message stringlengths 2 67k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 463 109k | cluster float64 19 19 | __index_level_0__ int64 926 217k |
|---|---|---|---|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.
Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding n cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).
The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints.
A color hint goes like that: a player names some color and points at all the cards of this color.
Similarly goes the value hint. A player names some value and points at all the cards that contain the value.
Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.
Input
The first line contains integer n (1 ≤ n ≤ 100) — the number of Borya's cards. The next line contains the descriptions of n cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.
Output
Print a single integer — the minimum number of hints that the other players should make.
Examples
Input
2
G3 G3
Output
0
Input
4
G4 R4 R3 B3
Output
2
Input
5
B1 Y1 W1 G1 R1
Output
4
Note
In the first sample Borya already knows for each card that it is a green three.
In the second sample we can show all fours and all red cards.
In the third sample you need to make hints about any four colors. | instruction | 0 | 33,740 | 19 | 67,480 |
Tags: bitmasks, brute force, implementation
Correct Solution:
```
from itertools import chain, combinations
from copy import deepcopy
def powerset(iterable):
s = list(iterable)
return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))
n = int(input())
locations = input().split()
matrixG = [[0]*5 for i in range(5)]
for i in locations:
if i[0] == "R":
matrixG[0][int(i[1])-1] += 1
elif i[0] == "G":
matrixG[1][int(i[1])-1] += 1
elif i[0] == "B":
matrixG[2][int(i[1])-1] += 1
elif i[0] == "Y":
matrixG[3][int(i[1])-1] += 1
elif i[0] == "W":
matrixG[4][int(i[1])-1] += 1
for i in list(powerset(range(10))):
matrix = deepcopy(matrixG)
color = []
value = []
for j in i:
if j <= 4:
color.append(j)
else:
value.append(j)
for v in value:
for c in color:
matrix[c][v-5] = 0
ctr = 0
for r in range(5):
if matrix[r][v-5] == 0:
ctr += 1
if ctr == 4:
for r in range(5):
matrix[r][v-5] = 0
for c in color:
if matrix[c].count(0) == 4:
matrix[c] = [0]*5
ctr = 0
for k in range(5):
for j in range(5):
if matrix[k][j] == 0:
ctr += 1
if ctr == 24:
print(len(i))
break
``` | output | 1 | 33,740 | 19 | 67,481 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.
Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding n cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).
The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints.
A color hint goes like that: a player names some color and points at all the cards of this color.
Similarly goes the value hint. A player names some value and points at all the cards that contain the value.
Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.
Input
The first line contains integer n (1 ≤ n ≤ 100) — the number of Borya's cards. The next line contains the descriptions of n cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.
Output
Print a single integer — the minimum number of hints that the other players should make.
Examples
Input
2
G3 G3
Output
0
Input
4
G4 R4 R3 B3
Output
2
Input
5
B1 Y1 W1 G1 R1
Output
4
Note
In the first sample Borya already knows for each card that it is a green three.
In the second sample we can show all fours and all red cards.
In the third sample you need to make hints about any four colors. | instruction | 0 | 33,741 | 19 | 67,482 |
Tags: bitmasks, brute force, implementation
Correct Solution:
```
import itertools
input()
cards = tuple(set(str.split(input())))
n = len(cards)
if n == 1:
print(0)
exit()
symbols = "RGBYW12345"
for l in range(1, 10):
for comb in itertools.combinations(symbols, l):
positions = [cards] * n
for symbol in comb:
for i in range(n):
if symbol in cards[i]:
positions[i] = tuple(filter(lambda c: symbol in c, positions[i]))
else:
positions[i] = tuple(filter(lambda c: symbol not in c, positions[i]))
if sum(map(len, positions)) == n:
print(l)
exit()
``` | output | 1 | 33,741 | 19 | 67,483 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.
Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding n cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).
The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints.
A color hint goes like that: a player names some color and points at all the cards of this color.
Similarly goes the value hint. A player names some value and points at all the cards that contain the value.
Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.
Input
The first line contains integer n (1 ≤ n ≤ 100) — the number of Borya's cards. The next line contains the descriptions of n cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.
Output
Print a single integer — the minimum number of hints that the other players should make.
Examples
Input
2
G3 G3
Output
0
Input
4
G4 R4 R3 B3
Output
2
Input
5
B1 Y1 W1 G1 R1
Output
4
Note
In the first sample Borya already knows for each card that it is a green three.
In the second sample we can show all fours and all red cards.
In the third sample you need to make hints about any four colors. | instruction | 0 | 33,742 | 19 | 67,484 |
Tags: bitmasks, brute force, implementation
Correct Solution:
```
from collections import Counter
n = int(input())
pcards = set(input().split())
qs = 'RGBYW12345'
best = 10
for mask in range(1024):
cnt = 0
tmp = mask
while tmp:
tmp &= tmp - 1
cnt += 1
knows = [qs[i] for i in range(10) if ((mask >> i) & 1)]
cards = [c for c in pcards if ((not c[0] in knows) or (not c[1] in knows))]
if not cards:
best = min(best, cnt)
continue
for q in knows:
cou = sum(1 for c in cards if q in c)
if cou > 1:
cnt = 100500
break
coun = sum(1 for c in cards if not c[0] in knows and not c[1] in knows)
if coun > 1:
cnt = 100500
best = min(best, cnt)
print(best)
``` | output | 1 | 33,742 | 19 | 67,485 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.
Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding n cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).
The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints.
A color hint goes like that: a player names some color and points at all the cards of this color.
Similarly goes the value hint. A player names some value and points at all the cards that contain the value.
Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.
Input
The first line contains integer n (1 ≤ n ≤ 100) — the number of Borya's cards. The next line contains the descriptions of n cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.
Output
Print a single integer — the minimum number of hints that the other players should make.
Examples
Input
2
G3 G3
Output
0
Input
4
G4 R4 R3 B3
Output
2
Input
5
B1 Y1 W1 G1 R1
Output
4
Note
In the first sample Borya already knows for each card that it is a green three.
In the second sample we can show all fours and all red cards.
In the third sample you need to make hints about any four colors. | instruction | 0 | 33,743 | 19 | 67,486 |
Tags: bitmasks, brute force, implementation
Correct Solution:
```
def check(hint, Card):
for i in Card :
for j in Card :
if i == j : continue
elif i[0] == j[0] :
if i[1] not in hint and j[1] not in hint :
return False
elif i[1] == j[1] :
if i[0] not in hint and j[0] not in hint :
return False
else :
if i[0] not in hint and i[1] not in hint and j[0] not in hint and j[1] not in hint :
return False
return True
HH = "RGBYW12345"
n = int(input())
Card = list(input().split(' '))
ans = 20
for i in range(1024):
hint = ""
cnt = 0
for j in range(10) :
if (2**j)&i > 0 :
hint += HH[j]
cnt+=1
if check(hint, Card) :
ans = min(ans, cnt)
print(ans)
``` | output | 1 | 33,743 | 19 | 67,487 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.
Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding n cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).
The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints.
A color hint goes like that: a player names some color and points at all the cards of this color.
Similarly goes the value hint. A player names some value and points at all the cards that contain the value.
Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.
Input
The first line contains integer n (1 ≤ n ≤ 100) — the number of Borya's cards. The next line contains the descriptions of n cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.
Output
Print a single integer — the minimum number of hints that the other players should make.
Examples
Input
2
G3 G3
Output
0
Input
4
G4 R4 R3 B3
Output
2
Input
5
B1 Y1 W1 G1 R1
Output
4
Note
In the first sample Borya already knows for each card that it is a green three.
In the second sample we can show all fours and all red cards.
In the third sample you need to make hints about any four colors.
Submitted Solution:
```
input()
colour = dict(zip('RGBYW', range(5)))
cards = {(colour[c], ord(v) - ord('1')) for c, v in input().split()}
print(min(bin(cs).count('1') + bin(vs).count('1')
for cs in range(1<<5) for vs in range(1<<5)
if len({
(c if (cs >> c) & 1 else -1, v if (vs >> v) & 1 else -1)
for c, v in cards
}) == len(cards)
))
``` | instruction | 0 | 33,744 | 19 | 67,488 |
Yes | output | 1 | 33,744 | 19 | 67,489 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.
Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding n cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).
The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints.
A color hint goes like that: a player names some color and points at all the cards of this color.
Similarly goes the value hint. A player names some value and points at all the cards that contain the value.
Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.
Input
The first line contains integer n (1 ≤ n ≤ 100) — the number of Borya's cards. The next line contains the descriptions of n cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.
Output
Print a single integer — the minimum number of hints that the other players should make.
Examples
Input
2
G3 G3
Output
0
Input
4
G4 R4 R3 B3
Output
2
Input
5
B1 Y1 W1 G1 R1
Output
4
Note
In the first sample Borya already knows for each card that it is a green three.
In the second sample we can show all fours and all red cards.
In the third sample you need to make hints about any four colors.
Submitted Solution:
```
n = int(input())
colour = dict(zip('RGBYW', range(5, 10)))
cards = list({2 ** colour[c] + 2 ** (ord(v) - ord('1')) for c, v in input().split()})
ans = 10
n = len(cards)
if n > 1:
for bit in range(2 ** 10):
ok = True
for i in range(n - 1):
for j in range(i + 1, n):
if cards[i] & cards[j] == 0:
if (cards[i] | cards[j]) & bit == 0:
ok = False
break
elif cards[i] != cards[j]:
if (cards[i] ^ cards[j]) & bit == 0:
ok = False
break
if not ok:
break
if ok:
ans = min(bin(bit).count('1'), ans)
print(ans)
else:
print(0)
``` | instruction | 0 | 33,745 | 19 | 67,490 |
Yes | output | 1 | 33,745 | 19 | 67,491 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.
Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding n cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).
The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints.
A color hint goes like that: a player names some color and points at all the cards of this color.
Similarly goes the value hint. A player names some value and points at all the cards that contain the value.
Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.
Input
The first line contains integer n (1 ≤ n ≤ 100) — the number of Borya's cards. The next line contains the descriptions of n cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.
Output
Print a single integer — the minimum number of hints that the other players should make.
Examples
Input
2
G3 G3
Output
0
Input
4
G4 R4 R3 B3
Output
2
Input
5
B1 Y1 W1 G1 R1
Output
4
Note
In the first sample Borya already knows for each card that it is a green three.
In the second sample we can show all fours and all red cards.
In the third sample you need to make hints about any four colors.
Submitted Solution:
```
n = int(input())
data = set(input().split())
cards = []
lets = 'RGBYW'
ans = 10
for i in data:
p1 = lets.find(i[0])
p2 = int(i[1]) - 1
cards.append(2 ** p1 + 2 ** (p2 + 5))
for i in range(1024):
good = True
for j in range(len(cards) - 1):
for k in range(j + 1, len(cards)):
if (cards[j] & i) == (cards[k] & i):
good = False
if good:
ones = 0
now = i
while now != 0:
ones += now % 2
now //= 2
ans = min(ans, ones)
print(ans)
``` | instruction | 0 | 33,746 | 19 | 67,492 |
Yes | output | 1 | 33,746 | 19 | 67,493 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.
Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding n cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).
The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints.
A color hint goes like that: a player names some color and points at all the cards of this color.
Similarly goes the value hint. A player names some value and points at all the cards that contain the value.
Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.
Input
The first line contains integer n (1 ≤ n ≤ 100) — the number of Borya's cards. The next line contains the descriptions of n cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.
Output
Print a single integer — the minimum number of hints that the other players should make.
Examples
Input
2
G3 G3
Output
0
Input
4
G4 R4 R3 B3
Output
2
Input
5
B1 Y1 W1 G1 R1
Output
4
Note
In the first sample Borya already knows for each card that it is a green three.
In the second sample we can show all fours and all red cards.
In the third sample you need to make hints about any four colors.
Submitted Solution:
```
def Checker(hint,card):
for a in card:
for b in card:
if a == b:
continue
elif a[0] == b[0]:
if a[1] not in hint and b[1] not in hint:
return False
elif a[1] == b[1]:
if a[0] not in hint and b[0] not in hint:
return False
elif a[0] not in hint and a[1] not in hint and b[0] not in hint and b[1] not in hint:
return False
return True
user_input=int(input())
user_input = input()
Card=user_input.split(' ')
possible_chars="RGBYW12345"
final_answer=10
card_set=set(Card)
if len(card_set)==1:
print ("0")
else:
for i in range(1024):
hint=""
counter=0
for j in range(9,-1,-1):
if (i-(2**j))>0:
hint+=possible_chars[j]
i-=2**j
counter+=1
if Checker(hint,card_set):
final_answer=min(final_answer,counter)
print (final_answer)
``` | instruction | 0 | 33,747 | 19 | 67,494 |
Yes | output | 1 | 33,747 | 19 | 67,495 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.
Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding n cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).
The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints.
A color hint goes like that: a player names some color and points at all the cards of this color.
Similarly goes the value hint. A player names some value and points at all the cards that contain the value.
Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.
Input
The first line contains integer n (1 ≤ n ≤ 100) — the number of Borya's cards. The next line contains the descriptions of n cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.
Output
Print a single integer — the minimum number of hints that the other players should make.
Examples
Input
2
G3 G3
Output
0
Input
4
G4 R4 R3 B3
Output
2
Input
5
B1 Y1 W1 G1 R1
Output
4
Note
In the first sample Borya already knows for each card that it is a green three.
In the second sample we can show all fours and all red cards.
In the third sample you need to make hints about any four colors.
Submitted Solution:
```
import itertools
input()
cards = tuple(set(str.split(input())))
n = len(cards)
if n == 1:
print(0)
exit()
symbols = "RGBYW12345"
for l in range(1, 10):
for comb in itertools.combinations(symbols, l):
positions = [cards] * n
for symbol in comb:
for i in range(n):
if symbol in cards[i]:
positions[i] = tuple(filter(lambda c: symbol in c, positions[i]))
else:
positions[i] = tuple(filter(lambda c: symbol not in c, positions[i]))
if sum(map(len, positions)) == n:
print(l, comb, positions)
exit()
``` | instruction | 0 | 33,748 | 19 | 67,496 |
No | output | 1 | 33,748 | 19 | 67,497 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.
Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding n cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).
The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints.
A color hint goes like that: a player names some color and points at all the cards of this color.
Similarly goes the value hint. A player names some value and points at all the cards that contain the value.
Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.
Input
The first line contains integer n (1 ≤ n ≤ 100) — the number of Borya's cards. The next line contains the descriptions of n cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.
Output
Print a single integer — the minimum number of hints that the other players should make.
Examples
Input
2
G3 G3
Output
0
Input
4
G4 R4 R3 B3
Output
2
Input
5
B1 Y1 W1 G1 R1
Output
4
Note
In the first sample Borya already knows for each card that it is a green three.
In the second sample we can show all fours and all red cards.
In the third sample you need to make hints about any four colors.
Submitted Solution:
```
A = {'R':0, 'G':1, 'B':2, 'Y':3, 'W':4}
def bit_m(s):
num = 1 << int(s[1])
symb = 1 << (A[s[0]] + 6)
return num | symb
n = int(input())
cards = list(set(input().split()))
res = [0 for i in range(len(cards))]
mask = [bit_m(cards[i]) for i in range(len(cards))]
def make_res(Q, cards):
for i in range(len(cards)):
if mask[i] & Q:
res[i] |= Q
def check():
for i in range(len(res)):
for j in range(i + 1, len(res)):
if res[i] == res[j]:
return 0
return 1
quest = [1 << i for i in range(10)]
cnt = 11
for i in range(0, 1023):
cnt_now = 0
res = [0 for i in range(len(cards))]
for j in range(10):
if (1 << j) & i != 0:
cnt_now += 1
make_res(quest[j], cards)
if check():
cnt = min(cnt, cnt_now)
print(cnt)
``` | instruction | 0 | 33,749 | 19 | 67,498 |
No | output | 1 | 33,749 | 19 | 67,499 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.
Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding n cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).
The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints.
A color hint goes like that: a player names some color and points at all the cards of this color.
Similarly goes the value hint. A player names some value and points at all the cards that contain the value.
Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.
Input
The first line contains integer n (1 ≤ n ≤ 100) — the number of Borya's cards. The next line contains the descriptions of n cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.
Output
Print a single integer — the minimum number of hints that the other players should make.
Examples
Input
2
G3 G3
Output
0
Input
4
G4 R4 R3 B3
Output
2
Input
5
B1 Y1 W1 G1 R1
Output
4
Note
In the first sample Borya already knows for each card that it is a green three.
In the second sample we can show all fours and all red cards.
In the third sample you need to make hints about any four colors.
Submitted Solution:
```
n = int(input())
l = input().split()
assert len(l) == n
colors = "RGBYW"
l2 = [(colors.index(x[0]),int(x[1])-1) for x in l]
#print(l2)
def hamming5(x):
h = 0
for a in range(5):
if ((1<<a) & x) > 0: h += 1
return h
def valid(mask,pts):
miss = 0
for x in pts:
if ((1<<x) & mask) == 0:
miss += 1
return miss <= 1
def count(disc,l2,coord):
best = 4
curi = 15
for i in range(32):
if hamming5(i) >= best: continue
good = True
for a in range(5):
if ((1 << a) & disc) == 0: continue
b = set([x[coord] for x in l2 if x[1-coord] == a])
if not valid(i,b):
good = False
break
b = set([x[coord] for x in l2 if ((1<<x[1-coord])&disc)==0])
if not valid(i,b):
good = False
if good:
best = hamming5(i)
curi = i
return best, curi
tot = 8
for coord in range(2):
a,disc = count(15,l2,coord)
b,disc2 = count(disc,l2,1-coord)
cur = a+b
if cur < tot: tot = cur
#print(best)
print(tot)
``` | instruction | 0 | 33,750 | 19 | 67,500 |
No | output | 1 | 33,750 | 19 | 67,501 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.
Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding n cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).
The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints.
A color hint goes like that: a player names some color and points at all the cards of this color.
Similarly goes the value hint. A player names some value and points at all the cards that contain the value.
Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.
Input
The first line contains integer n (1 ≤ n ≤ 100) — the number of Borya's cards. The next line contains the descriptions of n cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.
Output
Print a single integer — the minimum number of hints that the other players should make.
Examples
Input
2
G3 G3
Output
0
Input
4
G4 R4 R3 B3
Output
2
Input
5
B1 Y1 W1 G1 R1
Output
4
Note
In the first sample Borya already knows for each card that it is a green three.
In the second sample we can show all fours and all red cards.
In the third sample you need to make hints about any four colors.
Submitted Solution:
```
import sys
def hint(cards, n):
s = set()
for t in cards:
s.add(str(t[0]))
s.add(int(t[1:]))
return len(s) - 2
if __name__ == '__main__':
n = int(sys.stdin.readline())
line = sys.stdin.readline().split()
cards = map(str, line)
print(hint(cards, n))
``` | instruction | 0 | 33,751 | 19 | 67,502 |
No | output | 1 | 33,751 | 19 | 67,503 |
Provide a correct Python 3 solution for this coding contest problem.
Yuta is addicted to the popular game "Beat Panel" at a nearby arcade. The game consists of a total of 16 panel-type buttons, 4x4, arranged in a grid as shown.
<image>
As shown in the figure, the buttons are arranged in the order of button 1, button 2,…, button 16 from the upper left to the lower right. In the game, you will hear a beat sound at regular intervals and a final sound at the end. Multiple buttons light up at the same time as the beat sounds. In some cases, even one does not shine. The player can press multiple buttons at the same time using the fingers of both hands from immediately after the beat sound to the next sound. It is also possible not to press anything. The game ends as soon as the end sound is heard.
Yuta has mastered c ways of pressing, and each time a beat sounds, he decides one of those pressing methods and presses the button. If the buttons you press are lit, those buttons will be lit and the number of buttons that have disappeared will be added to the player's score. Also, once a button is lit, the light will not go out until the button is pressed.
A program that outputs the maximum score that Yuta can obtain by inputting how to illuminate the button when the beat sound is played n times and how to press the button in c ways that Yuta has learned. Please create.
input
The input consists of multiple datasets. The end of the input is indicated by two lines of zeros. Each dataset is given in the following format.
n c
a1,1 a1,2 ... a1,16
a2,1 a2,2 ... a2,16
...
an, 1 an, 2 ... an, 16
b1,1 b1,2 ... b1,16
b2,1 b2,2 ... b2,16
...
bc,1 bc,2 ... bc,16
The first line consists of two integers separated by one space. n (1 ≤ n ≤ 30) indicates the number of beat sounds, and c (1 ≤ c ≤ 30) indicates the number of button presses that you have learned. The following n + c lines give how to illuminate the button and how to press the button. The input item in the line is separated by one blank. ak and i indicate how the button i shines when the kth beat sound is heard, and bj and i indicate whether the button i is pressed by pressing the jth button in the middle of c. As for the values of ak and i, 0 means "does not shine" and 1 means "shines". For the values of bj and i, 0 means "do not press" and 1 means "press".
The number of datasets does not exceed 20.
output
For each data set, the maximum score is output on one line.
Example
Input
2 2
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
2 2
0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0
0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0
0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0
0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0
5 3
0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1
0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
0 0
Output
8
7
16 | instruction | 0 | 34,178 | 19 | 68,356 |
"Correct Solution:
```
bitcount = [bin(i).count('1') for i in range(0x10000)]
def solve(a, b):
global bitcount
b = [65535 ^ bi for bi in b]
pdp = {a[0]:0}
ndp = {}
for ai in a[1:] + [0]:
for k, v in pdp.items():
v += bitcount[k]
for bi in b:
bi &= k
vb = v - bitcount[bi]
bi |= ai
try:
if ndp[bi] < vb:
ndp[bi] = vb
except KeyError:
ndp[bi] = vb
pdp, ndp = ndp, {}
return max(pdp.values())
import sys
f = sys.stdin
while True:
n, c = map(int, f.readline().split())
if n == c == 0:
break
a = [int(''.join(f.readline().split()), 2) for i in range(n)]
b = [int(''.join(f.readline().split()), 2) for i in range(c)]
print(solve(a, b))
``` | output | 1 | 34,178 | 19 | 68,357 |
Provide a correct Python 3 solution for this coding contest problem.
Yuta is addicted to the popular game "Beat Panel" at a nearby arcade. The game consists of a total of 16 panel-type buttons, 4x4, arranged in a grid as shown.
<image>
As shown in the figure, the buttons are arranged in the order of button 1, button 2,…, button 16 from the upper left to the lower right. In the game, you will hear a beat sound at regular intervals and a final sound at the end. Multiple buttons light up at the same time as the beat sounds. In some cases, even one does not shine. The player can press multiple buttons at the same time using the fingers of both hands from immediately after the beat sound to the next sound. It is also possible not to press anything. The game ends as soon as the end sound is heard.
Yuta has mastered c ways of pressing, and each time a beat sounds, he decides one of those pressing methods and presses the button. If the buttons you press are lit, those buttons will be lit and the number of buttons that have disappeared will be added to the player's score. Also, once a button is lit, the light will not go out until the button is pressed.
A program that outputs the maximum score that Yuta can obtain by inputting how to illuminate the button when the beat sound is played n times and how to press the button in c ways that Yuta has learned. Please create.
input
The input consists of multiple datasets. The end of the input is indicated by two lines of zeros. Each dataset is given in the following format.
n c
a1,1 a1,2 ... a1,16
a2,1 a2,2 ... a2,16
...
an, 1 an, 2 ... an, 16
b1,1 b1,2 ... b1,16
b2,1 b2,2 ... b2,16
...
bc,1 bc,2 ... bc,16
The first line consists of two integers separated by one space. n (1 ≤ n ≤ 30) indicates the number of beat sounds, and c (1 ≤ c ≤ 30) indicates the number of button presses that you have learned. The following n + c lines give how to illuminate the button and how to press the button. The input item in the line is separated by one blank. ak and i indicate how the button i shines when the kth beat sound is heard, and bj and i indicate whether the button i is pressed by pressing the jth button in the middle of c. As for the values of ak and i, 0 means "does not shine" and 1 means "shines". For the values of bj and i, 0 means "do not press" and 1 means "press".
The number of datasets does not exceed 20.
output
For each data set, the maximum score is output on one line.
Example
Input
2 2
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
2 2
0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0
0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0
0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0
0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0
5 3
0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1
0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
0 0
Output
8
7
16 | instruction | 0 | 34,179 | 19 | 68,358 |
"Correct Solution:
```
# using DP
# time complexity: O(n * (2^16) * c)
# 1 <= n <= 30, 1 <= c <= 30
# worst case: 30 * (2^16) * 30 = 58982400
bc = [bin(i).count('1') for i in range(65536)] # bitcount
def solve():
from sys import stdin
f_i = stdin
while True:
n, c = map(int, f_i.readline().split())
if n == 0:
break
A = [int(f_i.readline().replace(' ', ''), 2) for i in range(n)]
B = [int(f_i.readline().replace(' ', ''), 2) for i in range(c)]
dp1 = {A[0]: 0} # {state: score}
dp2 = {}
for a in A[1:] + [0]:
for st1, sc1 in dp1.items():
for b in B:
cb = st1 & b
sc2 = sc1 + bc[cb]
st2 = (st1 - cb) | a
try:
if dp2[st2] < sc2:
dp2[st2] = sc2
except KeyError:
dp2[st2] = sc2
dp1, dp2 = dp2, {}
print(max(dp1.values()))
solve()
``` | output | 1 | 34,179 | 19 | 68,359 |
Provide a correct Python 3 solution for this coding contest problem.
Yuta is addicted to the popular game "Beat Panel" at a nearby arcade. The game consists of a total of 16 panel-type buttons, 4x4, arranged in a grid as shown.
<image>
As shown in the figure, the buttons are arranged in the order of button 1, button 2,…, button 16 from the upper left to the lower right. In the game, you will hear a beat sound at regular intervals and a final sound at the end. Multiple buttons light up at the same time as the beat sounds. In some cases, even one does not shine. The player can press multiple buttons at the same time using the fingers of both hands from immediately after the beat sound to the next sound. It is also possible not to press anything. The game ends as soon as the end sound is heard.
Yuta has mastered c ways of pressing, and each time a beat sounds, he decides one of those pressing methods and presses the button. If the buttons you press are lit, those buttons will be lit and the number of buttons that have disappeared will be added to the player's score. Also, once a button is lit, the light will not go out until the button is pressed.
A program that outputs the maximum score that Yuta can obtain by inputting how to illuminate the button when the beat sound is played n times and how to press the button in c ways that Yuta has learned. Please create.
input
The input consists of multiple datasets. The end of the input is indicated by two lines of zeros. Each dataset is given in the following format.
n c
a1,1 a1,2 ... a1,16
a2,1 a2,2 ... a2,16
...
an, 1 an, 2 ... an, 16
b1,1 b1,2 ... b1,16
b2,1 b2,2 ... b2,16
...
bc,1 bc,2 ... bc,16
The first line consists of two integers separated by one space. n (1 ≤ n ≤ 30) indicates the number of beat sounds, and c (1 ≤ c ≤ 30) indicates the number of button presses that you have learned. The following n + c lines give how to illuminate the button and how to press the button. The input item in the line is separated by one blank. ak and i indicate how the button i shines when the kth beat sound is heard, and bj and i indicate whether the button i is pressed by pressing the jth button in the middle of c. As for the values of ak and i, 0 means "does not shine" and 1 means "shines". For the values of bj and i, 0 means "do not press" and 1 means "press".
The number of datasets does not exceed 20.
output
For each data set, the maximum score is output on one line.
Example
Input
2 2
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
2 2
0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0
0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0
0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0
0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0
5 3
0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1
0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
0 0
Output
8
7
16 | instruction | 0 | 34,180 | 19 | 68,360 |
"Correct Solution:
```
def main():
while True:
n, c = map(int, input().split())
if n == 0:break
music = []
for _ in range(n):
line = list(map(int, input().split()))
add_panel = sum([2 ** i * line[i] for i in range(16)])
music.append(add_panel)
hand = []
for _ in range(c):
line = list(map(int, input().split()))
erase_panel = sum([2 ** i * line[i] for i in range(16)])
hand.append(erase_panel)
masks = tuple([2 ** i for i in range(16)])
move = [{} for _ in range(2 ** 16)]
dp = [{} for _ in range(n + 1)]
dp[0][0] = 0
for turn in range(n):
add_panel = music[turn]
dp_next_turn = dp[turn + 1]
used = {}
for state, score in sorted(dp[turn].items(), key=lambda x:-x[1]):
new_state = add_panel | state
if new_state in used:continue
used[new_state] = True
move_new_state = move[new_state]
for erase_panel in hand:
if erase_panel in move_new_state:
erased_state, add_score = move_new_state[erase_panel]
else:
add_score = 0
temp = erase_panel & new_state
for mask in masks:
if mask > temp:break
if temp & mask:
add_score += 1
erased_state = new_state & ~erase_panel
move_new_state[erase_panel] = (erased_state, add_score)
new_score = score + add_score
if erased_state not in dp_next_turn or dp_next_turn[erased_state] < new_score:
dp_next_turn[erased_state] = new_score
print(max(dp[n].values()))
main()
``` | output | 1 | 34,180 | 19 | 68,361 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yuta is addicted to the popular game "Beat Panel" at a nearby arcade. The game consists of a total of 16 panel-type buttons, 4x4, arranged in a grid as shown.
<image>
As shown in the figure, the buttons are arranged in the order of button 1, button 2,…, button 16 from the upper left to the lower right. In the game, you will hear a beat sound at regular intervals and a final sound at the end. Multiple buttons light up at the same time as the beat sounds. In some cases, even one does not shine. The player can press multiple buttons at the same time using the fingers of both hands from immediately after the beat sound to the next sound. It is also possible not to press anything. The game ends as soon as the end sound is heard.
Yuta has mastered c ways of pressing, and each time a beat sounds, he decides one of those pressing methods and presses the button. If the buttons you press are lit, those buttons will be lit and the number of buttons that have disappeared will be added to the player's score. Also, once a button is lit, the light will not go out until the button is pressed.
A program that outputs the maximum score that Yuta can obtain by inputting how to illuminate the button when the beat sound is played n times and how to press the button in c ways that Yuta has learned. Please create.
input
The input consists of multiple datasets. The end of the input is indicated by two lines of zeros. Each dataset is given in the following format.
n c
a1,1 a1,2 ... a1,16
a2,1 a2,2 ... a2,16
...
an, 1 an, 2 ... an, 16
b1,1 b1,2 ... b1,16
b2,1 b2,2 ... b2,16
...
bc,1 bc,2 ... bc,16
The first line consists of two integers separated by one space. n (1 ≤ n ≤ 30) indicates the number of beat sounds, and c (1 ≤ c ≤ 30) indicates the number of button presses that you have learned. The following n + c lines give how to illuminate the button and how to press the button. The input item in the line is separated by one blank. ak and i indicate how the button i shines when the kth beat sound is heard, and bj and i indicate whether the button i is pressed by pressing the jth button in the middle of c. As for the values of ak and i, 0 means "does not shine" and 1 means "shines". For the values of bj and i, 0 means "do not press" and 1 means "press".
The number of datasets does not exceed 20.
output
For each data set, the maximum score is output on one line.
Example
Input
2 2
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
2 2
0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0
0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0
0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0
0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0
5 3
0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1
0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
0 0
Output
8
7
16
Submitted Solution:
```
while True:
n,c = map(int,input().split())
if n == c == 0:
break
as_ = [int(input().replace(' ',''),2) for _ in range(n)]
bs = [int(input().replace(' ',''),2) for _ in range(c)]
ps = {0 : 0}
for a in as_:
qs = ((p|a,x) for p,x in ps.items())
ps = {}
for q,x in qs:
for b in bs:
p = q&~b
y = x + bin(q).count('1') - bin(p).count('1')
if p not in ps or ps[p] < y:
ps[p] = y
print(max(ps.values()))
``` | instruction | 0 | 34,181 | 19 | 68,362 |
No | output | 1 | 34,181 | 19 | 68,363 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yuta is addicted to the popular game "Beat Panel" at a nearby arcade. The game consists of a total of 16 panel-type buttons, 4x4, arranged in a grid as shown.
<image>
As shown in the figure, the buttons are arranged in the order of button 1, button 2,…, button 16 from the upper left to the lower right. In the game, you will hear a beat sound at regular intervals and a final sound at the end. Multiple buttons light up at the same time as the beat sounds. In some cases, even one does not shine. The player can press multiple buttons at the same time using the fingers of both hands from immediately after the beat sound to the next sound. It is also possible not to press anything. The game ends as soon as the end sound is heard.
Yuta has mastered c ways of pressing, and each time a beat sounds, he decides one of those pressing methods and presses the button. If the buttons you press are lit, those buttons will be lit and the number of buttons that have disappeared will be added to the player's score. Also, once a button is lit, the light will not go out until the button is pressed.
A program that outputs the maximum score that Yuta can obtain by inputting how to illuminate the button when the beat sound is played n times and how to press the button in c ways that Yuta has learned. Please create.
input
The input consists of multiple datasets. The end of the input is indicated by two lines of zeros. Each dataset is given in the following format.
n c
a1,1 a1,2 ... a1,16
a2,1 a2,2 ... a2,16
...
an, 1 an, 2 ... an, 16
b1,1 b1,2 ... b1,16
b2,1 b2,2 ... b2,16
...
bc,1 bc,2 ... bc,16
The first line consists of two integers separated by one space. n (1 ≤ n ≤ 30) indicates the number of beat sounds, and c (1 ≤ c ≤ 30) indicates the number of button presses that you have learned. The following n + c lines give how to illuminate the button and how to press the button. The input item in the line is separated by one blank. ak and i indicate how the button i shines when the kth beat sound is heard, and bj and i indicate whether the button i is pressed by pressing the jth button in the middle of c. As for the values of ak and i, 0 means "does not shine" and 1 means "shines". For the values of bj and i, 0 means "do not press" and 1 means "press".
The number of datasets does not exceed 20.
output
For each data set, the maximum score is output on one line.
Example
Input
2 2
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
2 2
0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0
0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0
0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0
0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0
5 3
0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1
0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
0 0
Output
8
7
16
Submitted Solution:
```
bitcount = [bin(i).count('1') for i in range(1<<16)]
while True:
n,c = map(int,input().split())
if n == c == 0:
break
as_ = [int(input().replace(' ',''),2) for _ in range(n)]
bs = [int(input().replace(' ',''),2) for _ in range(c)]
ps = {as_[0] : 0}
qs = {}
for a in as_:
for x,n in ps.items():
x |= a
for b in bs:
y = x&~b
m = n+bitcount[x&b]
if y not in qs or qs[y] < m:
qs[y] = m
ps,qs = qs,{}
print(max(ps.values()))
``` | instruction | 0 | 34,182 | 19 | 68,364 |
No | output | 1 | 34,182 | 19 | 68,365 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yuta is addicted to the popular game "Beat Panel" at a nearby arcade. The game consists of a total of 16 panel-type buttons, 4x4, arranged in a grid as shown.
<image>
As shown in the figure, the buttons are arranged in the order of button 1, button 2,…, button 16 from the upper left to the lower right. In the game, you will hear a beat sound at regular intervals and a final sound at the end. Multiple buttons light up at the same time as the beat sounds. In some cases, even one does not shine. The player can press multiple buttons at the same time using the fingers of both hands from immediately after the beat sound to the next sound. It is also possible not to press anything. The game ends as soon as the end sound is heard.
Yuta has mastered c ways of pressing, and each time a beat sounds, he decides one of those pressing methods and presses the button. If the buttons you press are lit, those buttons will be lit and the number of buttons that have disappeared will be added to the player's score. Also, once a button is lit, the light will not go out until the button is pressed.
A program that outputs the maximum score that Yuta can obtain by inputting how to illuminate the button when the beat sound is played n times and how to press the button in c ways that Yuta has learned. Please create.
input
The input consists of multiple datasets. The end of the input is indicated by two lines of zeros. Each dataset is given in the following format.
n c
a1,1 a1,2 ... a1,16
a2,1 a2,2 ... a2,16
...
an, 1 an, 2 ... an, 16
b1,1 b1,2 ... b1,16
b2,1 b2,2 ... b2,16
...
bc,1 bc,2 ... bc,16
The first line consists of two integers separated by one space. n (1 ≤ n ≤ 30) indicates the number of beat sounds, and c (1 ≤ c ≤ 30) indicates the number of button presses that you have learned. The following n + c lines give how to illuminate the button and how to press the button. The input item in the line is separated by one blank. ak and i indicate how the button i shines when the kth beat sound is heard, and bj and i indicate whether the button i is pressed by pressing the jth button in the middle of c. As for the values of ak and i, 0 means "does not shine" and 1 means "shines". For the values of bj and i, 0 means "do not press" and 1 means "press".
The number of datasets does not exceed 20.
output
For each data set, the maximum score is output on one line.
Example
Input
2 2
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
2 2
0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0
0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0
0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0
0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0
5 3
0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1
0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
0 0
Output
8
7
16
Submitted Solution:
```
bitcount = [bin(i).count('1') for i in range(1<<16)]
while True:
n,c = map(int,input().split())
if n == c == 0:
break
as_ = [int(input().replace(' ',''),2) for _ in range(n)]
bs = [int(input().replace(' ',''),2) for _ in range(c)]
ps = {0 : 0}
for a in as_:
qs = ((x|a,n) for x,n in ps.items())
ps = {}
for x,n in qs:
for b in bs:
m = n+bitcount[x&b]
y = x&~b
if y not in ps or ps[y] < m:
ps[y] = m
print(max(ps.values()))
``` | instruction | 0 | 34,183 | 19 | 68,366 |
No | output | 1 | 34,183 | 19 | 68,367 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yuta is addicted to the popular game "Beat Panel" at a nearby arcade. The game consists of a total of 16 panel-type buttons, 4x4, arranged in a grid as shown.
<image>
As shown in the figure, the buttons are arranged in the order of button 1, button 2,…, button 16 from the upper left to the lower right. In the game, you will hear a beat sound at regular intervals and a final sound at the end. Multiple buttons light up at the same time as the beat sounds. In some cases, even one does not shine. The player can press multiple buttons at the same time using the fingers of both hands from immediately after the beat sound to the next sound. It is also possible not to press anything. The game ends as soon as the end sound is heard.
Yuta has mastered c ways of pressing, and each time a beat sounds, he decides one of those pressing methods and presses the button. If the buttons you press are lit, those buttons will be lit and the number of buttons that have disappeared will be added to the player's score. Also, once a button is lit, the light will not go out until the button is pressed.
A program that outputs the maximum score that Yuta can obtain by inputting how to illuminate the button when the beat sound is played n times and how to press the button in c ways that Yuta has learned. Please create.
input
The input consists of multiple datasets. The end of the input is indicated by two lines of zeros. Each dataset is given in the following format.
n c
a1,1 a1,2 ... a1,16
a2,1 a2,2 ... a2,16
...
an, 1 an, 2 ... an, 16
b1,1 b1,2 ... b1,16
b2,1 b2,2 ... b2,16
...
bc,1 bc,2 ... bc,16
The first line consists of two integers separated by one space. n (1 ≤ n ≤ 30) indicates the number of beat sounds, and c (1 ≤ c ≤ 30) indicates the number of button presses that you have learned. The following n + c lines give how to illuminate the button and how to press the button. The input item in the line is separated by one blank. ak and i indicate how the button i shines when the kth beat sound is heard, and bj and i indicate whether the button i is pressed by pressing the jth button in the middle of c. As for the values of ak and i, 0 means "does not shine" and 1 means "shines". For the values of bj and i, 0 means "do not press" and 1 means "press".
The number of datasets does not exceed 20.
output
For each data set, the maximum score is output on one line.
Example
Input
2 2
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
2 2
0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0
0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0
0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0
0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0
5 3
0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1
0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
0 0
Output
8
7
16
Submitted Solution:
```
bitcount = [bin(i).count('1') for i in range(1<<16)]
def f(as_,bs):
global bitcount
ps = {0 : 0}
qs = {}
for a in as_:
for x,n in ps.items():
x |= a
for b in bs:
y = x&~b
m = n+bitcount[x&b]
try:
if qs[y] < m:
qs[y] = m
except KeyError:
qs[y] = m
ps,qs = qs,{}
return max(ps.values())
while True:
n,c = map(int,input().split())
if n == c == 0:
break
as_ = [int(input().replace(' ',''),2) for _ in range(n)]
bs = [int(input().replace(' ',''),2) for _ in range(c)]
print(f(as_,bs))
``` | instruction | 0 | 34,184 | 19 | 68,368 |
No | output | 1 | 34,184 | 19 | 68,369 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya likes permutations a lot. Recently his mom has presented him permutation q1, q2, ..., qn of length n.
A permutation a of length n is a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ n), all integers there are distinct.
There is only one thing Petya likes more than permutations: playing with little Masha. As it turns out, Masha also has a permutation of length n. Petya decided to get the same permutation, whatever the cost may be. For that, he devised a game with the following rules:
* Before the beginning of the game Petya writes permutation 1, 2, ..., n on the blackboard. After that Petya makes exactly k moves, which are described below.
* During a move Petya tosses a coin. If the coin shows heads, he performs point 1, if the coin shows tails, he performs point 2.
1. Let's assume that the board contains permutation p1, p2, ..., pn at the given moment. Then Petya removes the written permutation p from the board and writes another one instead: pq1, pq2, ..., pqn. In other words, Petya applies permutation q (which he has got from his mother) to permutation p.
2. All actions are similar to point 1, except that Petya writes permutation t on the board, such that: tqi = pi for all i from 1 to n. In other words, Petya applies a permutation that is inverse to q to permutation p.
We know that after the k-th move the board contained Masha's permutation s1, s2, ..., sn. Besides, we know that throughout the game process Masha's permutation never occurred on the board before the k-th move. Note that the game has exactly k moves, that is, throughout the game the coin was tossed exactly k times.
Your task is to determine whether the described situation is possible or else state that Petya was mistaken somewhere. See samples and notes to them for a better understanding.
Input
The first line contains two integers n and k (1 ≤ n, k ≤ 100). The second line contains n space-separated integers q1, q2, ..., qn (1 ≤ qi ≤ n) — the permutation that Petya's got as a present. The third line contains Masha's permutation s, in the similar format.
It is guaranteed that the given sequences q and s are correct permutations.
Output
If the situation that is described in the statement is possible, print "YES" (without the quotes), otherwise print "NO" (without the quotes).
Examples
Input
4 1
2 3 4 1
1 2 3 4
Output
NO
Input
4 1
4 3 1 2
3 4 2 1
Output
YES
Input
4 3
4 3 1 2
3 4 2 1
Output
YES
Input
4 2
4 3 1 2
2 1 4 3
Output
YES
Input
4 1
4 3 1 2
2 1 4 3
Output
NO
Note
In the first sample Masha's permutation coincides with the permutation that was written on the board before the beginning of the game. Consequently, that violates the condition that Masha's permutation never occurred on the board before k moves were performed.
In the second sample the described situation is possible, in case if after we toss a coin, we get tails.
In the third sample the possible coin tossing sequence is: heads-tails-tails.
In the fourth sample the possible coin tossing sequence is: heads-heads. | instruction | 0 | 34,561 | 19 | 69,122 |
Tags: implementation, math
Correct Solution:
```
import sys
from math import *
def minp():
return sys.stdin.readline().strip()
def mint():
return int(minp())
def mints():
return map(int, minp().split())
n, k = mints()
q = list(mints())
for i in range(n):
q[i] -= 1
s = list(mints())
a = [i for i in range(1,n+1)]
d = [0]*n
b = [False]*(k+1)
c = [False]*(k+1)
e = [10000]*2
f = [10000]*2
for i in range(k+1):
#print(a)
b[i] = (a == s)
if b[i]:
e[i%2] = min(e[i%2], i)
for j in range(n):
d[j] = a[q[j]]
a,d = d,a
#print('====')
a = [i for i in range(1,n+1)]
for i in range(k+1):
#print(a)
c[i] = (a == s)
if c[i]:
f[i%2] = min(f[i%2], i)
for j in range(n):
d[q[j]] = a[j]
a,d = d,a
#print('====')
#print(e)
#print(f)
if e[0] == 0:
print('NO')
elif e[1] == 1:
if f[1] == 1 and k > 1:
print('NO')
elif k%2 == 1 or f[k%2] <= k:
print('YES')
else:
print('NO')
elif f[1] == 1:
if k%2 == 1 or e[k%2] <= k:
print('YES')
else:
print('NO')
else:
if e[k%2] <= k or f[k%2] <= k:
print('YES')
else:
print('NO')
``` | output | 1 | 34,561 | 19 | 69,123 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya likes permutations a lot. Recently his mom has presented him permutation q1, q2, ..., qn of length n.
A permutation a of length n is a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ n), all integers there are distinct.
There is only one thing Petya likes more than permutations: playing with little Masha. As it turns out, Masha also has a permutation of length n. Petya decided to get the same permutation, whatever the cost may be. For that, he devised a game with the following rules:
* Before the beginning of the game Petya writes permutation 1, 2, ..., n on the blackboard. After that Petya makes exactly k moves, which are described below.
* During a move Petya tosses a coin. If the coin shows heads, he performs point 1, if the coin shows tails, he performs point 2.
1. Let's assume that the board contains permutation p1, p2, ..., pn at the given moment. Then Petya removes the written permutation p from the board and writes another one instead: pq1, pq2, ..., pqn. In other words, Petya applies permutation q (which he has got from his mother) to permutation p.
2. All actions are similar to point 1, except that Petya writes permutation t on the board, such that: tqi = pi for all i from 1 to n. In other words, Petya applies a permutation that is inverse to q to permutation p.
We know that after the k-th move the board contained Masha's permutation s1, s2, ..., sn. Besides, we know that throughout the game process Masha's permutation never occurred on the board before the k-th move. Note that the game has exactly k moves, that is, throughout the game the coin was tossed exactly k times.
Your task is to determine whether the described situation is possible or else state that Petya was mistaken somewhere. See samples and notes to them for a better understanding.
Input
The first line contains two integers n and k (1 ≤ n, k ≤ 100). The second line contains n space-separated integers q1, q2, ..., qn (1 ≤ qi ≤ n) — the permutation that Petya's got as a present. The third line contains Masha's permutation s, in the similar format.
It is guaranteed that the given sequences q and s are correct permutations.
Output
If the situation that is described in the statement is possible, print "YES" (without the quotes), otherwise print "NO" (without the quotes).
Examples
Input
4 1
2 3 4 1
1 2 3 4
Output
NO
Input
4 1
4 3 1 2
3 4 2 1
Output
YES
Input
4 3
4 3 1 2
3 4 2 1
Output
YES
Input
4 2
4 3 1 2
2 1 4 3
Output
YES
Input
4 1
4 3 1 2
2 1 4 3
Output
NO
Note
In the first sample Masha's permutation coincides with the permutation that was written on the board before the beginning of the game. Consequently, that violates the condition that Masha's permutation never occurred on the board before k moves were performed.
In the second sample the described situation is possible, in case if after we toss a coin, we get tails.
In the third sample the possible coin tossing sequence is: heads-tails-tails.
In the fourth sample the possible coin tossing sequence is: heads-heads. | instruction | 0 | 34,562 | 19 | 69,124 |
Tags: implementation, math
Correct Solution:
```
n,k=map(int,input().strip().split())
a=list(map(int,input().strip().split()))
b=list(map(int,input().strip().split()))
ups = [[i+1 for i in range(n)]]
downs = [[i+1 for i in range(n)]]
def apply(arr):
out = [0]*n
for i in range(n):
out[i] = arr[a[i]-1]
return out
def unapply(arr):
out = [0]*n
for i in range(n):
out[a[i]-1] = arr[i]
return out
for i in range(k):
ups.append(apply(ups[i]))
for i in range(k):
downs.append(unapply(downs[i]))
earliest = [None, None]
earliestPossible = [None, None]
for i in range(k,-1,-1):
if ups[i] == b:
earliest[0] = i
if downs[i] == b:
earliest[1] = i
# print("YES")
# exit(0)
for i in range(k,-1,-2):
if ups[i] == b:
earliestPossible[0] = i
if downs[i] == b:
earliestPossible[1] = i
if (not earliestPossible[0]) and (not earliestPossible[1]):
print("NO")
exit(0)
if ((not earliestPossible[0]) or earliest[0] < earliestPossible[0]) and ((not earliestPossible[1]) or earliest[1] < earliestPossible[1]):
print("NO")
exit(0)
if ups[0] == b or (ups[1] == b and downs[1] == b and k > 1):
print("NO")
exit(0)
print("YES")
# tem = [i+1 for i in range(n)]
# for i in range(k):
# tem = apply(tem)
# for i in range(k):
# tem = unapply(tem)
# print(tem)
``` | output | 1 | 34,562 | 19 | 69,125 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya likes permutations a lot. Recently his mom has presented him permutation q1, q2, ..., qn of length n.
A permutation a of length n is a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ n), all integers there are distinct.
There is only one thing Petya likes more than permutations: playing with little Masha. As it turns out, Masha also has a permutation of length n. Petya decided to get the same permutation, whatever the cost may be. For that, he devised a game with the following rules:
* Before the beginning of the game Petya writes permutation 1, 2, ..., n on the blackboard. After that Petya makes exactly k moves, which are described below.
* During a move Petya tosses a coin. If the coin shows heads, he performs point 1, if the coin shows tails, he performs point 2.
1. Let's assume that the board contains permutation p1, p2, ..., pn at the given moment. Then Petya removes the written permutation p from the board and writes another one instead: pq1, pq2, ..., pqn. In other words, Petya applies permutation q (which he has got from his mother) to permutation p.
2. All actions are similar to point 1, except that Petya writes permutation t on the board, such that: tqi = pi for all i from 1 to n. In other words, Petya applies a permutation that is inverse to q to permutation p.
We know that after the k-th move the board contained Masha's permutation s1, s2, ..., sn. Besides, we know that throughout the game process Masha's permutation never occurred on the board before the k-th move. Note that the game has exactly k moves, that is, throughout the game the coin was tossed exactly k times.
Your task is to determine whether the described situation is possible or else state that Petya was mistaken somewhere. See samples and notes to them for a better understanding.
Input
The first line contains two integers n and k (1 ≤ n, k ≤ 100). The second line contains n space-separated integers q1, q2, ..., qn (1 ≤ qi ≤ n) — the permutation that Petya's got as a present. The third line contains Masha's permutation s, in the similar format.
It is guaranteed that the given sequences q and s are correct permutations.
Output
If the situation that is described in the statement is possible, print "YES" (without the quotes), otherwise print "NO" (without the quotes).
Examples
Input
4 1
2 3 4 1
1 2 3 4
Output
NO
Input
4 1
4 3 1 2
3 4 2 1
Output
YES
Input
4 3
4 3 1 2
3 4 2 1
Output
YES
Input
4 2
4 3 1 2
2 1 4 3
Output
YES
Input
4 1
4 3 1 2
2 1 4 3
Output
NO
Note
In the first sample Masha's permutation coincides with the permutation that was written on the board before the beginning of the game. Consequently, that violates the condition that Masha's permutation never occurred on the board before k moves were performed.
In the second sample the described situation is possible, in case if after we toss a coin, we get tails.
In the third sample the possible coin tossing sequence is: heads-tails-tails.
In the fourth sample the possible coin tossing sequence is: heads-heads. | instruction | 0 | 34,563 | 19 | 69,126 |
Tags: implementation, math
Correct Solution:
```
def Solve(x,L):
if(x==k[0]):
return L==S
if((x,tuple(L)) in Mem):
return False
if(L==S):
return False
E=[]
for i in range(len(L)):
E.append(L[Q[i]-1])
if(Solve(x+1,E)):
return True
E=[0]*len(L)
for i in range(len(L)):
E[Q[i]-1]=L[i]
if(Solve(x+1,E)):
return True
Mem[(x,tuple(L))]=1
return False
Mem={}
k=[0]
n,k[0]=map(int,input().split())
P=list(range(1,n+1))
Q=list(map(int,input().split()))
S=list(map(int,input().split()))
if(Solve(0,P)):
print("YES")
else:
print("NO")
``` | output | 1 | 34,563 | 19 | 69,127 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes permutations a lot. Recently his mom has presented him permutation q1, q2, ..., qn of length n.
A permutation a of length n is a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ n), all integers there are distinct.
There is only one thing Petya likes more than permutations: playing with little Masha. As it turns out, Masha also has a permutation of length n. Petya decided to get the same permutation, whatever the cost may be. For that, he devised a game with the following rules:
* Before the beginning of the game Petya writes permutation 1, 2, ..., n on the blackboard. After that Petya makes exactly k moves, which are described below.
* During a move Petya tosses a coin. If the coin shows heads, he performs point 1, if the coin shows tails, he performs point 2.
1. Let's assume that the board contains permutation p1, p2, ..., pn at the given moment. Then Petya removes the written permutation p from the board and writes another one instead: pq1, pq2, ..., pqn. In other words, Petya applies permutation q (which he has got from his mother) to permutation p.
2. All actions are similar to point 1, except that Petya writes permutation t on the board, such that: tqi = pi for all i from 1 to n. In other words, Petya applies a permutation that is inverse to q to permutation p.
We know that after the k-th move the board contained Masha's permutation s1, s2, ..., sn. Besides, we know that throughout the game process Masha's permutation never occurred on the board before the k-th move. Note that the game has exactly k moves, that is, throughout the game the coin was tossed exactly k times.
Your task is to determine whether the described situation is possible or else state that Petya was mistaken somewhere. See samples and notes to them for a better understanding.
Input
The first line contains two integers n and k (1 ≤ n, k ≤ 100). The second line contains n space-separated integers q1, q2, ..., qn (1 ≤ qi ≤ n) — the permutation that Petya's got as a present. The third line contains Masha's permutation s, in the similar format.
It is guaranteed that the given sequences q and s are correct permutations.
Output
If the situation that is described in the statement is possible, print "YES" (without the quotes), otherwise print "NO" (without the quotes).
Examples
Input
4 1
2 3 4 1
1 2 3 4
Output
NO
Input
4 1
4 3 1 2
3 4 2 1
Output
YES
Input
4 3
4 3 1 2
3 4 2 1
Output
YES
Input
4 2
4 3 1 2
2 1 4 3
Output
YES
Input
4 1
4 3 1 2
2 1 4 3
Output
NO
Note
In the first sample Masha's permutation coincides with the permutation that was written on the board before the beginning of the game. Consequently, that violates the condition that Masha's permutation never occurred on the board before k moves were performed.
In the second sample the described situation is possible, in case if after we toss a coin, we get tails.
In the third sample the possible coin tossing sequence is: heads-tails-tails.
In the fourth sample the possible coin tossing sequence is: heads-heads.
Submitted Solution:
```
n,k=map(int,input().strip().split())
a=list(map(int,input().strip().split()))
b=list(map(int,input().strip().split()))
ups = [[i+1 for i in range(n)]]
downs = [[i+1 for i in range(n)]]
def apply(arr):
out = [0]*len(arr)
for i in range(len(arr)):
out[i] = arr[a[i]-1]
return out
def unapply(arr):
out = [0]*len(arr)
for i in range(len(arr)):
out[a[i]-1] = arr[i]
return out
for i in range(k):
ups.append(apply(ups[i]))
for i in range(k):
downs.append(unapply(downs[i]))
for i in range(k,-1,-2):
if ups[i] == b or downs[i] == b:
print("YES")
exit(0)
print("NO")
``` | instruction | 0 | 34,564 | 19 | 69,128 |
No | output | 1 | 34,564 | 19 | 69,129 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes permutations a lot. Recently his mom has presented him permutation q1, q2, ..., qn of length n.
A permutation a of length n is a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ n), all integers there are distinct.
There is only one thing Petya likes more than permutations: playing with little Masha. As it turns out, Masha also has a permutation of length n. Petya decided to get the same permutation, whatever the cost may be. For that, he devised a game with the following rules:
* Before the beginning of the game Petya writes permutation 1, 2, ..., n on the blackboard. After that Petya makes exactly k moves, which are described below.
* During a move Petya tosses a coin. If the coin shows heads, he performs point 1, if the coin shows tails, he performs point 2.
1. Let's assume that the board contains permutation p1, p2, ..., pn at the given moment. Then Petya removes the written permutation p from the board and writes another one instead: pq1, pq2, ..., pqn. In other words, Petya applies permutation q (which he has got from his mother) to permutation p.
2. All actions are similar to point 1, except that Petya writes permutation t on the board, such that: tqi = pi for all i from 1 to n. In other words, Petya applies a permutation that is inverse to q to permutation p.
We know that after the k-th move the board contained Masha's permutation s1, s2, ..., sn. Besides, we know that throughout the game process Masha's permutation never occurred on the board before the k-th move. Note that the game has exactly k moves, that is, throughout the game the coin was tossed exactly k times.
Your task is to determine whether the described situation is possible or else state that Petya was mistaken somewhere. See samples and notes to them for a better understanding.
Input
The first line contains two integers n and k (1 ≤ n, k ≤ 100). The second line contains n space-separated integers q1, q2, ..., qn (1 ≤ qi ≤ n) — the permutation that Petya's got as a present. The third line contains Masha's permutation s, in the similar format.
It is guaranteed that the given sequences q and s are correct permutations.
Output
If the situation that is described in the statement is possible, print "YES" (without the quotes), otherwise print "NO" (without the quotes).
Examples
Input
4 1
2 3 4 1
1 2 3 4
Output
NO
Input
4 1
4 3 1 2
3 4 2 1
Output
YES
Input
4 3
4 3 1 2
3 4 2 1
Output
YES
Input
4 2
4 3 1 2
2 1 4 3
Output
YES
Input
4 1
4 3 1 2
2 1 4 3
Output
NO
Note
In the first sample Masha's permutation coincides with the permutation that was written on the board before the beginning of the game. Consequently, that violates the condition that Masha's permutation never occurred on the board before k moves were performed.
In the second sample the described situation is possible, in case if after we toss a coin, we get tails.
In the third sample the possible coin tossing sequence is: heads-tails-tails.
In the fourth sample the possible coin tossing sequence is: heads-heads.
Submitted Solution:
```
def perest(p,q):
tmp=[]
for i in q:
tmp.append(p[i-1])
return tmp
def obperest(p,q):
tmp=dict()
for i in range(n):
tmp[q[i]-1]=p[i]
tt=[]
for i in range(n):
tt.append(tmp[i])
return tt
n,k=map(int,input().split())
p=[i for i in range(1,n+1)]
q=[int(i) for i in input().split()]
s=[int(i) for i in input().split()]
if p==s:
print("NO")
exit(0)
if q==s and k%2!=0:
print("YES")
exit(0)
x=perest(p,q)
y=obperest(p,q)
if x==y==s and k==1:
print("YES")
exit(0)
elif x==y==s:
print("NO")
exit(0)
kk=1
while kk<k and x!=s and x!=p:
x=perest(x,q)
kk+=1
if x==s and (k-kk)%2==0:
print("YES")
exit(0)
elif x==s and (k-kk)%2!=0:
print("NO")
exit(0)
kk=1
while kk<k and y!=s and y!=p:
y=obperest(y,q)
kk+=1
if y==s and (k-kk)%2==0:
print("YES")
exit(0)
else:
print("NO")
``` | instruction | 0 | 34,565 | 19 | 69,130 |
No | output | 1 | 34,565 | 19 | 69,131 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes permutations a lot. Recently his mom has presented him permutation q1, q2, ..., qn of length n.
A permutation a of length n is a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ n), all integers there are distinct.
There is only one thing Petya likes more than permutations: playing with little Masha. As it turns out, Masha also has a permutation of length n. Petya decided to get the same permutation, whatever the cost may be. For that, he devised a game with the following rules:
* Before the beginning of the game Petya writes permutation 1, 2, ..., n on the blackboard. After that Petya makes exactly k moves, which are described below.
* During a move Petya tosses a coin. If the coin shows heads, he performs point 1, if the coin shows tails, he performs point 2.
1. Let's assume that the board contains permutation p1, p2, ..., pn at the given moment. Then Petya removes the written permutation p from the board and writes another one instead: pq1, pq2, ..., pqn. In other words, Petya applies permutation q (which he has got from his mother) to permutation p.
2. All actions are similar to point 1, except that Petya writes permutation t on the board, such that: tqi = pi for all i from 1 to n. In other words, Petya applies a permutation that is inverse to q to permutation p.
We know that after the k-th move the board contained Masha's permutation s1, s2, ..., sn. Besides, we know that throughout the game process Masha's permutation never occurred on the board before the k-th move. Note that the game has exactly k moves, that is, throughout the game the coin was tossed exactly k times.
Your task is to determine whether the described situation is possible or else state that Petya was mistaken somewhere. See samples and notes to them for a better understanding.
Input
The first line contains two integers n and k (1 ≤ n, k ≤ 100). The second line contains n space-separated integers q1, q2, ..., qn (1 ≤ qi ≤ n) — the permutation that Petya's got as a present. The third line contains Masha's permutation s, in the similar format.
It is guaranteed that the given sequences q and s are correct permutations.
Output
If the situation that is described in the statement is possible, print "YES" (without the quotes), otherwise print "NO" (without the quotes).
Examples
Input
4 1
2 3 4 1
1 2 3 4
Output
NO
Input
4 1
4 3 1 2
3 4 2 1
Output
YES
Input
4 3
4 3 1 2
3 4 2 1
Output
YES
Input
4 2
4 3 1 2
2 1 4 3
Output
YES
Input
4 1
4 3 1 2
2 1 4 3
Output
NO
Note
In the first sample Masha's permutation coincides with the permutation that was written on the board before the beginning of the game. Consequently, that violates the condition that Masha's permutation never occurred on the board before k moves were performed.
In the second sample the described situation is possible, in case if after we toss a coin, we get tails.
In the third sample the possible coin tossing sequence is: heads-tails-tails.
In the fourth sample the possible coin tossing sequence is: heads-heads.
Submitted Solution:
```
n, k = map(int, input().split())
p = [int(i) for i in range(1, n + 1)]
q = [int(i) for i in input().split()]
m = [int(i) for i in input().split()]
t = [0] * n
leng_l = 0
leng_r = 0
for i in range(n):
t[q[i] - 1] = p[i]
s = p.copy()
while 1:
if leng_l != 0 and (s == m or s == p):
break
sp = [0] * n
for i in range(n):
sp[i] = s[q[i] - 1]
s = sp.copy()
leng_l += 1
s = p.copy()
while 1:
if leng_r != 0 and (s == m or s == p):
break
sp = [0] * n
for i in range(n):
sp[q[i] - 1] = s[i]
s = sp.copy()
leng_r += 1
if leng_l == 1 and leng_r == 1 and k != 1 or m == p:
print('NO')
elif leng_l <= k and leng_l % 2 == k % 2 or leng_r <= k and leng_r % 2 == k % 2:
print('YES')
else:
print('NO')
``` | instruction | 0 | 34,566 | 19 | 69,132 |
No | output | 1 | 34,566 | 19 | 69,133 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes permutations a lot. Recently his mom has presented him permutation q1, q2, ..., qn of length n.
A permutation a of length n is a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ n), all integers there are distinct.
There is only one thing Petya likes more than permutations: playing with little Masha. As it turns out, Masha also has a permutation of length n. Petya decided to get the same permutation, whatever the cost may be. For that, he devised a game with the following rules:
* Before the beginning of the game Petya writes permutation 1, 2, ..., n on the blackboard. After that Petya makes exactly k moves, which are described below.
* During a move Petya tosses a coin. If the coin shows heads, he performs point 1, if the coin shows tails, he performs point 2.
1. Let's assume that the board contains permutation p1, p2, ..., pn at the given moment. Then Petya removes the written permutation p from the board and writes another one instead: pq1, pq2, ..., pqn. In other words, Petya applies permutation q (which he has got from his mother) to permutation p.
2. All actions are similar to point 1, except that Petya writes permutation t on the board, such that: tqi = pi for all i from 1 to n. In other words, Petya applies a permutation that is inverse to q to permutation p.
We know that after the k-th move the board contained Masha's permutation s1, s2, ..., sn. Besides, we know that throughout the game process Masha's permutation never occurred on the board before the k-th move. Note that the game has exactly k moves, that is, throughout the game the coin was tossed exactly k times.
Your task is to determine whether the described situation is possible or else state that Petya was mistaken somewhere. See samples and notes to them for a better understanding.
Input
The first line contains two integers n and k (1 ≤ n, k ≤ 100). The second line contains n space-separated integers q1, q2, ..., qn (1 ≤ qi ≤ n) — the permutation that Petya's got as a present. The third line contains Masha's permutation s, in the similar format.
It is guaranteed that the given sequences q and s are correct permutations.
Output
If the situation that is described in the statement is possible, print "YES" (without the quotes), otherwise print "NO" (without the quotes).
Examples
Input
4 1
2 3 4 1
1 2 3 4
Output
NO
Input
4 1
4 3 1 2
3 4 2 1
Output
YES
Input
4 3
4 3 1 2
3 4 2 1
Output
YES
Input
4 2
4 3 1 2
2 1 4 3
Output
YES
Input
4 1
4 3 1 2
2 1 4 3
Output
NO
Note
In the first sample Masha's permutation coincides with the permutation that was written on the board before the beginning of the game. Consequently, that violates the condition that Masha's permutation never occurred on the board before k moves were performed.
In the second sample the described situation is possible, in case if after we toss a coin, we get tails.
In the third sample the possible coin tossing sequence is: heads-tails-tails.
In the fourth sample the possible coin tossing sequence is: heads-heads.
Submitted Solution:
```
def Solve(x,L):
if(x==k[0]):
return L==S
if((x,tuple(L)) in Mem):
return False
if(L==S):
return False
E=[]
for i in range(len(L)):
E.append(L[Q[i]-1])
if(Solve(x+1,E)):
return True
E=[0]*len(L)
for i in range(len(L)):
E[Q[i]-1]=L[i]
if(Solve(x+1,E)):
return True
Mem[(x,tuple(L))]=1
return False
Mem={}
k=[0]
n,k[0]=map(int,input().split())
P=list(range(1,n+1))
Q=list(map(int,input().split()))
S=list(map(int,input().split()))
print(Solve(0,P))
``` | instruction | 0 | 34,567 | 19 | 69,134 |
No | output | 1 | 34,567 | 19 | 69,135 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO | instruction | 0 | 34,616 | 19 | 69,232 |
Tags: implementation
Correct Solution:
```
n = int(input())
c = [[int(s) for s in input().split()][1:] for x in range (n)]
for i in range(n):
for j in range(n):
if i!=j:
for k in c[j]:
if k not in c[i]:
break;
else:
print("NO")
break;
else:
print("YES")
``` | output | 1 | 34,616 | 19 | 69,233 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO | instruction | 0 | 34,617 | 19 | 69,234 |
Tags: implementation
Correct Solution:
```
# link: https://codeforces.com/problemset/problem/370/B
import sys
def solve(info, n):
for i in range(n):
flag = False
for j in range(n):
if i==j:
continue
else:
if info[i].issuperset(info[j]):
flag = True
break
if not flag:
print("YES")
else:
print("NO")
if __name__ == "__main__":
i = sys.stdin.readline
n = int(i())
info = []
for _ in range(n):
l = list(map(int, i().split()))
info.append(set(l[1:]))
solve(info, n)
``` | output | 1 | 34,617 | 19 | 69,235 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO | instruction | 0 | 34,618 | 19 | 69,236 |
Tags: implementation
Correct Solution:
```
n = int(input())
a = []
for i in range(n):
a += [set(list(map(int, input().split()))[1:])]
for i in range(n):
for j in range(n):
if i != j and a[j] <= a[i]:
print("NO")
break
else:
print("YES")
``` | output | 1 | 34,618 | 19 | 69,237 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO | instruction | 0 | 34,619 | 19 | 69,238 |
Tags: implementation
Correct Solution:
```
k = int(input())
cards = []
res = []
for i in range(k):
str = input()
it = set(map(int,str.split(" ")[1:]))
cards.append(it)
s = []
for i in cards:
for j in cards:
s.append(len(j.difference(i)))
if s.count(0) != 1:
print('NO')
else:
print('YES')
s=[]
``` | output | 1 | 34,619 | 19 | 69,239 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO | instruction | 0 | 34,620 | 19 | 69,240 |
Tags: implementation
Correct Solution:
```
def s():
n = int(input())
a = [set(list(map(int,input().split()))[1:])for _ in range(n)]
res = 0
print(*['YES'if sum(i.issubset(j)for i in a) == 1 else 'NO' for j in a],sep = '\n')
s()
``` | output | 1 | 34,620 | 19 | 69,241 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO | instruction | 0 | 34,621 | 19 | 69,242 |
Tags: implementation
Correct Solution:
```
n = int(input())
cards = list()
for i in range(n):
cards.append(list())
inp = [int(j) for j in input().split()]
m = inp[0]
inp.pop(0)
inp.sort()
cards[i] = inp
c_have_equal_num = list()
for i in range(n):
c_have_equal_num.append(list())
for j in range(i + 1, n):
c_have_equal_num[i].append(int(0))
def num_is_in(num, card):
num_is_in_card = False
for ind in card:
if ind > num:
break
elif ind == num:
num_is_in_card = True
break
return num_is_in_card
for num in range(1, 101):
for i in range(n):
if num_is_in(num, cards[i]):
for j in range(n - i - 1):
if num_is_in(num, cards[i + j + 1]):
c_have_equal_num[i][j] += 1
winnable = list()
for i in range(n):
winnable.append(True)
for i in range(n):
for j in range(n - i - 1):
if c_have_equal_num[i][j] == len(cards[i]) and len(cards[i]) == len(cards[i + j + 1]):
winnable[i + j + 1] = False
winnable[i] = False
elif c_have_equal_num[i][j] == len(cards[i + j + 1]):
winnable[i] = False
elif c_have_equal_num[i][j] == len(cards[i]):
winnable[i + j + 1] = False
for i in winnable:
if i:
print("YES")
else:
print("NO")
``` | output | 1 | 34,621 | 19 | 69,243 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO | instruction | 0 | 34,622 | 19 | 69,244 |
Tags: implementation
Correct Solution:
```
n = int(input())
cards = [None] + [[] for i in range(n)]
for i in range(1, n+1):
cards[i] = list(map(int, input().split()))[1:]
ans = [None] + [True for i in range(n)]
#print(cards, ans)
for i in range(1, n + 1):
for j in range( 1, n + 1):
if i == j :
continue;
if set(cards[i]) & set(cards[j]) == set(cards[j]):
ans[i] = False
o = ''
for i in range(1, len(ans)):
if ans[i] == True:
o += 'YES\n'
elif ans[i] == False:
o += 'NO\n'
print(o)
``` | output | 1 | 34,622 | 19 | 69,245 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO | instruction | 0 | 34,623 | 19 | 69,246 |
Tags: implementation
Correct Solution:
```
n = int(input())
c = [[int(s) for s in input().split()][1:] for x in range (n)]
for i in range (n):
for j in range (n):
if i != j:
for k in c[j]:
if k not in c[i]:
break
else:
print("NO")
break
else:
print("YES")
``` | output | 1 | 34,623 | 19 | 69,247 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO
Submitted Solution:
```
p = [set(list(map(int, input().split()))[1:]) for i in range(int(input()))]
for i, s in enumerate(p):
print('YES' if all(i == i2 or not s2 <= s for i2, s2 in enumerate(p)) else 'NO')
``` | instruction | 0 | 34,624 | 19 | 69,248 |
Yes | output | 1 | 34,624 | 19 | 69,249 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO
Submitted Solution:
```
a=int(input());l=[list(map(int,input().split()[1:])) for _ in " "*a]
for i in range(a):
for j in range(a):
if i!=j and all(k in l[i] for k in l[j] ):print("NO");break
else:print("YES")
``` | instruction | 0 | 34,625 | 19 | 69,250 |
Yes | output | 1 | 34,625 | 19 | 69,251 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO
Submitted Solution:
```
n = int(input())
a = []
for i in range(n):
li = list(map(int, input().split()))
a.append(set(li[1:]))
for i in range(n):
s = a[i]
joke = 1
for j in range(n):
t = a[j]
if t <= s and i != j:
joke = 0
break
print("YES" * joke + "NO" * (1 - joke))
``` | instruction | 0 | 34,626 | 19 | 69,252 |
Yes | output | 1 | 34,626 | 19 | 69,253 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO
Submitted Solution:
```
mod = 1000000007
ii = lambda : int(input())
si = lambda : input()
dgl = lambda : list(map(int, input()))
f = lambda : map(int, input().split())
il = lambda : list(map(int, input().split()))
ls = lambda : list(input())
t=ii()
l=[]
for i in range(t):
x,*y=f()
l.append(set(y))
for i in range(t):
fg=0
for j in range(t):
if i!=j and len(l[i])>=len(l[j]):
if all(x in l[i] for x in l[j]):
fg=1
print('YNEOS'[fg==1::2])
``` | instruction | 0 | 34,627 | 19 | 69,254 |
Yes | output | 1 | 34,627 | 19 | 69,255 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO
Submitted Solution:
```
n = int(input())
cards = list()
for i in range(n):
cards.append(list())
inp = [int(j) for j in input().split()]
m = inp[0]
inp.pop(0)
inp.sort()
cards[i] = inp
c_have_equal_num = list()
for i in range(n):
c_have_equal_num.append(list())
for j in range(i + 1, n):
c_have_equal_num[i].append(int(0))
def num_is_in(num, card):
num_is_in_card = False
for ind in card:
if ind > num:
break
elif ind == num:
num_is_in_card = True
break
return num_is_in_card
for num in range(1, 101):
for i in range(n):
if num_is_in(num, cards[i]):
for j in range(n - i - 1):
if num_is_in(num, cards[i + j + 1]):
c_have_equal_num[i][j] += 1
winnable = list()
for i in range(n):
winnable.append(True)
for i in range(n):
for j in range(n - i - 1):
if c_have_equal_num[i][j] == len(cards[i]):
winnable[i + j + 1] = False
elif c_have_equal_num[i][j] == len(cards[i + j + 1]):
winnable[i] = False
for i in winnable:
if i:
print("YES")
else:
print("NO")
``` | instruction | 0 | 34,628 | 19 | 69,256 |
No | output | 1 | 34,628 | 19 | 69,257 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO
Submitted Solution:
```
a=int(input())
z=[1]*101
z1=[1]*101
k=[[-1]]
for i in range(a):k.append(sorted(map(int,input().split()[1:])))
for i in range(1,101):
for j in range(1,1+a):
if len(k[j])==i:
ok=1
for x in k[j]:
if z[x]==0:ok=0;break
if ok:
z1[j]=0
for x in k[j]:z[x]=0
for i in range(1,1+a):
if z1[i]==0 and k.count(k[i])>1:z1[i]=1
for i in range(1,a+1):
if z1[i]==0:print("YES")
else:print("NO")
``` | instruction | 0 | 34,629 | 19 | 69,258 |
No | output | 1 | 34,629 | 19 | 69,259 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO
Submitted Solution:
```
n = int(input())
a = []
for i in range(n):
a += [set(map(int, input().split()))]
for i in range(n):
for j in range(n):
if i != j and a[j] <= a[i]:
print("NO")
break
else:
print("YES")
``` | instruction | 0 | 34,630 | 19 | 69,260 |
No | output | 1 | 34,630 | 19 | 69,261 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lately, a national version of a bingo game has become very popular in Berland. There are n players playing the game, each player has a card with numbers. The numbers on each card are distinct, but distinct cards can have equal numbers. The card of the i-th player contains mi numbers.
During the game the host takes numbered balls one by one from a bag. He reads the number aloud in a high and clear voice and then puts the ball away. All participants cross out the number if it occurs on their cards. The person who crosses out all numbers from his card first, wins. If multiple people cross out all numbers from their cards at the same time, there are no winners in the game. At the beginning of the game the bag contains 100 balls numbered 1 through 100, the numbers of all balls are distinct.
You are given the cards for each player. Write a program that determines whether a player can win the game at the most favorable for him scenario or not.
Input
The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of the players. Then follow n lines, each line describes a player's card. The line that describes a card starts from integer mi (1 ≤ mi ≤ 100) that shows how many numbers the i-th player's card has. Then follows a sequence of integers ai, 1, ai, 2, ..., ai, mi (1 ≤ ai, k ≤ 100) — the numbers on the i-th player's card. The numbers in the lines are separated by single spaces.
It is guaranteed that all the numbers on each card are distinct.
Output
Print n lines, the i-th line must contain word "YES" (without the quotes), if the i-th player can win, and "NO" (without the quotes) otherwise.
Examples
Input
3
1 1
3 2 4 1
2 10 11
Output
YES
NO
YES
Input
2
1 1
1 1
Output
NO
NO
Submitted Solution:
```
from math import *
from copy import *
from string import * # alpha = ascii_lowercase
from random import *
from sys import stdin
from sys import maxsize
from operator import * # d = sorted(d.items(), key=itemgetter(1))
from itertools import *
from collections import Counter # d = dict(Counter(l))
n=int(input())
l=[]
for i in range(n):
l1=list(map(int,input().split(" ")))
l.append(l1)
boo=[]
for i in range(n):
b=False
for j in range(n):
if(j==i):
continue
else:
for i1 in range(1,len(l[i])):
for i2 in range(1,len(l[j])):
if(l[i][i1]==l[j][i2] and len(l[j])<=len(l[i])):
b=True
break
if(b):
break
boo.append(b)
for i in range(len(boo)):
if(boo[i]):
print("NO")
else:
print("YES")
``` | instruction | 0 | 34,631 | 19 | 69,262 |
No | output | 1 | 34,631 | 19 | 69,263 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two players play a game.
Initially there are n integers a_1, a_2, …, a_n written on the board. Each turn a player selects one number and erases it from the board. This continues until there is only one number left on the board, i. e. n - 1 turns are made. The first player makes the first move, then players alternate turns.
The first player wants to minimize the last number that would be left on the board, while the second player wants to maximize it.
You want to know what number will be left on the board after n - 1 turns if both players make optimal moves.
Input
The first line contains one integer n (1 ≤ n ≤ 1000) — the number of numbers on the board.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6).
Output
Print one number that will be left on the board.
Examples
Input
3
2 1 3
Output
2
Input
3
2 2 2
Output
2
Note
In the first sample, the first player erases 3 and the second erases 1. 2 is left on the board.
In the second sample, 2 is left on the board regardless of the actions of the players. | instruction | 0 | 34,881 | 19 | 69,762 |
Tags: sortings
Correct Solution:
```
def kstatic(array, key):
if len(array) > 1:
less, more = [], []
equal = []
pivot = array[0]
for i in range(len(array)):
if array[i] < pivot:
less.append(array[i])
elif array[i] > pivot:
more.append(array[i])
else:
equal.append(array[i])
if key < len(less):
return kstatic(less, key)
elif key < len(less) + len(equal):
return equal[0]
else:
return kstatic(more, key - len(less) - len(equal))
if len(array) == 1 and key == 0:
return array[0]
k = int(input())
a = input().split(' ')
array = []
for i in range(len(a)):
array.append(int(a[i]))
if len(array)%2 == 0:
key = k//2 - 1
print(kstatic(array, key))
elif k == 1:
print(array[0])
else:
key = k//2
print(kstatic(array, key))
``` | output | 1 | 34,881 | 19 | 69,763 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two players play a game.
Initially there are n integers a_1, a_2, …, a_n written on the board. Each turn a player selects one number and erases it from the board. This continues until there is only one number left on the board, i. e. n - 1 turns are made. The first player makes the first move, then players alternate turns.
The first player wants to minimize the last number that would be left on the board, while the second player wants to maximize it.
You want to know what number will be left on the board after n - 1 turns if both players make optimal moves.
Input
The first line contains one integer n (1 ≤ n ≤ 1000) — the number of numbers on the board.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6).
Output
Print one number that will be left on the board.
Examples
Input
3
2 1 3
Output
2
Input
3
2 2 2
Output
2
Note
In the first sample, the first player erases 3 and the second erases 1. 2 is left on the board.
In the second sample, 2 is left on the board regardless of the actions of the players. | instruction | 0 | 34,882 | 19 | 69,764 |
Tags: sortings
Correct Solution:
```
# A. Game
n, a = int(input()), list(map(int, input().split()))
a.sort()
print(a[(n-1)//2])
``` | output | 1 | 34,882 | 19 | 69,765 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two players play a game.
Initially there are n integers a_1, a_2, …, a_n written on the board. Each turn a player selects one number and erases it from the board. This continues until there is only one number left on the board, i. e. n - 1 turns are made. The first player makes the first move, then players alternate turns.
The first player wants to minimize the last number that would be left on the board, while the second player wants to maximize it.
You want to know what number will be left on the board after n - 1 turns if both players make optimal moves.
Input
The first line contains one integer n (1 ≤ n ≤ 1000) — the number of numbers on the board.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6).
Output
Print one number that will be left on the board.
Examples
Input
3
2 1 3
Output
2
Input
3
2 2 2
Output
2
Note
In the first sample, the first player erases 3 and the second erases 1. 2 is left on the board.
In the second sample, 2 is left on the board regardless of the actions of the players. | instruction | 0 | 34,883 | 19 | 69,766 |
Tags: sortings
Correct Solution:
```
n = int(input())
a = [int(x) for x in input().split()]
a = sorted(a)
print(a[(n-1)//2])
``` | output | 1 | 34,883 | 19 | 69,767 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two players play a game.
Initially there are n integers a_1, a_2, …, a_n written on the board. Each turn a player selects one number and erases it from the board. This continues until there is only one number left on the board, i. e. n - 1 turns are made. The first player makes the first move, then players alternate turns.
The first player wants to minimize the last number that would be left on the board, while the second player wants to maximize it.
You want to know what number will be left on the board after n - 1 turns if both players make optimal moves.
Input
The first line contains one integer n (1 ≤ n ≤ 1000) — the number of numbers on the board.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6).
Output
Print one number that will be left on the board.
Examples
Input
3
2 1 3
Output
2
Input
3
2 2 2
Output
2
Note
In the first sample, the first player erases 3 and the second erases 1. 2 is left on the board.
In the second sample, 2 is left on the board regardless of the actions of the players. | instruction | 0 | 34,884 | 19 | 69,768 |
Tags: sortings
Correct Solution:
```
n=int(input())
nums=list(map(int,input().strip().split()))
nums.sort()
mid=len(nums)//2
if(len(nums)%2==0):
print(nums[mid-1])
else:
print(nums[mid])
``` | output | 1 | 34,884 | 19 | 69,769 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two players play a game.
Initially there are n integers a_1, a_2, …, a_n written on the board. Each turn a player selects one number and erases it from the board. This continues until there is only one number left on the board, i. e. n - 1 turns are made. The first player makes the first move, then players alternate turns.
The first player wants to minimize the last number that would be left on the board, while the second player wants to maximize it.
You want to know what number will be left on the board after n - 1 turns if both players make optimal moves.
Input
The first line contains one integer n (1 ≤ n ≤ 1000) — the number of numbers on the board.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6).
Output
Print one number that will be left on the board.
Examples
Input
3
2 1 3
Output
2
Input
3
2 2 2
Output
2
Note
In the first sample, the first player erases 3 and the second erases 1. 2 is left on the board.
In the second sample, 2 is left on the board regardless of the actions of the players. | instruction | 0 | 34,885 | 19 | 69,770 |
Tags: sortings
Correct Solution:
```
if __name__ == '__main__':
n = int(input())
nums = list(map(int, input().split()))
length = len(nums)
nums = sorted(nums)
if length % 2 == 0:
print(nums[length // 2 - 1])
else:
print(nums[length // 2])
``` | output | 1 | 34,885 | 19 | 69,771 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two players play a game.
Initially there are n integers a_1, a_2, …, a_n written on the board. Each turn a player selects one number and erases it from the board. This continues until there is only one number left on the board, i. e. n - 1 turns are made. The first player makes the first move, then players alternate turns.
The first player wants to minimize the last number that would be left on the board, while the second player wants to maximize it.
You want to know what number will be left on the board after n - 1 turns if both players make optimal moves.
Input
The first line contains one integer n (1 ≤ n ≤ 1000) — the number of numbers on the board.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6).
Output
Print one number that will be left on the board.
Examples
Input
3
2 1 3
Output
2
Input
3
2 2 2
Output
2
Note
In the first sample, the first player erases 3 and the second erases 1. 2 is left on the board.
In the second sample, 2 is left on the board regardless of the actions of the players. | instruction | 0 | 34,886 | 19 | 69,772 |
Tags: sortings
Correct Solution:
```
from collections import deque
def solve(arr):
q = deque(sorted(arr))
m = True
while q:
if m:
c = q.pop()
m = not m
else:
c = q.popleft()
m = not m
return c
def main():
n = int(input())
arr = list(map(int, input().split()))
print(solve(arr))
if __name__ == '__main__':
main()
``` | output | 1 | 34,886 | 19 | 69,773 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two players play a game.
Initially there are n integers a_1, a_2, …, a_n written on the board. Each turn a player selects one number and erases it from the board. This continues until there is only one number left on the board, i. e. n - 1 turns are made. The first player makes the first move, then players alternate turns.
The first player wants to minimize the last number that would be left on the board, while the second player wants to maximize it.
You want to know what number will be left on the board after n - 1 turns if both players make optimal moves.
Input
The first line contains one integer n (1 ≤ n ≤ 1000) — the number of numbers on the board.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6).
Output
Print one number that will be left on the board.
Examples
Input
3
2 1 3
Output
2
Input
3
2 2 2
Output
2
Note
In the first sample, the first player erases 3 and the second erases 1. 2 is left on the board.
In the second sample, 2 is left on the board regardless of the actions of the players. | instruction | 0 | 34,887 | 19 | 69,774 |
Tags: sortings
Correct Solution:
```
""" *** Author--Saket Saumya ***
IIITM
"""
n=int(input())
arr=list(map(int,input().split()))
arr.sort()
x=(n-1)//2
print(arr[x])
``` | output | 1 | 34,887 | 19 | 69,775 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Two players play a game.
Initially there are n integers a_1, a_2, …, a_n written on the board. Each turn a player selects one number and erases it from the board. This continues until there is only one number left on the board, i. e. n - 1 turns are made. The first player makes the first move, then players alternate turns.
The first player wants to minimize the last number that would be left on the board, while the second player wants to maximize it.
You want to know what number will be left on the board after n - 1 turns if both players make optimal moves.
Input
The first line contains one integer n (1 ≤ n ≤ 1000) — the number of numbers on the board.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6).
Output
Print one number that will be left on the board.
Examples
Input
3
2 1 3
Output
2
Input
3
2 2 2
Output
2
Note
In the first sample, the first player erases 3 and the second erases 1. 2 is left on the board.
In the second sample, 2 is left on the board regardless of the actions of the players. | instruction | 0 | 34,888 | 19 | 69,776 |
Tags: sortings
Correct Solution:
```
n = int(input())
a = list(map(int,input().split()))
a.sort()
if (n%2==0):
result = a[n//2-1]
else:
result = a[n//2]
print(result)
``` | output | 1 | 34,888 | 19 | 69,777 |
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