message
stringlengths
2
28.7k
message_type
stringclasses
2 values
message_id
int64
0
1
conversation_id
int64
21
109k
cluster
float64
7
7
__index_level_0__
int64
42
217k
Provide a correct Python 3 solution for this coding contest problem. There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors. Find the number of the possible ways to paint the balls. Constraints * 1≦N≦1000 * 2≦K≦1000 * The correct answer is at most 2^{31}-1. Input The input is given from Standard Input in the following format: N K Output Print the number of the possible ways to paint the balls. Examples Input 2 2 Output 2 Input 1 10 Output 10
instruction
0
63,006
7
126,012
"Correct Solution: ``` iN,iK = [int(_) for _ in input().split()] print(iK*((iK-1)**(iN-1))) ```
output
1
63,006
7
126,013
Provide a correct Python 3 solution for this coding contest problem. There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors. Find the number of the possible ways to paint the balls. Constraints * 1≦N≦1000 * 2≦K≦1000 * The correct answer is at most 2^{31}-1. Input The input is given from Standard Input in the following format: N K Output Print the number of the possible ways to paint the balls. Examples Input 2 2 Output 2 Input 1 10 Output 10
instruction
0
63,007
7
126,014
"Correct Solution: ``` # ABC 046 B N, K = map(int, input().split()) print(K * (K-1)**(N-1)) ```
output
1
63,007
7
126,015
Provide a correct Python 3 solution for this coding contest problem. There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors. Find the number of the possible ways to paint the balls. Constraints * 1≦N≦1000 * 2≦K≦1000 * The correct answer is at most 2^{31}-1. Input The input is given from Standard Input in the following format: N K Output Print the number of the possible ways to paint the balls. Examples Input 2 2 Output 2 Input 1 10 Output 10
instruction
0
63,008
7
126,016
"Correct Solution: ``` N,K = map(int, input().split()) pattern = K*(K-1)**(N-1) print(pattern) ```
output
1
63,008
7
126,017
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors. Find the number of the possible ways to paint the balls. Constraints * 1≦N≦1000 * 2≦K≦1000 * The correct answer is at most 2^{31}-1. Input The input is given from Standard Input in the following format: N K Output Print the number of the possible ways to paint the balls. Examples Input 2 2 Output 2 Input 1 10 Output 10 Submitted Solution: ``` n,k=map(int, input().split()) case=k*((k-1)**(n-1)) print(case) ```
instruction
0
63,009
7
126,018
Yes
output
1
63,009
7
126,019
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors. Find the number of the possible ways to paint the balls. Constraints * 1≦N≦1000 * 2≦K≦1000 * The correct answer is at most 2^{31}-1. Input The input is given from Standard Input in the following format: N K Output Print the number of the possible ways to paint the balls. Examples Input 2 2 Output 2 Input 1 10 Output 10 Submitted Solution: ``` a=list(map(int,input().split())) print(((a[1]-1)**(a[0]-1))*a[1]) ```
instruction
0
63,010
7
126,020
Yes
output
1
63,010
7
126,021
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors. Find the number of the possible ways to paint the balls. Constraints * 1≦N≦1000 * 2≦K≦1000 * The correct answer is at most 2^{31}-1. Input The input is given from Standard Input in the following format: N K Output Print the number of the possible ways to paint the balls. Examples Input 2 2 Output 2 Input 1 10 Output 10 Submitted Solution: ``` N, K = map(int, input().split()) ans = K * (K - 1)**(N - 1) print(ans) ```
instruction
0
63,011
7
126,022
Yes
output
1
63,011
7
126,023
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors. Find the number of the possible ways to paint the balls. Constraints * 1≦N≦1000 * 2≦K≦1000 * The correct answer is at most 2^{31}-1. Input The input is given from Standard Input in the following format: N K Output Print the number of the possible ways to paint the balls. Examples Input 2 2 Output 2 Input 1 10 Output 10 Submitted Solution: ``` import math N,K=map(int,input().split()) print(K*((K-1)**(N-1))) ```
instruction
0
63,012
7
126,024
Yes
output
1
63,012
7
126,025
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors. Find the number of the possible ways to paint the balls. Constraints * 1≦N≦1000 * 2≦K≦1000 * The correct answer is at most 2^{31}-1. Input The input is given from Standard Input in the following format: N K Output Print the number of the possible ways to paint the balls. Examples Input 2 2 Output 2 Input 1 10 Output 10 Submitted Solution: ``` ball, color = map(int, input().split()) first = color * 1 second = 0 if ball != 1: second = (color - 1) ** (ball-1) print(first * second) ```
instruction
0
63,013
7
126,026
No
output
1
63,013
7
126,027
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors. Find the number of the possible ways to paint the balls. Constraints * 1≦N≦1000 * 2≦K≦1000 * The correct answer is at most 2^{31}-1. Input The input is given from Standard Input in the following format: N K Output Print the number of the possible ways to paint the balls. Examples Input 2 2 Output 2 Input 1 10 Output 10 Submitted Solution: ``` N,K =map(int,input().split()) print(N*((K-1)**(N-1))) ```
instruction
0
63,014
7
126,028
No
output
1
63,014
7
126,029
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors. Find the number of the possible ways to paint the balls. Constraints * 1≦N≦1000 * 2≦K≦1000 * The correct answer is at most 2^{31}-1. Input The input is given from Standard Input in the following format: N K Output Print the number of the possible ways to paint the balls. Examples Input 2 2 Output 2 Input 1 10 Output 10 Submitted Solution: ``` a=list(map(int,input().split())) print(a[1]+(a[0]-1)*(a[1]-1)) ```
instruction
0
63,015
7
126,030
No
output
1
63,015
7
126,031
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors. Find the number of the possible ways to paint the balls. Constraints * 1≦N≦1000 * 2≦K≦1000 * The correct answer is at most 2^{31}-1. Input The input is given from Standard Input in the following format: N K Output Print the number of the possible ways to paint the balls. Examples Input 2 2 Output 2 Input 1 10 Output 10 Submitted Solution: ``` a=list(map(int,input().split())) print(a[1]+(a[0]-1)*(a[1]-1) ```
instruction
0
63,016
7
126,032
No
output
1
63,016
7
126,033
Provide a correct Python 3 solution for this coding contest problem. Problem Statement Let's consider operations on monochrome images that consist of hexagonal pixels, each of which is colored in either black or white. Because of the shape of pixels, each of them has exactly six neighbors (e.g. pixels that share an edge with it.) "Filtering" is an operation to determine the color of a pixel from the colors of itself and its six neighbors. Examples of filterings are shown below. Example 1: Color a pixel in white when all of its neighboring pixels are white. Otherwise the color will not change. <image> Performing this operation on all the pixels simultaneously results in "noise canceling," which removes isolated black pixels. Example 2: Color a pixel in white when its all neighboring pixels are black. Otherwise the color will not change. <image> Performing this operation on all the pixels simultaneously results in "edge detection," which leaves only the edges of filled areas. Example 3: Color a pixel with the color of the pixel just below it, ignoring any other neighbors. <image> Performing this operation on all the pixels simultaneously results in "shifting up" the whole image by one pixel. Applying some filter, such as "noise canceling" and "edge detection," twice to any image yields the exactly same result as if they were applied only once. We call such filters idempotent. The "shifting up" filter is not idempotent since every repeated application shifts the image up by one pixel. Your task is to determine whether the given filter is idempotent or not. Input The input consists of multiple datasets. The number of dataset is less than $100$. Each dataset is a string representing a filter and has the following format (without spaces between digits). > $c_0c_1\cdots{}c_{127}$ $c_i$ is either '0' (represents black) or '1' (represents white), which indicates the output of the filter for a pixel when the binary representation of the pixel and its neighboring six pixels is $i$. The mapping from the pixels to the bits is as following: <image> and the binary representation $i$ is defined as $i = \sum_{j=0}^6{\mathit{bit}_j \times 2^j}$, where $\mathit{bit}_j$ is $0$ or $1$ if the corresponding pixel is in black or white, respectively. Note that the filter is applied on the center pixel, denoted as bit 3. The input ends with a line that contains only a single "#". Output For each dataset, print "yes" in a line if the given filter is idempotent, or "no" otherwise (quotes are for clarity). Sample Input 00000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000111111111 10000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000011111111 01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101 Output for the Sample Input yes yes no Example Input 00000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000111111111 10000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000011111111 01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101 # Output yes yes no
instruction
0
63,110
7
126,220
"Correct Solution: ``` import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools sys.setrecursionlimit(10**7) inf = 10**20 eps = 1.0 / 10**10 mod = 10**9+7 dd = [(-1,0),(0,1),(1,0),(0,-1)] ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)] def LI(): return [int(x) for x in sys.stdin.readline().split()] def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()] def LF(): return [float(x) for x in sys.stdin.readline().split()] def LS(): return sys.stdin.readline().split() def I(): return int(sys.stdin.readline()) def F(): return float(sys.stdin.readline()) def S(): return input() def pf(s): return print(s, flush=True) # 13 # 12 11 # 13 06 13 # 05 04 # 10 03 09 # 02 01 # 13 00 13 # 08 07 # 13 def main(): rr = [] tt = [ [13, 7, 8, 0, 1, 2, 3], [7, 13, 0, 1, 9, 3, 4], [8, 0, 13, 2, 3, 10, 5], [0, 1, 2, 3, 4, 5, 6], [1, 9, 3, 4, 13, 6, 11], [2, 3, 10, 5, 6, 13, 12], [3, 4, 5, 6, 11, 12, 13] ] while True: s = S() if s == '#': break fil = [int(c) for c in s] i2 = [2**i for i in range(128)] f3 = {} for k in range(3**7): a = [] kk = k for _ in range(7): a.append(k%3) k //= 3 if 2 in a: continue a.reverse() e = 0 for c in a: e *= 2 e += c f3[kk] = fil[e] for k in range(3**7): a = [] kk = k for _ in range(7): a.append(k%3) k //= 3 if 2 not in a: continue a.reverse() ki = a.index(2) e = 0 y = 0 for i in range(7): e *= 3 y *= 3 if i == ki: y += 1 else: e += a[i] y += a[i] fe = f3[e] fy = f3[y] if fe == fy: f3[kk] = fe else: f3[kk] = 2 f = True for k in range(2**13): ba = [1 if i2[i] & k else 0 for i in range(13)] + [2] ca = [] for i in range(7): ti = tt[i] e = 0 for c in ti: e *= 3 e += ba[c] ca.append(f3[e]) y = 0 for c in ca: y *= 3 y += c if ca[3] != f3[y]: f = False break if f: rr.append('yes') else: rr.append('no') return '\n'.join(rr) print(main()) ```
output
1
63,110
7
126,221
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Problem Statement Let's consider operations on monochrome images that consist of hexagonal pixels, each of which is colored in either black or white. Because of the shape of pixels, each of them has exactly six neighbors (e.g. pixels that share an edge with it.) "Filtering" is an operation to determine the color of a pixel from the colors of itself and its six neighbors. Examples of filterings are shown below. Example 1: Color a pixel in white when all of its neighboring pixels are white. Otherwise the color will not change. <image> Performing this operation on all the pixels simultaneously results in "noise canceling," which removes isolated black pixels. Example 2: Color a pixel in white when its all neighboring pixels are black. Otherwise the color will not change. <image> Performing this operation on all the pixels simultaneously results in "edge detection," which leaves only the edges of filled areas. Example 3: Color a pixel with the color of the pixel just below it, ignoring any other neighbors. <image> Performing this operation on all the pixels simultaneously results in "shifting up" the whole image by one pixel. Applying some filter, such as "noise canceling" and "edge detection," twice to any image yields the exactly same result as if they were applied only once. We call such filters idempotent. The "shifting up" filter is not idempotent since every repeated application shifts the image up by one pixel. Your task is to determine whether the given filter is idempotent or not. Input The input consists of multiple datasets. The number of dataset is less than $100$. Each dataset is a string representing a filter and has the following format (without spaces between digits). > $c_0c_1\cdots{}c_{127}$ $c_i$ is either '0' (represents black) or '1' (represents white), which indicates the output of the filter for a pixel when the binary representation of the pixel and its neighboring six pixels is $i$. The mapping from the pixels to the bits is as following: <image> and the binary representation $i$ is defined as $i = \sum_{j=0}^6{\mathit{bit}_j \times 2^j}$, where $\mathit{bit}_j$ is $0$ or $1$ if the corresponding pixel is in black or white, respectively. Note that the filter is applied on the center pixel, denoted as bit 3. The input ends with a line that contains only a single "#". Output For each dataset, print "yes" in a line if the given filter is idempotent, or "no" otherwise (quotes are for clarity). Sample Input 00000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000111111111 10000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000011111111 01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101 Output for the Sample Input yes yes no Example Input 00000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000111111111 10000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000011111111 01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101 # Output yes yes no Submitted Solution: ``` import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools sys.setrecursionlimit(10**7) inf = 10**20 eps = 1.0 / 10**10 mod = 10**9+7 dd = [(-1,0),(0,1),(1,0),(0,-1)] ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)] def LI(): return [int(x) for x in sys.stdin.readline().split()] def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()] def LF(): return [float(x) for x in sys.stdin.readline().split()] def LS(): return sys.stdin.readline().split() def I(): return int(sys.stdin.readline()) def F(): return float(sys.stdin.readline()) def S(): return input() def pf(s): return print(s, flush=True) # 18 # 17 16 # 15 06 14 # 05 04 # 13 03 12 # 02 01 # 11 00 10 # 09 08 # 07 def main(): rr = [] tt = [ [3, 0, 2, 5, 6, 4, 1], [0, 7, 9, 2, 3, 1, 8], [2, 9, 11, 13, 5, 3, 0], [5, 2, 13 ,15, 17, 6, 3], [6, 3, 5, 17, 18, 16, 4], [4, 1, 3, 6, 16, 14, 12], [1, 8, 0, 3, 4, 12, 10] ] while True: s = S() if s == '#': break fil = int(s[::-1], 2) ii = [2**i for i in range(128)] m = {} def u(a): key = tuple(a) if key in m: return m[key] t = 0 for i in range(7): if a[i]: t |= ii[tt[0][i]] if fil & ii[t]: m[key] = 1 return 1 m[key] = 0 return 0 f = True for k in range(ii[19]): # if k % ii[17] == 0: # print(k) a = [1 if k & ii[i] else 0 for i in range(19)] b = [u(list(map(lambda x: a[x], ta))) for ta in tt] if u(b) != b[0]: # print('false', a, b, u(b)) f = False break if f: rr.append('yes') else: rr.append('no') # print(rr) return '\n'.join(rr) print(main()) ```
instruction
0
63,111
7
126,222
No
output
1
63,111
7
126,223
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A state with $n$ flags of ON or OFF can be represented by a sequence of bits where $0, 1, ..., n-1$ -th flag corresponds to 1 (ON) or 0 (OFF). The state can be managed by the corresponding decimal integer, because the sequence of bits is a binary representation where each bit is 0 or 1. Given a sequence of bits with 64 flags which represent a state, perform the following operations. Note that each flag of the bits is initialized by OFF. * test(i): Print 1 if $i$-th flag is ON, otherwise 0 * set(i): Set $i$-th flag to ON * clear(i): Set $i$-th flag to OFF * flip(i): Inverse $i$-th flag * all: Print 1 if all flags are ON, otherwise 0 * any: Print 1 if at least one flag is ON, otherwise 0 * none: Print 1 if all flags are OFF, otherwise 0 * count: Print the number of ON flags * val: Print the decimal value of the state Constraints * $1 \leq q \leq 200,000$ * $0 \leq i < 64$ Input The input is given in the following format. $q$ $query_1$ $query_2$ : $query_q$ Each query $query_i$ is given in the following format: 0 $i$ or 1 $i$ or 2 $i$ or 3 $i$ or 4 or 5 or 6 or 7 or 8 The first digit 0, 1,...,8 represents the operation test(i), set(i), clear(i), flip(i), all, any, none, count or val respectively. Output Print the result in a line for each test, all, any, none, count and val operation. Example Input 14 1 0 1 1 1 2 2 1 0 0 0 1 0 2 0 3 3 3 4 5 6 7 8 Output 1 0 1 0 0 1 0 3 13 Submitted Solution: ``` import sys class BitFlag: ALL_ON = 0xffffffffffffffff ALL_OFF = 0x0000000000000000 def __init__(self): self.FLAGS = self.ALL_OFF self.Masks = [1 << i for i in range(64)] def _test(self, i): return self.FLAGS & self.Masks[i] != 0b00 def _set(self, i): self.FLAGS |= self.Masks[i] def _clear(self, i): self.FLAGS &= ~self.Masks[i] def _flip(self, i): self.FLAGS ^= self.Masks[i] def _all(self): return self.FLAGS & self.ALL_ON == self.ALL_ON def _any(self): return self.FLAGS & self.ALL_ON != self.ALL_OFF def _none(self): return self.FLAGS & self.ALL_ON == self.ALL_OFF def _count(self): return bin(self.FLAGS).count('1') def _val(self): return self.FLAGS bf = BitFlag() commands = {'0': bf._test, '1': bf._set, '2': bf._clear, '3': bf._flip, '4': bf._all, '5': bf._any, '6': bf._none, '7': bf._count, '8': bf._val } qn = int(input()) lines = sys.stdin.readlines() ans = [None] * qn for i in range(qn): q, *arg = lines[i].split() if len(arg): ans[i] = commands[q](int(arg[0])) else: ans[i] = commands[q]() [print(int(x)) for x in ans if x is not None] ```
instruction
0
63,151
7
126,302
Yes
output
1
63,151
7
126,303
Provide tags and a correct Python 3 solution for this coding contest problem. In this task Anna and Maria play the following game. Initially they have a checkered piece of paper with a painted n × m rectangle (only the border, no filling). Anna and Maria move in turns and Anna starts. During each move one should paint inside the last-painted rectangle a new lesser rectangle (along the grid lines). The new rectangle should have no common points with the previous one. Note that when we paint a rectangle, we always paint only the border, the rectangles aren't filled. Nobody wins the game — Anna and Maria simply play until they have done k moves in total. Count the number of different ways to play this game. Input The first and only line contains three integers: n, m, k (1 ≤ n, m, k ≤ 1000). Output Print the single number — the number of the ways to play the game. As this number can be very big, print the value modulo 1000000007 (109 + 7). Examples Input 3 3 1 Output 1 Input 4 4 1 Output 9 Input 6 7 2 Output 75 Note Two ways to play the game are considered different if the final pictures are different. In other words, if one way contains a rectangle that is not contained in the other way. In the first sample Anna, who performs her first and only move, has only one possible action plan — insert a 1 × 1 square inside the given 3 × 3 square. In the second sample Anna has as much as 9 variants: 4 ways to paint a 1 × 1 square, 2 ways to insert a 1 × 2 rectangle vertically, 2 more ways to insert it horizontally and one more way is to insert a 2 × 2 square.
instruction
0
63,257
7
126,514
Tags: combinatorics, dp Correct Solution: ``` MOD = 10 ** 9 + 7 def egcd(a, b): if a == 0: return (b, 0, 1) else: g, y, x = egcd(b % a, a) return (g, x - (b // a) * y, y) def modinv(a, m): g, x, y = egcd(a, m) if g != 1: raise Exception('modular inverse does not exist') else: return x % m def combination(n,k,MOD): if n < k or k < 0: return 0 ans = 1 for i in range(n - k + 1, n + 1): ans *= i ans %= MOD for i in range(1,k+1): ans *= modinv(i,MOD) ans %= MOD return ans n,m,k = map(int,input().split()) print(combination(n-1,n-2 * k-1,MOD) * combination(m-1,m - 2 * k - 1,MOD) % MOD) ```
output
1
63,257
7
126,515
Provide tags and a correct Python 3 solution for this coding contest problem. In this task Anna and Maria play the following game. Initially they have a checkered piece of paper with a painted n × m rectangle (only the border, no filling). Anna and Maria move in turns and Anna starts. During each move one should paint inside the last-painted rectangle a new lesser rectangle (along the grid lines). The new rectangle should have no common points with the previous one. Note that when we paint a rectangle, we always paint only the border, the rectangles aren't filled. Nobody wins the game — Anna and Maria simply play until they have done k moves in total. Count the number of different ways to play this game. Input The first and only line contains three integers: n, m, k (1 ≤ n, m, k ≤ 1000). Output Print the single number — the number of the ways to play the game. As this number can be very big, print the value modulo 1000000007 (109 + 7). Examples Input 3 3 1 Output 1 Input 4 4 1 Output 9 Input 6 7 2 Output 75 Note Two ways to play the game are considered different if the final pictures are different. In other words, if one way contains a rectangle that is not contained in the other way. In the first sample Anna, who performs her first and only move, has only one possible action plan — insert a 1 × 1 square inside the given 3 × 3 square. In the second sample Anna has as much as 9 variants: 4 ways to paint a 1 × 1 square, 2 ways to insert a 1 × 2 rectangle vertically, 2 more ways to insert it horizontally and one more way is to insert a 2 × 2 square.
instruction
0
63,258
7
126,516
Tags: combinatorics, dp Correct Solution: ``` import time def Binc(bcs, n, k): if (k > n): return 0 if k > n // 2: k = n - k if k == 0: return 1 if k == 1: return n while len(bcs) < n - 3: for i in range(len(bcs), n - 3): r = [] for j in range(2, i // 2 + 3): r.append(Binc(bcs, i + 3, j - 1) + Binc(bcs, i + 3, j)) bcs.append(r) r = bcs[n - 4] if len(r) < k - 1: for i in range(len(r), k - 1): r.append(Binc(bcs, n - 1, k - 1) + Binc(bcs, n - 1, k)) return bcs[n - 4][k - 2] bcs = [] bcs_ = [] mod_ = 1000000007 n, m, k = map(int, input().split()) nk = Binc(bcs, n - 1, 2*k) % mod_ mk = Binc(bcs_, m - 1, 2*k) % mod_ print((nk * mk) % mod_) ```
output
1
63,258
7
126,517
Provide tags and a correct Python 3 solution for this coding contest problem. In this task Anna and Maria play the following game. Initially they have a checkered piece of paper with a painted n × m rectangle (only the border, no filling). Anna and Maria move in turns and Anna starts. During each move one should paint inside the last-painted rectangle a new lesser rectangle (along the grid lines). The new rectangle should have no common points with the previous one. Note that when we paint a rectangle, we always paint only the border, the rectangles aren't filled. Nobody wins the game — Anna and Maria simply play until they have done k moves in total. Count the number of different ways to play this game. Input The first and only line contains three integers: n, m, k (1 ≤ n, m, k ≤ 1000). Output Print the single number — the number of the ways to play the game. As this number can be very big, print the value modulo 1000000007 (109 + 7). Examples Input 3 3 1 Output 1 Input 4 4 1 Output 9 Input 6 7 2 Output 75 Note Two ways to play the game are considered different if the final pictures are different. In other words, if one way contains a rectangle that is not contained in the other way. In the first sample Anna, who performs her first and only move, has only one possible action plan — insert a 1 × 1 square inside the given 3 × 3 square. In the second sample Anna has as much as 9 variants: 4 ways to paint a 1 × 1 square, 2 ways to insert a 1 × 2 rectangle vertically, 2 more ways to insert it horizontally and one more way is to insert a 2 × 2 square.
instruction
0
63,259
7
126,518
Tags: combinatorics, dp Correct Solution: ``` from sys import stdin, stdout, stderr, exit from math import log, factorial import re # inputf = open('input.txt', 'r') # outputf = open('output.txt', 'w') def readil(): return list(map(int, stdin.readline().strip().split())) def C(n, k): if(n-k >= 0): return factorial(n) // factorial(k) // factorial(n-k) else: return 0 def main(): n, m, k = readil() stdout.write(str((C(n - 1, 2 * k) * C(m - 1, 2 * k)) % 1000000007)) if __name__ == '__main__': main() # inputf.close() # outputf.close() ```
output
1
63,259
7
126,519
Provide tags and a correct Python 3 solution for this coding contest problem. In this task Anna and Maria play the following game. Initially they have a checkered piece of paper with a painted n × m rectangle (only the border, no filling). Anna and Maria move in turns and Anna starts. During each move one should paint inside the last-painted rectangle a new lesser rectangle (along the grid lines). The new rectangle should have no common points with the previous one. Note that when we paint a rectangle, we always paint only the border, the rectangles aren't filled. Nobody wins the game — Anna and Maria simply play until they have done k moves in total. Count the number of different ways to play this game. Input The first and only line contains three integers: n, m, k (1 ≤ n, m, k ≤ 1000). Output Print the single number — the number of the ways to play the game. As this number can be very big, print the value modulo 1000000007 (109 + 7). Examples Input 3 3 1 Output 1 Input 4 4 1 Output 9 Input 6 7 2 Output 75 Note Two ways to play the game are considered different if the final pictures are different. In other words, if one way contains a rectangle that is not contained in the other way. In the first sample Anna, who performs her first and only move, has only one possible action plan — insert a 1 × 1 square inside the given 3 × 3 square. In the second sample Anna has as much as 9 variants: 4 ways to paint a 1 × 1 square, 2 ways to insert a 1 × 2 rectangle vertically, 2 more ways to insert it horizontally and one more way is to insert a 2 × 2 square.
instruction
0
63,260
7
126,520
Tags: combinatorics, dp Correct Solution: ``` def inv(a): return pow(a, mod - 2, mod) n, m, k = map(int, input().split()) if (2 * k >= min(n, m)): print(0) exit() fact = [1] mod = 1000000007 for i in range(1, 2001): fact.append(fact[-1] * i % mod) print(fact[n - 1] * inv(fact[2 * k]) * inv(fact[n - 2 * k - 1]) * fact[m - 1] * inv(fact[2 * k]) * inv(fact[m - 2 * k - 1]) % mod) ```
output
1
63,260
7
126,521
Provide tags and a correct Python 3 solution for this coding contest problem. In this task Anna and Maria play the following game. Initially they have a checkered piece of paper with a painted n × m rectangle (only the border, no filling). Anna and Maria move in turns and Anna starts. During each move one should paint inside the last-painted rectangle a new lesser rectangle (along the grid lines). The new rectangle should have no common points with the previous one. Note that when we paint a rectangle, we always paint only the border, the rectangles aren't filled. Nobody wins the game — Anna and Maria simply play until they have done k moves in total. Count the number of different ways to play this game. Input The first and only line contains three integers: n, m, k (1 ≤ n, m, k ≤ 1000). Output Print the single number — the number of the ways to play the game. As this number can be very big, print the value modulo 1000000007 (109 + 7). Examples Input 3 3 1 Output 1 Input 4 4 1 Output 9 Input 6 7 2 Output 75 Note Two ways to play the game are considered different if the final pictures are different. In other words, if one way contains a rectangle that is not contained in the other way. In the first sample Anna, who performs her first and only move, has only one possible action plan — insert a 1 × 1 square inside the given 3 × 3 square. In the second sample Anna has as much as 9 variants: 4 ways to paint a 1 × 1 square, 2 ways to insert a 1 × 2 rectangle vertically, 2 more ways to insert it horizontally and one more way is to insert a 2 × 2 square.
instruction
0
63,261
7
126,522
Tags: combinatorics, dp Correct Solution: ``` from math import * n, m, k = map(int, input().split()) c = lambda n, k: 0 if k > n else factorial(n) // (factorial(k) * factorial(n - k)) print(c(n - 1, 2 * k) * c(m - 1, 2 * k) % 1000000007) ```
output
1
63,261
7
126,523
Provide tags and a correct Python 3 solution for this coding contest problem. In this task Anna and Maria play the following game. Initially they have a checkered piece of paper with a painted n × m rectangle (only the border, no filling). Anna and Maria move in turns and Anna starts. During each move one should paint inside the last-painted rectangle a new lesser rectangle (along the grid lines). The new rectangle should have no common points with the previous one. Note that when we paint a rectangle, we always paint only the border, the rectangles aren't filled. Nobody wins the game — Anna and Maria simply play until they have done k moves in total. Count the number of different ways to play this game. Input The first and only line contains three integers: n, m, k (1 ≤ n, m, k ≤ 1000). Output Print the single number — the number of the ways to play the game. As this number can be very big, print the value modulo 1000000007 (109 + 7). Examples Input 3 3 1 Output 1 Input 4 4 1 Output 9 Input 6 7 2 Output 75 Note Two ways to play the game are considered different if the final pictures are different. In other words, if one way contains a rectangle that is not contained in the other way. In the first sample Anna, who performs her first and only move, has only one possible action plan — insert a 1 × 1 square inside the given 3 × 3 square. In the second sample Anna has as much as 9 variants: 4 ways to paint a 1 × 1 square, 2 ways to insert a 1 × 2 rectangle vertically, 2 more ways to insert it horizontally and one more way is to insert a 2 × 2 square.
instruction
0
63,262
7
126,524
Tags: combinatorics, dp Correct Solution: ``` from math import factorial MOD = 1000000007 def c(n, k): if k > n: return 0 return factorial(n) //(factorial(k) * factorial(n - k)) n, m, k = map(int, input().split()) print ((c(n - 1, 2 * k) * c(m - 1, 2 * k)) % MOD) ```
output
1
63,262
7
126,525
Provide tags and a correct Python 3 solution for this coding contest problem. In this task Anna and Maria play the following game. Initially they have a checkered piece of paper with a painted n × m rectangle (only the border, no filling). Anna and Maria move in turns and Anna starts. During each move one should paint inside the last-painted rectangle a new lesser rectangle (along the grid lines). The new rectangle should have no common points with the previous one. Note that when we paint a rectangle, we always paint only the border, the rectangles aren't filled. Nobody wins the game — Anna and Maria simply play until they have done k moves in total. Count the number of different ways to play this game. Input The first and only line contains three integers: n, m, k (1 ≤ n, m, k ≤ 1000). Output Print the single number — the number of the ways to play the game. As this number can be very big, print the value modulo 1000000007 (109 + 7). Examples Input 3 3 1 Output 1 Input 4 4 1 Output 9 Input 6 7 2 Output 75 Note Two ways to play the game are considered different if the final pictures are different. In other words, if one way contains a rectangle that is not contained in the other way. In the first sample Anna, who performs her first and only move, has only one possible action plan — insert a 1 × 1 square inside the given 3 × 3 square. In the second sample Anna has as much as 9 variants: 4 ways to paint a 1 × 1 square, 2 ways to insert a 1 × 2 rectangle vertically, 2 more ways to insert it horizontally and one more way is to insert a 2 × 2 square.
instruction
0
63,263
7
126,526
Tags: combinatorics, dp Correct Solution: ``` from math import factorial n, m, k = map(int, input().split()) def combinacion(n, k): if k > n: return 0 return factorial(n)//(factorial(k)*factorial(n-k)) result = (combinacion(n-1, 2 * k) * combinacion(m-1, 2 * k)) % 1000000007 print(result) ```
output
1
63,263
7
126,527
Provide tags and a correct Python 3 solution for this coding contest problem. You have a card deck of n cards, numbered from top to bottom, i. e. the top card has index 1 and bottom card — index n. Each card has its color: the i-th card has color a_i. You should process q queries. The j-th query is described by integer t_j. For each query you should: * find the highest card in the deck with color t_j, i. e. the card with minimum index; * print the position of the card you found; * take the card and place it on top of the deck. Input The first line contains two integers n and q (2 ≤ n ≤ 3 ⋅ 10^5; 1 ≤ q ≤ 3 ⋅ 10^5) — the number of cards in the deck and the number of queries. The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 50) — the colors of cards. The third line contains q integers t_1, t_2, ..., t_q (1 ≤ t_j ≤ 50) — the query colors. It's guaranteed that queries ask only colors that are present in the deck. Output Print q integers — the answers for each query. Example Input 7 5 2 1 1 4 3 3 1 3 2 1 1 4 Output 5 2 3 1 5 Note Description of the sample: 1. the deck is [2, 1, 1, 4, \underline{3}, 3, 1] and the first card with color t_1 = 3 has position 5; 2. the deck is [3, \underline{2}, 1, 1, 4, 3, 1] and the first card with color t_2 = 2 has position 2; 3. the deck is [2, 3, \underline{1}, 1, 4, 3, 1] and the first card with color t_3 = 1 has position 3; 4. the deck is [\underline{1}, 2, 3, 1, 4, 3, 1] and the first card with color t_4 = 1 has position 1; 5. the deck is [1, 2, 3, 1, \underline{4}, 3, 1] and the first card with color t_5 = 4 has position 5.
instruction
0
63,370
7
126,740
Tags: brute force, data structures, implementation, trees Correct Solution: ``` import sys from collections import deque def read_ints(): return [int(i) for i in sys.stdin.readline().strip().split()] def read_int(): return int(sys.stdin.readline().strip()) def rfind(seq, el): # distance from end, zero is last element for i, e in enumerate(seq[::-1]): if e == el: return i tops = [-1] * 51 # position of the top card of each colour (0-indexed) n, q = read_ints() ns = read_ints() qs = read_ints() for i, col in enumerate(ns): if tops[col] == -1: tops[col] = i #print(tops) small_deck = [] found = set() results = [] for col in qs: if col in found: # check small deck pos = rfind(small_deck, col) idx = len(small_deck) - pos - 1 small_deck = small_deck[:idx] + small_deck[idx+1:] + [col] results.append(pos + 1) else: # top card in the big deck pos = tops[col] found.add(col) small_deck.append(col) for i in range(51): if tops[i] < pos: tops[i] += 1 results.append(pos + 1) #print("small deck: ", small_deck) #print("found: ", found) print(" ".join(str(i) for i in results)) ```
output
1
63,370
7
126,741
Provide tags and a correct Python 3 solution for this coding contest problem. You have a card deck of n cards, numbered from top to bottom, i. e. the top card has index 1 and bottom card — index n. Each card has its color: the i-th card has color a_i. You should process q queries. The j-th query is described by integer t_j. For each query you should: * find the highest card in the deck with color t_j, i. e. the card with minimum index; * print the position of the card you found; * take the card and place it on top of the deck. Input The first line contains two integers n and q (2 ≤ n ≤ 3 ⋅ 10^5; 1 ≤ q ≤ 3 ⋅ 10^5) — the number of cards in the deck and the number of queries. The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 50) — the colors of cards. The third line contains q integers t_1, t_2, ..., t_q (1 ≤ t_j ≤ 50) — the query colors. It's guaranteed that queries ask only colors that are present in the deck. Output Print q integers — the answers for each query. Example Input 7 5 2 1 1 4 3 3 1 3 2 1 1 4 Output 5 2 3 1 5 Note Description of the sample: 1. the deck is [2, 1, 1, 4, \underline{3}, 3, 1] and the first card with color t_1 = 3 has position 5; 2. the deck is [3, \underline{2}, 1, 1, 4, 3, 1] and the first card with color t_2 = 2 has position 2; 3. the deck is [2, 3, \underline{1}, 1, 4, 3, 1] and the first card with color t_3 = 1 has position 3; 4. the deck is [\underline{1}, 2, 3, 1, 4, 3, 1] and the first card with color t_4 = 1 has position 1; 5. the deck is [1, 2, 3, 1, \underline{4}, 3, 1] and the first card with color t_5 = 4 has position 5.
instruction
0
63,371
7
126,742
Tags: brute force, data structures, implementation, trees Correct Solution: ``` import os,sys;from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno();self.buffer = BytesIO();self.writable = "x" in file.mode or "r" not in file.mode;self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b:break ptr = self.buffer.tell();self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0:b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE));self.newlines = b.count(b"\n") + (not b);ptr = self.buffer.tell();self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable:os.write(self._fd, self.buffer.getvalue());self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file);self.flush = self.buffer.flush;self.writable = self.buffer.writable;self.write = lambda s: self.buffer.write(s.encode("ascii"));self.read = lambda: self.buffer.read().decode("ascii");self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) try:sys.stdin,sys.stdout=open('in.txt','r'),open('out.txt','w') except:pass ii1=lambda:int(sys.stdin.readline().strip()) # for interger is1=lambda:sys.stdin.readline().strip() # for str iia=lambda:list(map(int,sys.stdin.readline().strip().split())) # for List[int] isa=lambda:sys.stdin.readline().strip().split() # for List[str] # mod=int(1e9 + 7);from collections import *;from math import * # abc = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' # sys.setrecursionlimit(500000) ###################### Start Here ###################### # from functools import lru_cache # from collections import defaultdict as dd from collections import deque,defaultdict from collections import deque as dq n,q = iia() arr = iia() query = iia() dq = [] first = defaultdict(int) for idx,v in enumerate(arr): if v not in first: first[v]=idx dq_map = defaultdict(int) ans = [] extra = 0 for q in query: if q not in dq_map: dq_map[q]=1 idx = first[q] dq.insert(0,q) for key,val in first.items(): if idx>val: first[key]+=1 ans.append(idx+1) else: for j in range(len(dq)): if dq[j] == q: val = dq.pop(j) ans.append(j+1) dq.insert(0,q) print(*ans) ```
output
1
63,371
7
126,743
Provide tags and a correct Python 3 solution for this coding contest problem. You have a card deck of n cards, numbered from top to bottom, i. e. the top card has index 1 and bottom card — index n. Each card has its color: the i-th card has color a_i. You should process q queries. The j-th query is described by integer t_j. For each query you should: * find the highest card in the deck with color t_j, i. e. the card with minimum index; * print the position of the card you found; * take the card and place it on top of the deck. Input The first line contains two integers n and q (2 ≤ n ≤ 3 ⋅ 10^5; 1 ≤ q ≤ 3 ⋅ 10^5) — the number of cards in the deck and the number of queries. The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 50) — the colors of cards. The third line contains q integers t_1, t_2, ..., t_q (1 ≤ t_j ≤ 50) — the query colors. It's guaranteed that queries ask only colors that are present in the deck. Output Print q integers — the answers for each query. Example Input 7 5 2 1 1 4 3 3 1 3 2 1 1 4 Output 5 2 3 1 5 Note Description of the sample: 1. the deck is [2, 1, 1, 4, \underline{3}, 3, 1] and the first card with color t_1 = 3 has position 5; 2. the deck is [3, \underline{2}, 1, 1, 4, 3, 1] and the first card with color t_2 = 2 has position 2; 3. the deck is [2, 3, \underline{1}, 1, 4, 3, 1] and the first card with color t_3 = 1 has position 3; 4. the deck is [\underline{1}, 2, 3, 1, 4, 3, 1] and the first card with color t_4 = 1 has position 1; 5. the deck is [1, 2, 3, 1, \underline{4}, 3, 1] and the first card with color t_5 = 4 has position 5.
instruction
0
63,372
7
126,744
Tags: brute force, data structures, implementation, trees Correct Solution: ``` n, q = [int(token) for token in input().split()] a = [int(token) for token in input().split()] t = [int(token) for token in input().split()] first_index_of_color = [-1 for i in range(50)] for i in range(n): if first_index_of_color[a[i] - 1] == -1: first_index_of_color[a[i] - 1] = i + 1 result = [] for current_t in t: current_t -= 1 answer_index = first_index_of_color[current_t] result.append(answer_index) for i in range(50): if first_index_of_color[i] < answer_index and first_index_of_color[i] != -1: first_index_of_color[i] += 1 elif first_index_of_color[i] == answer_index: first_index_of_color[i] = 1 print(*result) ```
output
1
63,372
7
126,745
Provide tags and a correct Python 3 solution for this coding contest problem. You have a card deck of n cards, numbered from top to bottom, i. e. the top card has index 1 and bottom card — index n. Each card has its color: the i-th card has color a_i. You should process q queries. The j-th query is described by integer t_j. For each query you should: * find the highest card in the deck with color t_j, i. e. the card with minimum index; * print the position of the card you found; * take the card and place it on top of the deck. Input The first line contains two integers n and q (2 ≤ n ≤ 3 ⋅ 10^5; 1 ≤ q ≤ 3 ⋅ 10^5) — the number of cards in the deck and the number of queries. The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 50) — the colors of cards. The third line contains q integers t_1, t_2, ..., t_q (1 ≤ t_j ≤ 50) — the query colors. It's guaranteed that queries ask only colors that are present in the deck. Output Print q integers — the answers for each query. Example Input 7 5 2 1 1 4 3 3 1 3 2 1 1 4 Output 5 2 3 1 5 Note Description of the sample: 1. the deck is [2, 1, 1, 4, \underline{3}, 3, 1] and the first card with color t_1 = 3 has position 5; 2. the deck is [3, \underline{2}, 1, 1, 4, 3, 1] and the first card with color t_2 = 2 has position 2; 3. the deck is [2, 3, \underline{1}, 1, 4, 3, 1] and the first card with color t_3 = 1 has position 3; 4. the deck is [\underline{1}, 2, 3, 1, 4, 3, 1] and the first card with color t_4 = 1 has position 1; 5. the deck is [1, 2, 3, 1, \underline{4}, 3, 1] and the first card with color t_5 = 4 has position 5.
instruction
0
63,373
7
126,746
Tags: brute force, data structures, implementation, trees Correct Solution: ``` # -*- coding: utf-8 -*- """ Created on Fri Apr 16 09:12:19 2021 @author: MridulSachdeva """ n, q = map(int, input().split()) s = list(map(int, input().split())) t = list(map(int, input().split())) ans = [] for i in range(q): index = s.index(t[i]) ans.append(index + 1) s[:index+1] = [t[i]] + s[:index] print(*ans) ```
output
1
63,373
7
126,747
Provide tags and a correct Python 3 solution for this coding contest problem. You have a card deck of n cards, numbered from top to bottom, i. e. the top card has index 1 and bottom card — index n. Each card has its color: the i-th card has color a_i. You should process q queries. The j-th query is described by integer t_j. For each query you should: * find the highest card in the deck with color t_j, i. e. the card with minimum index; * print the position of the card you found; * take the card and place it on top of the deck. Input The first line contains two integers n and q (2 ≤ n ≤ 3 ⋅ 10^5; 1 ≤ q ≤ 3 ⋅ 10^5) — the number of cards in the deck and the number of queries. The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 50) — the colors of cards. The third line contains q integers t_1, t_2, ..., t_q (1 ≤ t_j ≤ 50) — the query colors. It's guaranteed that queries ask only colors that are present in the deck. Output Print q integers — the answers for each query. Example Input 7 5 2 1 1 4 3 3 1 3 2 1 1 4 Output 5 2 3 1 5 Note Description of the sample: 1. the deck is [2, 1, 1, 4, \underline{3}, 3, 1] and the first card with color t_1 = 3 has position 5; 2. the deck is [3, \underline{2}, 1, 1, 4, 3, 1] and the first card with color t_2 = 2 has position 2; 3. the deck is [2, 3, \underline{1}, 1, 4, 3, 1] and the first card with color t_3 = 1 has position 3; 4. the deck is [\underline{1}, 2, 3, 1, 4, 3, 1] and the first card with color t_4 = 1 has position 1; 5. the deck is [1, 2, 3, 1, \underline{4}, 3, 1] and the first card with color t_5 = 4 has position 5.
instruction
0
63,374
7
126,748
Tags: brute force, data structures, implementation, trees Correct Solution: ``` from collections import deque n, q = list(map(int, input().split(" "))) colors = deque(list(map(int, input().split(" ")))) Qs = list(map(int, input().split(" "))) for i in Qs: ind = colors.index(i) print(ind + 1, end=' ') colors.remove(i) colors.appendleft(i) ```
output
1
63,374
7
126,749
Provide tags and a correct Python 3 solution for this coding contest problem. You have a card deck of n cards, numbered from top to bottom, i. e. the top card has index 1 and bottom card — index n. Each card has its color: the i-th card has color a_i. You should process q queries. The j-th query is described by integer t_j. For each query you should: * find the highest card in the deck with color t_j, i. e. the card with minimum index; * print the position of the card you found; * take the card and place it on top of the deck. Input The first line contains two integers n and q (2 ≤ n ≤ 3 ⋅ 10^5; 1 ≤ q ≤ 3 ⋅ 10^5) — the number of cards in the deck and the number of queries. The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 50) — the colors of cards. The third line contains q integers t_1, t_2, ..., t_q (1 ≤ t_j ≤ 50) — the query colors. It's guaranteed that queries ask only colors that are present in the deck. Output Print q integers — the answers for each query. Example Input 7 5 2 1 1 4 3 3 1 3 2 1 1 4 Output 5 2 3 1 5 Note Description of the sample: 1. the deck is [2, 1, 1, 4, \underline{3}, 3, 1] and the first card with color t_1 = 3 has position 5; 2. the deck is [3, \underline{2}, 1, 1, 4, 3, 1] and the first card with color t_2 = 2 has position 2; 3. the deck is [2, 3, \underline{1}, 1, 4, 3, 1] and the first card with color t_3 = 1 has position 3; 4. the deck is [\underline{1}, 2, 3, 1, 4, 3, 1] and the first card with color t_4 = 1 has position 1; 5. the deck is [1, 2, 3, 1, \underline{4}, 3, 1] and the first card with color t_5 = 4 has position 5.
instruction
0
63,375
7
126,750
Tags: brute force, data structures, implementation, trees Correct Solution: ``` n,q = map(int, input().split()) li = list(map(int, input().split())) d = {} cnt = 0 front = 0 qr = list(map(int, input().split())) for i in range(n): if li[i] not in d.keys(): d[li[i]] = i+1 # print(d) for i in qr: tmp = d[i] print(d[i],end=' ') d[i] = 0 for j in d: if d[j] < tmp: d[j] += 1 ```
output
1
63,375
7
126,751
Provide tags and a correct Python 3 solution for this coding contest problem. You have a card deck of n cards, numbered from top to bottom, i. e. the top card has index 1 and bottom card — index n. Each card has its color: the i-th card has color a_i. You should process q queries. The j-th query is described by integer t_j. For each query you should: * find the highest card in the deck with color t_j, i. e. the card with minimum index; * print the position of the card you found; * take the card and place it on top of the deck. Input The first line contains two integers n and q (2 ≤ n ≤ 3 ⋅ 10^5; 1 ≤ q ≤ 3 ⋅ 10^5) — the number of cards in the deck and the number of queries. The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 50) — the colors of cards. The third line contains q integers t_1, t_2, ..., t_q (1 ≤ t_j ≤ 50) — the query colors. It's guaranteed that queries ask only colors that are present in the deck. Output Print q integers — the answers for each query. Example Input 7 5 2 1 1 4 3 3 1 3 2 1 1 4 Output 5 2 3 1 5 Note Description of the sample: 1. the deck is [2, 1, 1, 4, \underline{3}, 3, 1] and the first card with color t_1 = 3 has position 5; 2. the deck is [3, \underline{2}, 1, 1, 4, 3, 1] and the first card with color t_2 = 2 has position 2; 3. the deck is [2, 3, \underline{1}, 1, 4, 3, 1] and the first card with color t_3 = 1 has position 3; 4. the deck is [\underline{1}, 2, 3, 1, 4, 3, 1] and the first card with color t_4 = 1 has position 1; 5. the deck is [1, 2, 3, 1, \underline{4}, 3, 1] and the first card with color t_5 = 4 has position 5.
instruction
0
63,376
7
126,752
Tags: brute force, data structures, implementation, trees Correct Solution: ``` def main(): n,q=map(int,input().split()) t=list(map(int,input().split())) queries=list(map(int,input().split())) for query in queries: ind=t.index(query) num=t[ind] t[1:ind+1]=t[:ind] t[0]=num print(ind+1,end=" ") main() ```
output
1
63,376
7
126,753
Provide tags and a correct Python 3 solution for this coding contest problem. You have a card deck of n cards, numbered from top to bottom, i. e. the top card has index 1 and bottom card — index n. Each card has its color: the i-th card has color a_i. You should process q queries. The j-th query is described by integer t_j. For each query you should: * find the highest card in the deck with color t_j, i. e. the card with minimum index; * print the position of the card you found; * take the card and place it on top of the deck. Input The first line contains two integers n and q (2 ≤ n ≤ 3 ⋅ 10^5; 1 ≤ q ≤ 3 ⋅ 10^5) — the number of cards in the deck and the number of queries. The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 50) — the colors of cards. The third line contains q integers t_1, t_2, ..., t_q (1 ≤ t_j ≤ 50) — the query colors. It's guaranteed that queries ask only colors that are present in the deck. Output Print q integers — the answers for each query. Example Input 7 5 2 1 1 4 3 3 1 3 2 1 1 4 Output 5 2 3 1 5 Note Description of the sample: 1. the deck is [2, 1, 1, 4, \underline{3}, 3, 1] and the first card with color t_1 = 3 has position 5; 2. the deck is [3, \underline{2}, 1, 1, 4, 3, 1] and the first card with color t_2 = 2 has position 2; 3. the deck is [2, 3, \underline{1}, 1, 4, 3, 1] and the first card with color t_3 = 1 has position 3; 4. the deck is [\underline{1}, 2, 3, 1, 4, 3, 1] and the first card with color t_4 = 1 has position 1; 5. the deck is [1, 2, 3, 1, \underline{4}, 3, 1] and the first card with color t_5 = 4 has position 5.
instruction
0
63,377
7
126,754
Tags: brute force, data structures, implementation, trees Correct Solution: ``` n, q = map(int, input().split()) ans = [0]*51 nums = list(map(int, input().split())) for i in range(n): a = nums[i] if not ans[a]: ans[a] = i+1 query = list(map(int, input().split())) for i in query: print(ans[i], end=' ') for j in range(51): if ans[j] < ans[i]: ans[j] += 1 ans[i] = 1 ```
output
1
63,377
7
126,755
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Like all children, Alesha loves New Year celebration. During the celebration he and his whole family dress up the fir-tree. Like all children, Alesha likes to play with garlands — chains consisting of a lightbulbs. Alesha uses a grid field sized n × m for playing. The rows of the field are numbered from 1 to n from the top to the bottom and columns are numbered from 1 to m from the left to the right. Alesha has k garlands which he places at the field. He does so in the way such that each lightbulb of each garland lies in the center of some cell in the field, and each cell contains at most one lightbulb. Of course lightbulbs, which are neighbours in some garland, appears in cells neighbouring by a side. <image> The example of garland placing. Each garland is turned off or turned on at any moment. If some garland is turned on then each of its lightbulbs is turned on, the same applies for garland turned off. Each lightbulb in the whole garland set is unique, and thus, being turned on, brings Alesha some pleasure, described by an integer value. Turned off lightbulbs don't bring Alesha any pleasure. Alesha can turn garlands on and off and wants to know the sum of pleasure value which the lightbulbs, placed in the centers of the cells in some rectangular part of the field, bring him. Initially all the garlands are turned on. Alesha is still very little and can't add big numbers. He extremely asks you to help him. Input The first line of the input contains three integers n, m and k (1 ≤ n, m, k ≤ 2000) — the number of field rows, the number of field columns and the number of garlands placed at the field respectively. Next lines contains garlands set description in the following format: The first line of a single garland description contains a single integer len (1 ≤ len ≤ 2000) — the number of lightbulbs in the garland. Each of the next len lines contains three integers i, j and w (1 ≤ i ≤ n, 1 ≤ j ≤ m, 1 ≤ w ≤ 109) — the coordinates of the cell containing a lightbullb and pleasure value Alesha gets from it if it is turned on. The lightbulbs are given in the order they are forming a chain in the garland. It is guaranteed that neighbouring lightbulbs are placed in the cells neighbouring by a side. The next line contains single integer q (1 ≤ q ≤ 106) — the number of events in Alesha's game. The next q lines describes events in chronological order. The i-th of them describes the i-th event in the one of the following formats: * SWITCH i — Alesha turns off i-th garland if it is turned on, or turns it on if it is turned off. It is guaranteed that 1 ≤ i ≤ k. * ASK x1 y1 x2 y2 — Alesha wants to know the sum of pleasure values the lightbulbs, placed in a rectangular part of the field. Top-left cell of a part has coordinates (x1, y1) and right-bottom cell has coordinates (x2, y2). It is guaranteed that 1 ≤ x1 ≤ x2 ≤ n and 1 ≤ y1 ≤ y2 ≤ m. There is no more than 2000 events of this type in the input. All the numbers in the input are integers. Please note that the input is quite large, so be careful while using some input ways. In particular, it's not recommended to use cin in codes on C++ and class Scanner in codes on Java. Output For each ASK operation print the sum Alesha wants to know in a separate line. Print the answers in chronological order. Examples Input 4 4 3 5 1 1 2 1 2 3 2 2 1 2 1 4 3 1 7 4 1 3 1 2 3 3 2 4 3 1 4 1 7 4 1 1 4 2 9 3 2 8 3 3 3 4 3 4 4 4 1 3 4 1 2 ASK 2 2 3 3 ASK 1 1 4 4 Output 15 52 Input 4 4 1 8 4 1 1 3 1 2 2 1 1 1 1 7 1 2 5 2 2 4 2 3 1 1 3 1 3 ASK 1 1 3 2 SWITCH 1 ASK 1 1 3 2 Output 19 0 Note <image> This image illustrates the first sample case. Submitted Solution: ``` import sys import collections n, m, q = map(int, str.split(sys.stdin.readline())) shelve = collections.ChainMap(collections.defaultdict(int)) shelve["count"] = 0 for _ in range(q): shelve = shelve.new_child() op, *args = map(int, str.split(sys.stdin.readline())) args = tuple(args) if op == 1: if not shelve[args]: shelve[args] = 1 shelve["count"] += 1 elif op == 2: if shelve[args]: shelve[args] = 0 shelve["count"] -= 1 elif op == 3: for j in range(1, m + 1): index = args[0], j if shelve[index]: shelve["count"] -= 1 else: shelve["count"] += 1 shelve[index] ^= 1 elif op == 4: previous = collections.ChainMap(*shelve.maps[-args[0] - 1:]) for index, value in previous.items(): shelve[index] = value sys.stdout.write(str.format("{}\n", shelve["count"])) ```
instruction
0
63,576
7
127,152
No
output
1
63,576
7
127,153
Provide tags and a correct Python 3 solution for this coding contest problem. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2
instruction
0
63,704
7
127,408
Tags: bitmasks, brute force, implementation Correct Solution: ``` N = int(input()) a = [0,1] * N a2 = [1,0] * N pt1 = [] pt2 = [] cnt = 0 for j in range(N): arr = input() for k in range(N): if j % 2 == 1 and int(arr[k]) == a2[k]: cnt += 1 elif j % 2 == 0 and int(arr[k]) == a[k]: cnt += 1 pt1.append(cnt) pt2.append(N*N-cnt) cnt = 0 s = input() for j in range(N): arr = input() for k in range(N): if j % 2 == 1 and int(arr[k]) == a2[k]: cnt += 1 elif j % 2 == 0 and int(arr[k]) == a[k]: cnt += 1 pt1.append(cnt) pt2.append(N*N-cnt) s = input() cnt = 0 for j in range(N): arr = input() for k in range(N): if j % 2 == 1 and int(arr[k]) == a2[k]: cnt += 1 elif j % 2 == 0 and int(arr[k]) == a[k]: cnt += 1 pt1.append(cnt) pt2.append(N*N-cnt) s = input() cnt = 0 for j in range(N): arr = input() for k in range(N): if j % 2 == 1 and int(arr[k]) == a2[k]: cnt += 1 elif j % 2 == 0 and int(arr[k]) == a[k]: cnt += 1 pt1.append(cnt) pt2.append(N*N-cnt) pt1.sort() pt2.sort() print(pt1[0]+pt1[1]+pt2[0]+pt2[1]) ```
output
1
63,704
7
127,409
Provide tags and a correct Python 3 solution for this coding contest problem. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2
instruction
0
63,705
7
127,410
Tags: bitmasks, brute force, implementation Correct Solution: ``` import math from decimal import Decimal def na(): n = int(input()) b = [int(x) for x in input().split()] return n,b def nab(): n = int(input()) b = [int(x) for x in input().split()] c = [int(x) for x in input().split()] return n,b,c def dv(): n, m = map(int, input().split()) return n,m def dva(): n, m = map(int, input().split()) a = [int(x) for x in input().split()] b = [int(x) for x in input().split()] return n,m,b def eratosthenes(n): sieve = list(range(n + 1)) for i in sieve: if i > 1: for j in range(i + i, len(sieve), i): sieve[j] = 0 return sorted(set(sieve)) def nm(): n = int(input()) b = [int(x) for x in input().split()] m = int(input()) c = [int(x) for x in input().split()] return n,b,m,c def dvs(): n = int(input()) m = int(input()) return n, m n = int(input()) d = [0] * 4 for i in range(4): for j in range(n): s = input() for k in range(n): if (k + j) % 2 == 0: if s[k] == '1': d[i] += 1 else: if s[k] == '0': d[i] += 1 if i < 3: input() dop = n * n d = sorted(d) ans = dop * 2 + d[0] + d[1] - d[2] - d[3] print(ans) ```
output
1
63,705
7
127,411
Provide tags and a correct Python 3 solution for this coding contest problem. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2
instruction
0
63,706
7
127,412
Tags: bitmasks, brute force, implementation Correct Solution: ``` n = int(input()) l = list() for i in range(4): l.append([list(input()) for x in range(n)]) if i < 3: input() lt = [0, 0, 0, 0] min_f = (n * 2) ** 2 for i in range(1, 4): ll = [1, 2, 3] lt[1] = ll.pop(i - 1) for x in range(2): lb = list() lt[2] = ll[x] lt[3] = ll[x - 1] for y in range(n * 2): if y < n: lb.append(list(map(int, l[lt[0]][y % n] + l[lt[1]][y % n]))) else: lb.append(list(map(int, l[lt[2]][y % n] + l[lt[3]][y % n]))) for y in range(2): f = 0 for y1 in range(n * 2): for x1 in range(n * 2): if (x1 + y1) % 2: if lb[y1][x1] != y: f += 1 else: if lb[y1][x1] == y: f += 1 if f < min_f: min_f = f print(min_f) ```
output
1
63,706
7
127,413
Provide tags and a correct Python 3 solution for this coding contest problem. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2
instruction
0
63,707
7
127,414
Tags: bitmasks, brute force, implementation Correct Solution: ``` n=int(input()) s1="" s2="" for i in range(0,n): s1+=str(i%2) s2+=str((i+1)%2) a=[] for i in range(0,7): b=0 if i%2==0: for j in range(0,n): s=input() if j%2==0: for k in range(0,n): if s1[k]!=s[k]: b+=1 else: for k in range(0,n): if s2[k]!=s[k]: b+=1 a.append(b) a.append(n*n-b) else: x=input() print(min(a[0]+a[2]+a[5]+a[7],a[0]+a[3]+a[4]+a[7],a[0]+a[3]+a[5]+a[6],a[1]+a[2]+a[4]+a[7],a[1]+a[2]+a[5]+a[6],a[1]+a[3]+a[4]+a[6])) ```
output
1
63,707
7
127,415
Provide tags and a correct Python 3 solution for this coding contest problem. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2
instruction
0
63,708
7
127,416
Tags: bitmasks, brute force, implementation Correct Solution: ``` import sys n=int(input()) M=[['0' for k in range(n)]for _ in range(n)] L=[['0' for k in range(n)]for _ in range(n)] for i in range(n): for j in range(n): if j%2==i%2: M[i][j]='1' for i in range(n): for j in range(n): if j%2!=i%2: L[i][j]='1' def test(K): m=0 for i in range(n): for j in range(n): if M[i][j]!=K[i][j]: m+=1 return m A=[] for _ in range(4): K=[] for i in range(n): K.append(list(input())) f=sys.stdin.readline() A.append(test(K)) mini=100000 a=min(A[0]+A[1]+2*n*n-A[2]-A[3],A[0]+A[2]+2*n*n-A[1]-A[3],A[0]+A[3]+2*n*n-A[2]-A[1]) b=min(A[1]+A[2]+2*n*n-A[0]-A[3],A[1]+A[3]+2*n*n-A[2]-A[0]) c=A[2]+A[3]+2*n*n-A[1]-A[0] mini=min(a,b,c) print(mini) ```
output
1
63,708
7
127,417
Provide tags and a correct Python 3 solution for this coding contest problem. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2
instruction
0
63,709
7
127,418
Tags: bitmasks, brute force, implementation Correct Solution: ``` def read_data(): n = int(input().strip()) pieces = [] for j in range(4): a = [] for i in range(n): a.append(input().strip()) if j<3: input().strip() pieces.append(a) return n, pieces def solve(): counts = [] for piece in pieces: cur = 0 sum = 0 for i in range(n): for j in range(n): if ord(piece[i][j])-48 == cur: sum += 1 cur += 1 cur %= 2 counts.append(sum) max= n*n counts.sort() sum = 0 for i in range(4): if i < 2: sum += counts[i] else: sum += max - counts[i] return sum n, pieces = read_data() print(solve()) ```
output
1
63,709
7
127,419
Provide tags and a correct Python 3 solution for this coding contest problem. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2
instruction
0
63,710
7
127,420
Tags: bitmasks, brute force, implementation Correct Solution: ``` n = int(input()) p = [0] * 4 for k in range(4): for i in range(n): s = input() for j in range(n): if int(s[j]) != (i + j) % 2: p[k] += 1 if k < 3: input() p.sort() print(p[0] + p[1] + 2*n*n - p[2] - p[3]) ```
output
1
63,710
7
127,421
Provide tags and a correct Python 3 solution for this coding contest problem. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2
instruction
0
63,711
7
127,422
Tags: bitmasks, brute force, implementation Correct Solution: ``` ## necessary imports import sys input = sys.stdin.readline #from math import ceil, floor, factorial; # swap_array function def swaparr(arr, a,b): temp = arr[a]; arr[a] = arr[b]; arr[b] = temp ## gcd function def gcd(a,b): if b == 0: return a return gcd(b, a % b); ## nCr function efficient using Binomial Cofficient def nCr(n, k): if(k > n - k): k = n - k res = 1 for i in range(k): res = res * (n - i) res = res / (i + 1) return int(res) ## upper bound function code -- such that e in a[:i] e < x; def upper_bound(a, x, lo=0): hi = len(a) while lo < hi: mid = (lo+hi)//2 if a[mid] < x: lo = mid+1 else: hi = mid return lo ## prime factorization def primefs(n): ## if n == 1 ## calculating primes primes = {} while(n%2 == 0 and n > 0): primes[2] = primes.get(2, 0) + 1 n = n//2 for i in range(3, int(n**0.5)+2, 2): while(n%i == 0 and n > 0): primes[i] = primes.get(i, 0) + 1 n = n//i if n > 2: primes[n] = primes.get(n, 0) + 1 ## prime factoriazation of n is stored in dictionary ## primes and can be accesed. O(sqrt n) return primes ## MODULAR EXPONENTIATION FUNCTION def power(x, y, p): res = 1 x = x % p if (x == 0) : return 0 while (y > 0) : if ((y & 1) == 1) : res = (res * x) % p y = y >> 1 x = (x * x) % p return res ## DISJOINT SET UNINON FUNCTIONS def swap(a,b): temp = a a = b b = temp return a,b # find function with path compression included (recursive) # def find(x, link): # if link[x] == x: # return x # link[x] = find(link[x], link); # return link[x]; # find function with path compression (ITERATIVE) def find(x, link): p = x; while( p != link[p]): p = link[p]; while( x != p): nex = link[x]; link[x] = p; x = nex; return p; # the union function which makes union(x,y) # of two nodes x and y def union(x, y, link, size): x = find(x, link) y = find(y, link) if size[x] < size[y]: x,y = swap(x,y) if x != y: size[x] += size[y] link[y] = x ## returns an array of boolean if primes or not USING SIEVE OF ERATOSTHANES def sieve(n): prime = [True for i in range(n+1)] p = 2 while (p * p <= n): if (prime[p] == True): for i in range(p * p, n+1, p): prime[i] = False p += 1 return prime #### PRIME FACTORIZATION IN O(log n) using Sieve #### MAXN = int(1e6 + 5) def spf_sieve(): spf[1] = 1; for i in range(2, MAXN): spf[i] = i; for i in range(4, MAXN, 2): spf[i] = 2; for i in range(3, ceil(MAXN ** 0.5), 2): if spf[i] == i: for j in range(i*i, MAXN, i): if spf[j] == j: spf[j] = i; ## function for storing smallest prime factors (spf) in the array ################## un-comment below 2 lines when using factorization ################# # spf = [0 for i in range(MAXN)] # spf_sieve() def factoriazation(x): ret = {}; while x != 1: ret[spf[x]] = ret.get(spf[x], 0) + 1; x = x//spf[x] return ret ## this function is useful for multiple queries only, o/w use ## primefs function above. complexity O(log n) ## taking integer array input def int_array(): return list(map(int, input().strip().split())) ## taking string array input def str_array(): return input().strip().split(); #defining a couple constants MOD = int(1e9)+7; CMOD = 998244353; INF = float('inf'); NINF = -float('inf'); ################### ---------------- TEMPLATE ENDS HERE ---------------- ################### n = int(input()); board = []; for _ in range(4): mine = []; for i in range(n): mine.append(list(input().strip())); board.append(mine); if _ != 3: literally_useless = input().strip(); one = [['0' for _ in range(n)] for __ in range(n)]; zero = [['1' for _ in range(n)] for __ in range(n)]; for i in range(n): for j in range(n): if (i + j) & 1: one[i][j] = '1'; zero[i][j] = '0'; one_d = []; zero_d = []; for i in range(4): count_one = 0; count_zero = 0; for j in range(n): for k in range(n): if board[i][j][k] != one[j][k]: count_one += 1; if board[i][j][k] != zero[j][k]: count_zero += 1; one_d.append(count_one); zero_d.append(count_zero); ans = INF; for i in range(4): for j in range(4): if i == j: continue; this = [0, 1, 2, 3]; this.remove(i); this.remove(j); kaguya = one_d[i] + one_d[j] + zero_d[this[0]] + zero_d[this[1]]; ans = min(ans, kaguya); print(ans); ```
output
1
63,711
7
127,423
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2 Submitted Solution: ``` n=int(input()) l=[] for i in range(4): l.append(0) for q in range(4): for i in range(1,n+1): s=input() for j in range(1,n+1): if i%2==j%2 and s[j-1]=='1': l[q]+=1 if i%2!=j%2 and s[j-1]=='0': l[q]+=1 if q<3: z=input() #print(l) l.sort() n2=n**2 count=0 count+=l[0]+l[1] count+=2*n2-l[2]-l[3] print(count) ```
instruction
0
63,712
7
127,424
Yes
output
1
63,712
7
127,425
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2 Submitted Solution: ``` n=int(input()) a1=[] for i in range(n): a=str(input()) a=list(a) a1.append(a) x1=str(input()) a2=[] for i in range(n): a=str(input()) a=list(a) a2.append(a) x1=str(input()) a3=[] for i in range(n): a=str(input()) a=list(a) a3.append(a) x1=str(input()) a4=[] for i in range(n): a=str(input()) a=list(a) a4.append(a) ab=[] ab.append(a1) ab.append(a2) ab.append(a3) ab.append(a4) x=[] one=[] for i in range(n): z=[] for j in range(n): if((i+j)%2==0): z.append('1') else: z.append('0') one.append(z) two=[] for i in range(n): z=[] for j in range(n): if((i+j)%2==0): z.append('0') else: z.append('1') two.append(z) for i in range(4): e1=0 o1=0 for j in range(n): for k in range(n): if(ab[i][j][k]!=one[j][k]): e1+=1 if(ab[i][j][k]!=two[j][k]): o1+=1 x.append([e1,o1]) s=x[0][0]+x[1][1]+x[2][0]+x[3][1] if(x[0][0]+x[1][0]+x[2][1]+x[3][1]<s): s=x[0][0]+x[1][0]+x[2][1]+x[3][1] if(x[0][0]+x[1][1]+x[2][1]+x[3][0]<s): s=x[0][0]+x[1][1]+x[2][1]+x[3][0] if(x[0][1]+x[1][0]+x[2][1]+x[3][0]<s): s=x[0][1]+x[1][0]+x[2][1]+x[3][0] if(x[0][1]+x[1][1]+x[2][0]+x[3][0]<s): s=x[0][1]+x[1][1]+x[2][0]+x[3][0] if(x[0][1]+x[1][0]+x[2][0]+x[3][1]<s): s=x[0][1]+x[1][0]+x[2][0]+x[3][1] print(s) ```
instruction
0
63,713
7
127,426
Yes
output
1
63,713
7
127,427
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2 Submitted Solution: ``` from itertools import permutations n = int(input()) p1, _, p2, _, p3, _, p4 = [input() for _ in range(n)], input(), [input() for _ in range(n)], input(), [input() for _ in range(n)], input(), [input() for _ in range(n)] def count(a,b,c,d): board = [a[i] + b[i] for i in range(n)] + [c[i] + d[i] for i in range(n)] res = 0 for i in range(2*n): for j in range(2*n): clr = '1' if (i+j)%2 == 0 else '0' res += board[i][j] != clr return res print(min(count(*p) for p in permutations([p1, p2, p3, p4]))) ```
instruction
0
63,714
7
127,428
Yes
output
1
63,714
7
127,429
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2 Submitted Solution: ``` n = int(input()) vs = [0]*4 for i in range(4): w=v=0 for _ in range(n): for k in input(): w^=1 if w==int(k): v+=1 vs[i]=v if i < 3: input() base = 2*n**2+sum(vs) minv = 4*n**2 for i in range(4): for j in range(i+1,4): minv = min(minv, base-2*(vs[i]+vs[j])) print(minv) ```
instruction
0
63,715
7
127,430
Yes
output
1
63,715
7
127,431
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2 Submitted Solution: ``` n=int(input()) if n==1: d=dict() d[0]=0 d[1]=0 for i in range(4): x=int(input()) d[x]+=1 if i<3: vide=input() v=list(d.values()) print(abs(v[0]-2)) else: ch1='01'*(n//2)+'0' ch2='10'*(n//2)+'1' c1=(ch1+ch2)*(n//2)+ch1 c2=(ch2+ch1)*(n//2)+ch2 d=dict() cas1=0 cas2=0 for j in range(4): ch='' for i in range(n): ch+=input() if j<3: vide=input() com1=com2=0 for i in range(len(c1)): if c1[i]== ch[i]: com1+=1 else: com2+=1 if com1>com2: d[(ch,j)]=[1,n**2-com1] cas1+=1 else: d[(ch,j)]=[2,n**2-com2] cas2+=1 v=list(d.keys()) if cas1<cas2: while cas1<cas2: m=0 p=tuple() for i in v: if d[i][0]==2: if d[i][1]>m: m=d[i][1] p=i d[p]=[1,n**2-m] cas1+=1 elif cas2<cas1: while cas2<cas1: m=0 p=tuple() for i in v: if d[i][0]==1: if d[i][1]>m: m=d[i][1] p=i d[p]=[2,n**2-d[p][1]] cas2+=2 ans=0 for i in v: ans+=d[i][1] print(ans) ```
instruction
0
63,716
7
127,432
No
output
1
63,716
7
127,433
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2 Submitted Solution: ``` a=int(input()) l=[] total=0 for i in range(4): line='' for x in [0]*a: line+=input() l.append(line) input() if i!=3 else 0 l=sorted(l,key=lambda i: i[0::2].count('1'))[::-1] for z,v in enumerate(l): if z<2: for i in range(a**2): total += v[i]!='0' if i%2 else v[i]!='1' else: for i in range(a**2): total += v[i]!='1' if i%2 else v[i]!='0' print(total) ```
instruction
0
63,717
7
127,434
No
output
1
63,717
7
127,435
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2 Submitted Solution: ``` def main(): count=int(input()) value=[0,0,0,0] for x in range(3): store=0 pole=True for y in range(count): arr=list(input()) for z in range(count): if arr[z]=="1" and pole: store+=1 if arr[z]=="0" and not pole: store+=1 pole=not pole value[x]=store y=input() #print(value) mini=value[0]+value[1]+2*count*count-(value[2]+value[3]) for a in range(15): hit=0 for b in range(4): if 1<<b & a: hit+=1 if hit==2: store=0 for b in range(4): if 1<<b & a: store+=value[b] else: store+=count*count-value[b] #print(a,store) mini=min(mini,store) print(mini) main() ```
instruction
0
63,718
7
127,436
No
output
1
63,718
7
127,437
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them. Input The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line. Output Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard. Examples Input 1 0 0 1 0 Output 1 Input 3 101 010 101 101 000 101 010 101 011 010 101 010 Output 2 Submitted Solution: ``` import itertools n = int(input()) l = [None] * 4 for _ in range(4): tmp = 0 for i in range(n): line = input().strip() for j, s in enumerate(line): tmp += (i + j) % 2 and s == '1' or (not (i + j) % 2) and s == '0' l[_] = tmp if _ != 3: input() min_ = 1000000 for i1, i2, i3, i4 in itertools.combinations([0, 1, 2, 3], 4): min_ = min(min_, l[i1] + l[i2] + n * n - l[i3] + n * n - l[i4]) print(min_) ```
instruction
0
63,719
7
127,438
No
output
1
63,719
7
127,439
Provide a correct Python 3 solution for this coding contest problem. We will create an artwork by painting black some squares in a white square grid with 10^9 rows and N columns. The current plan is as follows: for the i-th column from the left, we will paint the H_i bottommost squares and will not paint the other squares in that column. Before starting to work, you can choose at most K columns (possibly zero) and change the values of H_i for these columns to any integers of your choice between 0 and 10^9 (inclusive). Different values can be chosen for different columns. Then, you will create the modified artwork by repeating the following operation: * Choose one or more consecutive squares in one row and paint them black. (Squares already painted black can be painted again, but squares not to be painted according to the modified plan should not be painted.) Find the minimum number of times you need to perform this operation. Constraints * 1 \leq N \leq 300 * 0 \leq K \leq N * 0 \leq H_i \leq 10^9 * All values in input are integers. Input Input is given from Standard Input in the following format: N K H_1 H_2 ... H_N Output Print the minimum number of operations required. Examples Input 4 1 2 3 4 1 Output 3 Input 6 2 8 6 9 1 2 1 Output 7 Input 10 0 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 Output 4999999996
instruction
0
63,768
7
127,536
"Correct Solution: ``` n,k=map(int,input().split()) dp=[] for i in range(n+2): dp.append([]) for j in range(n+2): dp[-1].append([]) for l in range(k+1): dp[-1][-1].append(10**12) for l in range(k+1): dp[0][0][l]=0 h=list(map(int,input().split())) h.append(0) h.reverse() h.append(0) h.reverse() for i in range(1,n+2): for j in range(n+2): for l in range(k+1): dp[i][i][l]=min(dp[i][i][l],dp[i-1][j][l]+max(0,h[i]-h[j])) if l>0: dp[i][j][l]=min(dp[i][j][l],dp[i-1][j][l-1]) dp[i][0][l]=min(dp[i][0][l],dp[i-1][j][l-1]+h[j]) ans=dp[n+1][0][0] for j in range(n+2): for l in range(k+1): ans=min(ans,dp[n+1][j][l]) print(ans) ```
output
1
63,768
7
127,537
Provide a correct Python 3 solution for this coding contest problem. We will create an artwork by painting black some squares in a white square grid with 10^9 rows and N columns. The current plan is as follows: for the i-th column from the left, we will paint the H_i bottommost squares and will not paint the other squares in that column. Before starting to work, you can choose at most K columns (possibly zero) and change the values of H_i for these columns to any integers of your choice between 0 and 10^9 (inclusive). Different values can be chosen for different columns. Then, you will create the modified artwork by repeating the following operation: * Choose one or more consecutive squares in one row and paint them black. (Squares already painted black can be painted again, but squares not to be painted according to the modified plan should not be painted.) Find the minimum number of times you need to perform this operation. Constraints * 1 \leq N \leq 300 * 0 \leq K \leq N * 0 \leq H_i \leq 10^9 * All values in input are integers. Input Input is given from Standard Input in the following format: N K H_1 H_2 ... H_N Output Print the minimum number of operations required. Examples Input 4 1 2 3 4 1 Output 3 Input 6 2 8 6 9 1 2 1 Output 7 Input 10 0 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 Output 4999999996
instruction
0
63,769
7
127,538
"Correct Solution: ``` N,K = map(int,input().split()) H = [0] + list(map(int,input().split())) INF = float('inf') dp = [[INF]*(N-K+1) for _ in range(N+1)] dp[0][0] = 0 for i,h in enumerate(H): if i==0: continue for j in range(N-K,0,-1): for k in range(i): c = max(0, h - H[k]) dp[i][j] = min(dp[i][j], dp[k][j-1] + c) print(min(row[-1] for row in dp)) ```
output
1
63,769
7
127,539
Provide a correct Python 3 solution for this coding contest problem. We will create an artwork by painting black some squares in a white square grid with 10^9 rows and N columns. The current plan is as follows: for the i-th column from the left, we will paint the H_i bottommost squares and will not paint the other squares in that column. Before starting to work, you can choose at most K columns (possibly zero) and change the values of H_i for these columns to any integers of your choice between 0 and 10^9 (inclusive). Different values can be chosen for different columns. Then, you will create the modified artwork by repeating the following operation: * Choose one or more consecutive squares in one row and paint them black. (Squares already painted black can be painted again, but squares not to be painted according to the modified plan should not be painted.) Find the minimum number of times you need to perform this operation. Constraints * 1 \leq N \leq 300 * 0 \leq K \leq N * 0 \leq H_i \leq 10^9 * All values in input are integers. Input Input is given from Standard Input in the following format: N K H_1 H_2 ... H_N Output Print the minimum number of operations required. Examples Input 4 1 2 3 4 1 Output 3 Input 6 2 8 6 9 1 2 1 Output 7 Input 10 0 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 Output 4999999996
instruction
0
63,770
7
127,540
"Correct Solution: ``` # dp[i][j] := i 列目まで見て、i 列目を使うとして、 # j 列無視した場合の min N, K = map(int, input().split()) H = [0] + list(map(int, input().split())) + [0] N += 1 inf = 10**18 dp = [[inf]*(K+1) for _ in range(N+1)] dp[0][0] = 0 for i, h in enumerate(H[1:], 1): for j in range(K+1): for k in range(K+1): # k 列無視する if i-k-1 < 0 or j-k < 0: continue h_p = H[i-k-1] dp[i][j] = min(dp[i][j], dp[i-k-1][j-k] + max(0, h - h_p)) #for d in dp: # print(d) print(min(dp[-1])) ```
output
1
63,770
7
127,541
Provide a correct Python 3 solution for this coding contest problem. We will create an artwork by painting black some squares in a white square grid with 10^9 rows and N columns. The current plan is as follows: for the i-th column from the left, we will paint the H_i bottommost squares and will not paint the other squares in that column. Before starting to work, you can choose at most K columns (possibly zero) and change the values of H_i for these columns to any integers of your choice between 0 and 10^9 (inclusive). Different values can be chosen for different columns. Then, you will create the modified artwork by repeating the following operation: * Choose one or more consecutive squares in one row and paint them black. (Squares already painted black can be painted again, but squares not to be painted according to the modified plan should not be painted.) Find the minimum number of times you need to perform this operation. Constraints * 1 \leq N \leq 300 * 0 \leq K \leq N * 0 \leq H_i \leq 10^9 * All values in input are integers. Input Input is given from Standard Input in the following format: N K H_1 H_2 ... H_N Output Print the minimum number of operations required. Examples Input 4 1 2 3 4 1 Output 3 Input 6 2 8 6 9 1 2 1 Output 7 Input 10 0 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 Output 4999999996
instruction
0
63,771
7
127,542
"Correct Solution: ``` # -*- coding: utf-8 -*- import sys def input(): return sys.stdin.readline().strip() def list2d(a, b, c): return [[c] * b for i in range(a)] def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)] def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)] def ceil(x, y=1): return int(-(-x // y)) def INT(): return int(input()) def MAP(): return map(int, input().split()) def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)] def Yes(): print('Yes') def No(): print('No') def YES(): print('YES') def NO(): print('NO') sys.setrecursionlimit(10 ** 9) INF = 10 ** 18 MOD = 10 ** 9 + 7 N, K = MAP() M = N - K A = [0] + LIST() # dp[i][j] := 列をi個使って、最後に使ったのがj列目の時の最小コスト dp = list2d(M+1, N+1, INF) dp[0][0] = 0 for i in range(1, M+1): for j, h1 in enumerate(A): for k in range(max(j-N, 0), j): h2 = A[k] dp[i][j] = min(dp[i][j], dp[i-1][k] + max(h1 - h2, 0)) print(min(dp[M])) ```
output
1
63,771
7
127,543