) >> 24
def yes():
print("Yes")
def no():
print("No")
def YES():
print("YES")
def NO():
print("NO")
# from random import randint
rng=range
def solve():
n,m,k=sep()
ar=[]
for _ in rng(n):
ar.append(lis())
total=n+m-2
first=total//2
second=total-first
d1=defaultdict(int)
def isvalid(i,j):
if 0<=i<n and 0<=j<m:
return 1
return 0
for mask in rng(1<<first):
curry=0
currx=0
currxor=ar[0][0]
f = 1
for i in range(first):
if mask&(1<<i):
if not isvalid(currx+1,curry):
f = -1
break
currx+=1
currxor^=ar[currx][curry]
else:
if not isvalid(currx,curry+1):
f = -1
break
curry+=1
currxor^=ar[currx][curry]
# print((currx,curry,currxor,mask))
if f==1:
d1[(currx,curry,currxor)]+=1
ans = 0
for mask in rng(1<<second):
curry=m-1
currx=n-1
currxor=ar[n-1][m-1]
f=1
for i in range(second):
if mask&(1<<i):
if not isvalid(currx-1,curry):
f=-1
break
currx-=1
currxor^=ar[currx][curry]
else:
if not isvalid(currx,curry-1):
f=-1
break
curry-=1
currxor^=ar[currx][curry]
# print((currx, curry, currxor, mask))
if f==1:
ans+=d1[(currx,curry,currxor^k^ar[currx][curry])]
print(ans)
solve()
#testcase(int(inp()))
``` | output | 1 | 34,244 | 15 | 68,489 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a rectangular grid of size n Γ m. Each cell has a number written on it; the number on the cell (i, j) is a_{i, j}. Your task is to calculate the number of paths from the upper-left cell (1, 1) to the bottom-right cell (n, m) meeting the following constraints:
* You can move to the right or to the bottom only. Formally, from the cell (i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j). The target cell can't be outside of the grid.
* The xor of all the numbers on the path from the cell (1, 1) to the cell (n, m) must be equal to k (xor operation is the bitwise exclusive OR, it is represented as '^' in Java or C++ and "xor" in Pascal).
Find the number of such paths in the given grid.
Input
The first line of the input contains three integers n, m and k (1 β€ n, m β€ 20, 0 β€ k β€ 10^{18}) β the height and the width of the grid, and the number k.
The next n lines contain m integers each, the j-th element in the i-th line is a_{i, j} (0 β€ a_{i, j} β€ 10^{18}).
Output
Print one integer β the number of paths from (1, 1) to (n, m) with xor sum equal to k.
Examples
Input
3 3 11
2 1 5
7 10 0
12 6 4
Output
3
Input
3 4 2
1 3 3 3
0 3 3 2
3 0 1 1
Output
5
Input
3 4 1000000000000000000
1 3 3 3
0 3 3 2
3 0 1 1
Output
0
Note
All the paths from the first example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (3, 3);
* (1, 1) β (1, 2) β (2, 2) β (3, 2) β (3, 3).
All the paths from the second example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (2, 4) β (3, 4);
* (1, 1) β (1, 2) β (2, 2) β (2, 3) β (3, 3) β (3, 4);
* (1, 1) β (1, 2) β (1, 3) β (2, 3) β (3, 3) β (3, 4). | instruction | 0 | 34,245 | 15 | 68,490 |
Tags: bitmasks, brute force, dp, meet-in-the-middle
Correct Solution:
```
from collections import defaultdict
n, m, k = map(int, input().split())
a = [[0 for j in range(m)] for i in range(n)]
for i in range(n):
a[i] = list(map(int, input().split()))
total = n + m - 2
half = total // 2
b = defaultdict(dict)
def upper(i, j, val, cnt):
val ^= a[i][j]
if cnt == half:
s = str(i) + ' ' + str(j)
if val in b[s]:
b[s][val] += 1
else:
b[s][val] = 1
return
if i + 1 < n:
upper(i + 1, j, val, cnt + 1)
if j + 1 < m:
upper(i, j + 1, val, cnt + 1)
answer = 0
def lower(i, j, val, cnt):
global answer
s = str(i) + ' ' + str(j)
if cnt == total - half:
aim = k ^ val
if aim in b[s]:
answer += b[s][aim]
return
if i > 0:
lower(i - 1, j, val ^ a[i][j], cnt + 1)
if j > 0:
lower(i, j - 1, val ^ a[i][j], cnt + 1)
upper(0, 0, 0, 0)
lower(n - 1, m - 1, 0, 0)
print(answer)
``` | output | 1 | 34,245 | 15 | 68,491 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a rectangular grid of size n Γ m. Each cell has a number written on it; the number on the cell (i, j) is a_{i, j}. Your task is to calculate the number of paths from the upper-left cell (1, 1) to the bottom-right cell (n, m) meeting the following constraints:
* You can move to the right or to the bottom only. Formally, from the cell (i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j). The target cell can't be outside of the grid.
* The xor of all the numbers on the path from the cell (1, 1) to the cell (n, m) must be equal to k (xor operation is the bitwise exclusive OR, it is represented as '^' in Java or C++ and "xor" in Pascal).
Find the number of such paths in the given grid.
Input
The first line of the input contains three integers n, m and k (1 β€ n, m β€ 20, 0 β€ k β€ 10^{18}) β the height and the width of the grid, and the number k.
The next n lines contain m integers each, the j-th element in the i-th line is a_{i, j} (0 β€ a_{i, j} β€ 10^{18}).
Output
Print one integer β the number of paths from (1, 1) to (n, m) with xor sum equal to k.
Examples
Input
3 3 11
2 1 5
7 10 0
12 6 4
Output
3
Input
3 4 2
1 3 3 3
0 3 3 2
3 0 1 1
Output
5
Input
3 4 1000000000000000000
1 3 3 3
0 3 3 2
3 0 1 1
Output
0
Note
All the paths from the first example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (3, 3);
* (1, 1) β (1, 2) β (2, 2) β (3, 2) β (3, 3).
All the paths from the second example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (2, 4) β (3, 4);
* (1, 1) β (1, 2) β (2, 2) β (2, 3) β (3, 3) β (3, 4);
* (1, 1) β (1, 2) β (1, 3) β (2, 3) β (3, 3) β (3, 4). | instruction | 0 | 34,246 | 15 | 68,492 |
Tags: bitmasks, brute force, dp, meet-in-the-middle
Correct Solution:
```
from collections import*
n, m, k = map(int, input().split())
b = [[int(v) for v in input().split()] for _ in range(n)]
if m < n:
a = [[b[j][i] for j in range(n)] for i in range(m)]
b = a
m, n = n, m
cntrs = [Counter() for _ in range(n)]
d = (n + m-1) // 2
for i in range(1<<d):
ones = bin(i).count('1')
z = d - ones
if ones >= n or z >= m: continue
xor = b[0][0]
x, y = 0, 0
for j in range(d):
if i&(1<<j):
x += 1
else:
y += 1
xor ^= b[x][y]
cntrs[x][xor] += 1
sm = 0
sleft = n + m - 2 - d
for i in range(1<<sleft):
ones = bin(i).count('1')
z = sleft - ones
if ones >= n or z >= m: continue
xor = b[n-1][m-1]
x, y = n-1, m-1
for j in range(sleft):
if i&(1<<j):
x -= 1
else:
y -= 1
xor ^= b[x][y]
xor ^= b[x][y] ^ k
sm += cntrs[x][xor]
print(sm)
``` | output | 1 | 34,246 | 15 | 68,493 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a rectangular grid of size n Γ m. Each cell has a number written on it; the number on the cell (i, j) is a_{i, j}. Your task is to calculate the number of paths from the upper-left cell (1, 1) to the bottom-right cell (n, m) meeting the following constraints:
* You can move to the right or to the bottom only. Formally, from the cell (i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j). The target cell can't be outside of the grid.
* The xor of all the numbers on the path from the cell (1, 1) to the cell (n, m) must be equal to k (xor operation is the bitwise exclusive OR, it is represented as '^' in Java or C++ and "xor" in Pascal).
Find the number of such paths in the given grid.
Input
The first line of the input contains three integers n, m and k (1 β€ n, m β€ 20, 0 β€ k β€ 10^{18}) β the height and the width of the grid, and the number k.
The next n lines contain m integers each, the j-th element in the i-th line is a_{i, j} (0 β€ a_{i, j} β€ 10^{18}).
Output
Print one integer β the number of paths from (1, 1) to (n, m) with xor sum equal to k.
Examples
Input
3 3 11
2 1 5
7 10 0
12 6 4
Output
3
Input
3 4 2
1 3 3 3
0 3 3 2
3 0 1 1
Output
5
Input
3 4 1000000000000000000
1 3 3 3
0 3 3 2
3 0 1 1
Output
0
Note
All the paths from the first example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (3, 3);
* (1, 1) β (1, 2) β (2, 2) β (3, 2) β (3, 3).
All the paths from the second example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (2, 4) β (3, 4);
* (1, 1) β (1, 2) β (2, 2) β (2, 3) β (3, 3) β (3, 4);
* (1, 1) β (1, 2) β (1, 3) β (2, 3) β (3, 3) β (3, 4). | instruction | 0 | 34,247 | 15 | 68,494 |
Tags: bitmasks, brute force, dp, meet-in-the-middle
Correct Solution:
```
from collections import defaultdict
import itertools
import sys
input = sys.stdin.readline
n, m, k = map(int, input().split())
a = [list(map(int, input().split())) for _ in range(n)]
l = n + m - 2
l0 = l // 2
l1 = (l + 1) // 2
p = [i for i in range(l0)]
xx = defaultdict(lambda : defaultdict(lambda : 0))
for i in range(l0 + 1):
ok = 1
for p0 in itertools.combinations(p, i):
s = set(p0)
now = 0
x, y = 0, 0
for j in range(l0):
now ^= a[x][y]
if j in s:
x += 1
else:
y += 1
if not 0 <= x < n or not 0 <= y < m:
ok = 0
break
if not ok:
break
now ^= a[x][y]
xx[(x, y)][now] += 1
p = [i for i in range(l1)]
ans = 0
for i in range(l1 + 1):
ok = 1
for p0 in itertools.combinations(p, i):
s = set(p0)
now = 0
x, y = n - 1, m - 1
for j in range(l1):
now ^= a[x][y]
if j in s:
x -= 1
else:
y -= 1
if not 0 <= x < n or not 0 <= y < m:
ok = 0
break
if not ok:
break
ans += xx[(x, y)][now ^ k]
print(ans)
``` | output | 1 | 34,247 | 15 | 68,495 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a rectangular grid of size n Γ m. Each cell has a number written on it; the number on the cell (i, j) is a_{i, j}. Your task is to calculate the number of paths from the upper-left cell (1, 1) to the bottom-right cell (n, m) meeting the following constraints:
* You can move to the right or to the bottom only. Formally, from the cell (i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j). The target cell can't be outside of the grid.
* The xor of all the numbers on the path from the cell (1, 1) to the cell (n, m) must be equal to k (xor operation is the bitwise exclusive OR, it is represented as '^' in Java or C++ and "xor" in Pascal).
Find the number of such paths in the given grid.
Input
The first line of the input contains three integers n, m and k (1 β€ n, m β€ 20, 0 β€ k β€ 10^{18}) β the height and the width of the grid, and the number k.
The next n lines contain m integers each, the j-th element in the i-th line is a_{i, j} (0 β€ a_{i, j} β€ 10^{18}).
Output
Print one integer β the number of paths from (1, 1) to (n, m) with xor sum equal to k.
Examples
Input
3 3 11
2 1 5
7 10 0
12 6 4
Output
3
Input
3 4 2
1 3 3 3
0 3 3 2
3 0 1 1
Output
5
Input
3 4 1000000000000000000
1 3 3 3
0 3 3 2
3 0 1 1
Output
0
Note
All the paths from the first example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (3, 3);
* (1, 1) β (1, 2) β (2, 2) β (3, 2) β (3, 3).
All the paths from the second example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (2, 4) β (3, 4);
* (1, 1) β (1, 2) β (2, 2) β (2, 3) β (3, 3) β (3, 4);
* (1, 1) β (1, 2) β (1, 3) β (2, 3) β (3, 3) β (3, 4). | instruction | 0 | 34,248 | 15 | 68,496 |
Tags: bitmasks, brute force, dp, meet-in-the-middle
Correct Solution:
```
d = {}
for i in range(22):
d[i] = {}
#print(cnt)
n,m,k = list(map(int, input().split()))
arr = [list(map(int, input().split())) for i in range(n)]
def check(x,y):
if x < 0 or x >= n or y < 0 or y >= m:
return False
else:
return True
def go(x,y,now):
if check(x,y) == False:
return
now ^= arr[x][y]
if x + y == m - 1:
#print('yes')
if now in d[x]:
d[x][now] += 1
else:
d[x][now] = 1
return
go(x+1,y,now)
go(x,y+1,now)
ans = 0
def goRev(x,y,now):
if check(x,y) == False:
return
if x + y == m - 1:
cur = k ^ now
if cur in d[x]:
global ans
#print(ans)
ans += d[x][cur]
return
now ^= arr[x][y]
goRev(x-1,y,now)
goRev(x,y-1,now)
go(0,0,0)
goRev(n-1,m-1,0)
print(ans)
``` | output | 1 | 34,248 | 15 | 68,497 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a rectangular grid of size n Γ m. Each cell has a number written on it; the number on the cell (i, j) is a_{i, j}. Your task is to calculate the number of paths from the upper-left cell (1, 1) to the bottom-right cell (n, m) meeting the following constraints:
* You can move to the right or to the bottom only. Formally, from the cell (i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j). The target cell can't be outside of the grid.
* The xor of all the numbers on the path from the cell (1, 1) to the cell (n, m) must be equal to k (xor operation is the bitwise exclusive OR, it is represented as '^' in Java or C++ and "xor" in Pascal).
Find the number of such paths in the given grid.
Input
The first line of the input contains three integers n, m and k (1 β€ n, m β€ 20, 0 β€ k β€ 10^{18}) β the height and the width of the grid, and the number k.
The next n lines contain m integers each, the j-th element in the i-th line is a_{i, j} (0 β€ a_{i, j} β€ 10^{18}).
Output
Print one integer β the number of paths from (1, 1) to (n, m) with xor sum equal to k.
Examples
Input
3 3 11
2 1 5
7 10 0
12 6 4
Output
3
Input
3 4 2
1 3 3 3
0 3 3 2
3 0 1 1
Output
5
Input
3 4 1000000000000000000
1 3 3 3
0 3 3 2
3 0 1 1
Output
0
Note
All the paths from the first example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (3, 3);
* (1, 1) β (1, 2) β (2, 2) β (3, 2) β (3, 3).
All the paths from the second example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (2, 4) β (3, 4);
* (1, 1) β (1, 2) β (2, 2) β (2, 3) β (3, 3) β (3, 4);
* (1, 1) β (1, 2) β (1, 3) β (2, 3) β (3, 3) β (3, 4).
Submitted Solution:
```
def go_up_to_down(w, h, value, steps):
value ^= matrix[h][w]
if steps == half_steps:
if value not in counts[h][w]:
counts[h][w][value] = 0
counts[h][w][value] += 1
return
if w < width - 1:
go_up_to_down(w + 1, h, value, steps + 1)
if h < height - 1:
go_up_to_down(w, h + 1, value, steps + 1)
def go_down_to_up(w, h, value, steps, count_ways):
if steps == width + height - 2 - half_steps:
if (value ^ res_find) in counts[h][w]:
count_ways += counts[h][w][value ^ res_find]
return count_ways
delta = 0
if w > 0:
delta += go_down_to_up(w - 1, h, value ^ matrix[h][w], steps + 1, count_ways)
if h > 0:
delta += go_down_to_up(w, h - 1, value ^ matrix[h][w], steps + 1, count_ways)
return count_ways + delta
height, width, res_find = [int(num) for num in input().split()]
matrix = []
for h in range(height):
row = [int(num) for num in input().split()]
matrix.append(row)
counts = [[dict()] * width for h in range(height)]
half_steps = (width + height - 2) // 2
go_up_to_down(0, 0, 0, 0)
count_ways = go_down_to_up(width - 1, height - 1, 0, 0, 0)
print(count_ways)
``` | instruction | 0 | 34,249 | 15 | 68,498 |
Yes | output | 1 | 34,249 | 15 | 68,499 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a rectangular grid of size n Γ m. Each cell has a number written on it; the number on the cell (i, j) is a_{i, j}. Your task is to calculate the number of paths from the upper-left cell (1, 1) to the bottom-right cell (n, m) meeting the following constraints:
* You can move to the right or to the bottom only. Formally, from the cell (i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j). The target cell can't be outside of the grid.
* The xor of all the numbers on the path from the cell (1, 1) to the cell (n, m) must be equal to k (xor operation is the bitwise exclusive OR, it is represented as '^' in Java or C++ and "xor" in Pascal).
Find the number of such paths in the given grid.
Input
The first line of the input contains three integers n, m and k (1 β€ n, m β€ 20, 0 β€ k β€ 10^{18}) β the height and the width of the grid, and the number k.
The next n lines contain m integers each, the j-th element in the i-th line is a_{i, j} (0 β€ a_{i, j} β€ 10^{18}).
Output
Print one integer β the number of paths from (1, 1) to (n, m) with xor sum equal to k.
Examples
Input
3 3 11
2 1 5
7 10 0
12 6 4
Output
3
Input
3 4 2
1 3 3 3
0 3 3 2
3 0 1 1
Output
5
Input
3 4 1000000000000000000
1 3 3 3
0 3 3 2
3 0 1 1
Output
0
Note
All the paths from the first example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (3, 3);
* (1, 1) β (1, 2) β (2, 2) β (3, 2) β (3, 3).
All the paths from the second example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (2, 4) β (3, 4);
* (1, 1) β (1, 2) β (2, 2) β (2, 3) β (3, 3) β (3, 4);
* (1, 1) β (1, 2) β (1, 3) β (2, 3) β (3, 3) β (3, 4).
Submitted Solution:
```
d = {}
for i in range(22):
d[i] = {}
n,m,k = list(map(int, input().split()))
l = [list(map(int, input().split())) for i in range(n)]
def check(x,y):
if x < 0 or x >= n or y < 0 or y >= m:
return False
else:
return True
def go(x,y,now):
if check(x,y) == False:
return
now ^= l[x][y]
if x + y == m - 1:
#print('yes')
if now in d[x]:
d[x][now] += 1
else:
d[x][now] = 1
return
go(x+1,y,now)
go(x,y+1,now)
re = 0
def goRev(i,j,now):
if check(i,j) == False:
return
if i + j == m - 1:
cur = k ^ now
if cur in d[i]:
global re
#print(ans)
re += d[i][cur]
return
now ^= l[i][j]
goRev(i-1,j,now)
goRev(i,j-1,now)
go(0, 0, 0)
goRev(n-1, m-1, 0)
#print(d)
print(re)
``` | instruction | 0 | 34,250 | 15 | 68,500 |
Yes | output | 1 | 34,250 | 15 | 68,501 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a rectangular grid of size n Γ m. Each cell has a number written on it; the number on the cell (i, j) is a_{i, j}. Your task is to calculate the number of paths from the upper-left cell (1, 1) to the bottom-right cell (n, m) meeting the following constraints:
* You can move to the right or to the bottom only. Formally, from the cell (i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j). The target cell can't be outside of the grid.
* The xor of all the numbers on the path from the cell (1, 1) to the cell (n, m) must be equal to k (xor operation is the bitwise exclusive OR, it is represented as '^' in Java or C++ and "xor" in Pascal).
Find the number of such paths in the given grid.
Input
The first line of the input contains three integers n, m and k (1 β€ n, m β€ 20, 0 β€ k β€ 10^{18}) β the height and the width of the grid, and the number k.
The next n lines contain m integers each, the j-th element in the i-th line is a_{i, j} (0 β€ a_{i, j} β€ 10^{18}).
Output
Print one integer β the number of paths from (1, 1) to (n, m) with xor sum equal to k.
Examples
Input
3 3 11
2 1 5
7 10 0
12 6 4
Output
3
Input
3 4 2
1 3 3 3
0 3 3 2
3 0 1 1
Output
5
Input
3 4 1000000000000000000
1 3 3 3
0 3 3 2
3 0 1 1
Output
0
Note
All the paths from the first example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (3, 3);
* (1, 1) β (1, 2) β (2, 2) β (3, 2) β (3, 3).
All the paths from the second example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (2, 4) β (3, 4);
* (1, 1) β (1, 2) β (2, 2) β (2, 3) β (3, 3) β (3, 4);
* (1, 1) β (1, 2) β (1, 3) β (2, 3) β (3, 3) β (3, 4).
Submitted Solution:
```
from collections import defaultdict
n, m, aim = map(int, input().split())
g = [[0 for i in range(m + 1)] for j in range(n + 1)]
for i in range(n):
ls = [int(i) for i in input().split()]
for j in range(m):
g[i + 1][j + 1] = ls[j]
ans = 0
dp = defaultdict(int)
def search(x, y, is_l, mk):
if x < 1 or y < 1 or x > n or y > m:
return
if is_l:
mk ^= g[x][y]
if x + y - 1 == n:
dp[(x, y, mk)] += 1
else:
search(x + 1, y, is_l, mk)
search(x, y + 1, is_l, mk)
else:
if abs(x - n) + abs(y - m) + 1 == m:
# print(x, y, mk)
global ans
ans += dp[(x, y, mk)]
else:
mk ^= g[x][y]
search(x - 1, y, is_l, mk)
search(x, y - 1, is_l, mk)
search(1, 1, True, 0)
search(n, m, False, aim)
print(ans)
``` | instruction | 0 | 34,251 | 15 | 68,502 |
Yes | output | 1 | 34,251 | 15 | 68,503 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a rectangular grid of size n Γ m. Each cell has a number written on it; the number on the cell (i, j) is a_{i, j}. Your task is to calculate the number of paths from the upper-left cell (1, 1) to the bottom-right cell (n, m) meeting the following constraints:
* You can move to the right or to the bottom only. Formally, from the cell (i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j). The target cell can't be outside of the grid.
* The xor of all the numbers on the path from the cell (1, 1) to the cell (n, m) must be equal to k (xor operation is the bitwise exclusive OR, it is represented as '^' in Java or C++ and "xor" in Pascal).
Find the number of such paths in the given grid.
Input
The first line of the input contains three integers n, m and k (1 β€ n, m β€ 20, 0 β€ k β€ 10^{18}) β the height and the width of the grid, and the number k.
The next n lines contain m integers each, the j-th element in the i-th line is a_{i, j} (0 β€ a_{i, j} β€ 10^{18}).
Output
Print one integer β the number of paths from (1, 1) to (n, m) with xor sum equal to k.
Examples
Input
3 3 11
2 1 5
7 10 0
12 6 4
Output
3
Input
3 4 2
1 3 3 3
0 3 3 2
3 0 1 1
Output
5
Input
3 4 1000000000000000000
1 3 3 3
0 3 3 2
3 0 1 1
Output
0
Note
All the paths from the first example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (3, 3);
* (1, 1) β (1, 2) β (2, 2) β (3, 2) β (3, 3).
All the paths from the second example:
* (1, 1) β (2, 1) β (3, 1) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (3, 2) β (3, 3) β (3, 4);
* (1, 1) β (2, 1) β (2, 2) β (2, 3) β (2, 4) β (3, 4);
* (1, 1) β (1, 2) β (2, 2) β (2, 3) β (3, 3) β (3, 4);
* (1, 1) β (1, 2) β (1, 3) β (2, 3) β (3, 3) β (3, 4).
Submitted Solution:
```
d = {}
ans = 0
for i in range(22):
d[i] = {}
#print(cnt)
n,m,k = list(map(int, input().split()))
arr = [list(map(int, input().split())) for i in range(n)]
def check(x,y):
if x < 0 or x >= n or y < 0 or y >= m:
return False
else:
return True
def go(x,y,now):
if check(x,y) == False:
return
now ^= arr[x][y]
if x + y == m - 1:
#print('yes')
if now in d[x]:
d[x][now] += 1
else:
d[x][now] = 1
return
go(x+1,y,now)
go(x,y+1,now)
def goRev111(x,y,now):
if check(x,y) == False:
return
if x + y == m - 1:
cur = k ^ now
if cur in d[x]:
global ans
#print(ans)
ans += d[x][cur]
return
now ^= arr[x][y]
goRev111(x-1,y,now)
goRev111(x,y-1,now)
go(0,0,0)
goRev111(n-1,m-1,0)
print(ans)
``` | instruction | 0 | 34,252 | 15 | 68,504 |
Yes | output | 1 | 34,252 | 15 | 68,505 |
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