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Provide tags and a correct Python 3 solution for this coding contest problem. Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks. What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase. Input The only line contains 4 integers n, a, b, c (1 ≤ n, a, b, c ≤ 109). Output Print the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4. Examples Input 1 1 3 4 Output 3 Input 6 2 1 1 Output 1 Input 4 4 4 4 Output 0 Input 999999999 1000000000 1000000000 1000000000 Output 1000000000 Note In the first example Alyona can buy 3 packs of 1 copybook for 3a = 3 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b = 1 ruble. She will have 8 copybooks in total. In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything. In the fourth example Alyona should buy one pack of one copybook.
instruction
0
43,460
10
86,920
Tags: brute force, implementation Correct Solution: ``` n,a,b,c=map(int,input().split()) xx=(n%4) if xx==0: print("0") elif xx==1: print(min(a*3,a+b,c)) elif xx==2: print(min(2*a,b,2*c)) else: print(min(a,b+c,3*c)) ```
output
1
43,460
10
86,921
Provide tags and a correct Python 3 solution for this coding contest problem. Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks. What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase. Input The only line contains 4 integers n, a, b, c (1 ≤ n, a, b, c ≤ 109). Output Print the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4. Examples Input 1 1 3 4 Output 3 Input 6 2 1 1 Output 1 Input 4 4 4 4 Output 0 Input 999999999 1000000000 1000000000 1000000000 Output 1000000000 Note In the first example Alyona can buy 3 packs of 1 copybook for 3a = 3 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b = 1 ruble. She will have 8 copybooks in total. In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything. In the fourth example Alyona should buy one pack of one copybook.
instruction
0
43,461
10
86,922
Tags: brute force, implementation Correct Solution: ``` n,a,b,c=map(int,input().split()) if n%4==0:print(0) else: x = 4 - n%4 if x == 1: print(min(a,b+c,c*3)) if x == 2: print(min(a*2,b,c*2)) if x == 3: print(min(a*3,a+b,c)) ```
output
1
43,461
10
86,923
Provide tags and a correct Python 3 solution for this coding contest problem. Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks. What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase. Input The only line contains 4 integers n, a, b, c (1 ≤ n, a, b, c ≤ 109). Output Print the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4. Examples Input 1 1 3 4 Output 3 Input 6 2 1 1 Output 1 Input 4 4 4 4 Output 0 Input 999999999 1000000000 1000000000 1000000000 Output 1000000000 Note In the first example Alyona can buy 3 packs of 1 copybook for 3a = 3 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b = 1 ruble. She will have 8 copybooks in total. In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything. In the fourth example Alyona should buy one pack of one copybook.
instruction
0
43,462
10
86,924
Tags: brute force, implementation Correct Solution: ``` n, a, b, c = map(int, input().split()) if n % 4 == 0: print(0) if n % 4 == 1: print(min(3 * a, b + a, c)) if n % 4 == 2: print(min(2 * a, b, 2 * c)) if n % 4 == 3: print(min(a, b + c, 3 * c)) ```
output
1
43,462
10
86,925
Provide tags and a correct Python 3 solution for this coding contest problem. Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks. What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase. Input The only line contains 4 integers n, a, b, c (1 ≤ n, a, b, c ≤ 109). Output Print the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4. Examples Input 1 1 3 4 Output 3 Input 6 2 1 1 Output 1 Input 4 4 4 4 Output 0 Input 999999999 1000000000 1000000000 1000000000 Output 1000000000 Note In the first example Alyona can buy 3 packs of 1 copybook for 3a = 3 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b = 1 ruble. She will have 8 copybooks in total. In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything. In the fourth example Alyona should buy one pack of one copybook.
instruction
0
43,463
10
86,926
Tags: brute force, implementation Correct Solution: ``` line=[int(x) for x in input().split(' ')] N=line[0] a=line[1] b=line[2] c=line[3] prices1=[0,a,b,c] prices2=[a+b,a+c,b+c,a+b+c] price=10**9 for i in range(4): for t in range(1,4): if (N+i*t)%4==0 and prices1[i]*t<price: price=prices1[i]*t for j in range(3,7): for t in range(1,2): if (N+j*t)%4==0 and prices2[j-3]*t<price: price=prices2[j-3] print(price) ```
output
1
43,463
10
86,927
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks. What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase. Input The only line contains 4 integers n, a, b, c (1 ≤ n, a, b, c ≤ 109). Output Print the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4. Examples Input 1 1 3 4 Output 3 Input 6 2 1 1 Output 1 Input 4 4 4 4 Output 0 Input 999999999 1000000000 1000000000 1000000000 Output 1000000000 Note In the first example Alyona can buy 3 packs of 1 copybook for 3a = 3 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b = 1 ruble. She will have 8 copybooks in total. In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything. In the fourth example Alyona should buy one pack of one copybook. Submitted Solution: ``` n, a, b, c = map(int, input().strip().split()) cost = 0 if n%4 == 0 else a * (4 - n % 4) for i in range(20): for j in range(20): for k in range(20): if (n + i + 2*j + 3*k) % 4 == 0: cost = min(cost, i*a + j*b + k*c) print(cost) ```
instruction
0
43,464
10
86,928
Yes
output
1
43,464
10
86,929
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks. What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase. Input The only line contains 4 integers n, a, b, c (1 ≤ n, a, b, c ≤ 109). Output Print the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4. Examples Input 1 1 3 4 Output 3 Input 6 2 1 1 Output 1 Input 4 4 4 4 Output 0 Input 999999999 1000000000 1000000000 1000000000 Output 1000000000 Note In the first example Alyona can buy 3 packs of 1 copybook for 3a = 3 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b = 1 ruble. She will have 8 copybooks in total. In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything. In the fourth example Alyona should buy one pack of one copybook. Submitted Solution: ``` n, a, b, c = (int(x) for x in input().split()) nd = 4 - n % 4 if n % 4 == 0: print(0) elif nd == 1: print(min(a, b + c, 3 * c, c + 3 * b)) elif nd == 2: print(min(2 * a, b, 2 * c)) else: print(min(3 * a, min(a + b, c))) ```
instruction
0
43,465
10
86,930
Yes
output
1
43,465
10
86,931
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks. What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase. Input The only line contains 4 integers n, a, b, c (1 ≤ n, a, b, c ≤ 109). Output Print the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4. Examples Input 1 1 3 4 Output 3 Input 6 2 1 1 Output 1 Input 4 4 4 4 Output 0 Input 999999999 1000000000 1000000000 1000000000 Output 1000000000 Note In the first example Alyona can buy 3 packs of 1 copybook for 3a = 3 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b = 1 ruble. She will have 8 copybooks in total. In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything. In the fourth example Alyona should buy one pack of one copybook. Submitted Solution: ``` def func(n): if n[0]%4==1:return min(n[3],n[1]*3,n[2]+n[1]) elif n[0]%4==2:return min(n[2],n[3]*2,n[1]*2) elif n[0]%4==3:return min(n[1],n[2]+n[3],n[3]*3) else:return 0 print(func(list(map(int,input().split())))) ```
instruction
0
43,466
10
86,932
Yes
output
1
43,466
10
86,933
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks. What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase. Input The only line contains 4 integers n, a, b, c (1 ≤ n, a, b, c ≤ 109). Output Print the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4. Examples Input 1 1 3 4 Output 3 Input 6 2 1 1 Output 1 Input 4 4 4 4 Output 0 Input 999999999 1000000000 1000000000 1000000000 Output 1000000000 Note In the first example Alyona can buy 3 packs of 1 copybook for 3a = 3 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b = 1 ruble. She will have 8 copybooks in total. In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything. In the fourth example Alyona should buy one pack of one copybook. Submitted Solution: ``` import sys INF = sys.maxsize def solution(n, prices, k): if k>10: return INF if n % 4 == 0: return 0 else: ans = min(solution(n + 1, prices,k+1) + prices[0], solution(n + 2, prices,k+2) + prices[1], solution(n + 3, prices,k+3) + prices[2]) return ans def main(): n,a,b,c = map(int, input().split()) prices = [a,b,c] print(solution(n,prices,0)) main() ```
instruction
0
43,467
10
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Yes
output
1
43,467
10
86,935
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks. What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase. Input The only line contains 4 integers n, a, b, c (1 ≤ n, a, b, c ≤ 109). Output Print the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4. Examples Input 1 1 3 4 Output 3 Input 6 2 1 1 Output 1 Input 4 4 4 4 Output 0 Input 999999999 1000000000 1000000000 1000000000 Output 1000000000 Note In the first example Alyona can buy 3 packs of 1 copybook for 3a = 3 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b = 1 ruble. She will have 8 copybooks in total. In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything. In the fourth example Alyona should buy one pack of one copybook. Submitted Solution: ``` n,a,b,c=map(int,input().strip().split(" ")) if(n%4==1): y=min(3*a,a+b,c) print(y) elif(n%4==2): y=min(2*a,b) print(y) elif(n%4==0): print(0) else: print(a) ```
instruction
0
43,468
10
86,936
No
output
1
43,468
10
86,937
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks. What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase. Input The only line contains 4 integers n, a, b, c (1 ≤ n, a, b, c ≤ 109). Output Print the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4. Examples Input 1 1 3 4 Output 3 Input 6 2 1 1 Output 1 Input 4 4 4 4 Output 0 Input 999999999 1000000000 1000000000 1000000000 Output 1000000000 Note In the first example Alyona can buy 3 packs of 1 copybook for 3a = 3 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b = 1 ruble. She will have 8 copybooks in total. In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything. In the fourth example Alyona should buy one pack of one copybook. Submitted Solution: ``` n, a, b, c = map(int, input().split()) mod = n % 4 if mod == 0: print(0) elif mod == 1: print(min(3 * a, c)) elif mod == 2: print(min(2 * a, b, 2 * c)) elif mod == 3: print(min(a, 3 * c)) ```
instruction
0
43,469
10
86,938
No
output
1
43,469
10
86,939
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks. What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase. Input The only line contains 4 integers n, a, b, c (1 ≤ n, a, b, c ≤ 109). Output Print the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4. Examples Input 1 1 3 4 Output 3 Input 6 2 1 1 Output 1 Input 4 4 4 4 Output 0 Input 999999999 1000000000 1000000000 1000000000 Output 1000000000 Note In the first example Alyona can buy 3 packs of 1 copybook for 3a = 3 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b = 1 ruble. She will have 8 copybooks in total. In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything. In the fourth example Alyona should buy one pack of one copybook. Submitted Solution: ``` n, a, b, c = (int(x) for x in input().split()) sum, k = 0, 4 - n % 4 if 2 * a > b: sum = min(k // 2 * b + (k % 2) * a, 2 * c) elif 3 * a > c and a + b > c: sum = k // 3 * c + (k % 3) * a if k % 3 == 0: sum = min(sum, c * k // 3) if k % 2 == 0: sum = min(sum, b * k // 2) print(min(sum, a * k)) ```
instruction
0
43,470
10
86,940
No
output
1
43,470
10
86,941
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks. What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase. Input The only line contains 4 integers n, a, b, c (1 ≤ n, a, b, c ≤ 109). Output Print the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4. Examples Input 1 1 3 4 Output 3 Input 6 2 1 1 Output 1 Input 4 4 4 4 Output 0 Input 999999999 1000000000 1000000000 1000000000 Output 1000000000 Note In the first example Alyona can buy 3 packs of 1 copybook for 3a = 3 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b = 1 ruble. She will have 8 copybooks in total. In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything. In the fourth example Alyona should buy one pack of one copybook. Submitted Solution: ``` def get_min_rubles(n, l): if n % 4 == 0: return 0 a, b, c = l[0], l[1], l[2] k_a, price_a = 1, 0, ## xa, xa + b, xa + c while(True): if (n + k_a) % 4 == 0: price_a = k_a * a break elif (n + k_a + 3) % 4 == 0: price_a = k_a * a + b break elif (n + k_a + 4) % 4 == 0: price_a = k_a * a + c break k_a += 1 ## xb, xb + a, xb + c k_b, price_b = 2, 0 while(True): if (n + k_b) % 4 == 0: price_b = (k_b //2) * b break elif (n + k_b + 1) % 4 == 0: price_b = (k_b //2) * b + a break elif (n + k_b + 3) % 4 == 0: price_b = (k_b //2) * b + c break k_b += 2 ## xc, xc + a, xc + b k_c, price_c = 3, 0 while(True): if (n + k_c) % 4 == 0: price_c = (k_c//3) * c break elif (n + k_c + 1) % 4 == 0: price_c = (k_c//3) * c + a break elif (n + k_c + 2) % 4 == 0: price_c = (k_c//3) * c + b break k_c += 3 return min(price_a, price_b, price_c) prices = list(map(int, input().split())) print(get_min_rubles(prices[0], prices[1:])) ```
instruction
0
43,471
10
86,942
No
output
1
43,471
10
86,943
Provide a correct Python 3 solution for this coding contest problem. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666
instruction
0
43,560
10
87,120
"Correct Solution: ``` from functools import lru_cache t=int(input()) for i in range(t): n,a,b,c,d=map(int,input().split()) @lru_cache(maxsize=None) def f(n): if n==0: return 0 if n==1: return d else: x=n*d q,r=divmod(n,2) if r==0: x=min(x,f(q)+a) else: x=min(x,f(q)+a+d,f(q+1)+a+d) q,r=divmod(n,3) if r==0: x=min(x,f(q)+b) elif r==1: x=min(x,f(q)+b+d,f(q+1)+b+d*2) else: x=min(x,f(q)+b+d*2,f(q+1)+b+d) q,r=divmod(n,5) if r==0: x=min(x,f(q)+c) elif r==1: x=min(x,f(q)+c+d,f(q+1)+c+d*4) elif r==2: x=min(x,f(q)+c+d*2,f(q+1)+c+d*3) elif r==3: x=min(x,f(q)+c+d*3,f(q+1)+c+d*2) else: x=min(x,f(q)+c+d*4,f(q+1)+c+d) return x print(f(n)) ```
output
1
43,560
10
87,121
Provide a correct Python 3 solution for this coding contest problem. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666
instruction
0
43,561
10
87,122
"Correct Solution: ``` t = int(input()) def calc(x): if x not in dp: divs = [5, 3, 2] costs = [c, b, a] values = lambda div, cost: [calc((x + i) // div) + cost + (sign * x) % div * d for i, sign in [(0, 1), (div - 1, -1)]] dp[x] = min(*[value for div, cost in zip(divs, costs) for value in values(div, cost)], x * d) return dp[x] for _ in range(t): n, a, b, c, d = map(int, input().split()) dp = {0: 0, 1: d} print(calc(n)) ```
output
1
43,561
10
87,123
Provide a correct Python 3 solution for this coding contest problem. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666
instruction
0
43,562
10
87,124
"Correct Solution: ``` import sys sys.setrecursionlimit(10000100) t = int(input()) for _ in range(t): n, a, b, c, d = map(int, input().split()) used = {} def solve(t): if t in used: return used[t] if t <= 1: return t * d res = d * t for x, y in zip([2, 3, 5], [a, b, c]): if t % x == 0: res = min(res, solve(t // x) + y) else: res = min(res, solve(t // x) + y + (t - t // x * x) * d) res = min(res, solve(t // x + 1) + y + ((t // x + 1) * x - t) * d) used[t] = res return res print(solve(n)) ```
output
1
43,562
10
87,125
Provide a correct Python 3 solution for this coding contest problem. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666
instruction
0
43,563
10
87,126
"Correct Solution: ``` from functools import lru_cache z = 0 n = 0 a = 0 b = 0 c = 0 d = 0 @lru_cache(maxsize=None) def solve(x): global a global b global c global d if x==0: return 0 if x==1: return d ans = d*x for p in [2,3,5]: m = x%p nxt = x//p A = a if p == 3: A = b if p == 5: A = c if nxt < x: cst = m*d + min(A, (nxt*p-nxt)*d) + solve(nxt) ans = min(ans, cst) nxt = (x+p-m)//p if nxt < x: cst = min((p-m)*d + A + solve(nxt), (x-nxt)*d + solve(nxt)) ans = min(ans, cst) #print(x, ans) return ans z = int(input()) for _ in range(z): n, a, b, c, d = map(int, input().split()) print(solve(n)) solve.cache_clear() ```
output
1
43,563
10
87,127
Provide a correct Python 3 solution for this coding contest problem. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666
instruction
0
43,564
10
87,128
"Correct Solution: ``` from functools import lru_cache import sys sys.setrecursionlimit(10**7) T = int(input()) INF = 10**18 for _ in range(T): N, A, B, C, D = map(int, input().split()) V = set() @lru_cache(maxsize=None) def search(now): if now == 0: return 0 ret = INF for div, cost in zip((2, 3, 5), (A, B, C)): q, r = divmod(now, div) ret = min( ret, search(q) + cost + r * D, search(q + 1) + cost + (div - r) * D if q + 1 < now else INF, now * D ) return ret print(search(N)) ```
output
1
43,564
10
87,129
Provide a correct Python 3 solution for this coding contest problem. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666
instruction
0
43,565
10
87,130
"Correct Solution: ``` T = int(input()) for t in range(T): N, A, B, C, D = map(int, input().split()) memo = {} def dist(n): if n == 0: return 0 if n == 1: return D if n in memo: return memo[n] ret = min( D * n, D * abs(n - n//5*5) + C + dist(n//5), D * abs(n - (n+4)//5*5) + C + dist((n+4)//5), D * abs(n - n//3*3) + B + dist(n//3), D * abs(n - (n+2)//3*3) + B + dist((n+2)//3), D * abs(n - n//2*2) + A + dist(n//2), D * abs(n - (n+1)//2*2) + A + dist((n+1)//2) ) memo[n] = ret return ret print(dist(N)) ```
output
1
43,565
10
87,131
Provide a correct Python 3 solution for this coding contest problem. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666
instruction
0
43,566
10
87,132
"Correct Solution: ``` import sys sys.setrecursionlimit(10 ** 7) input = sys.stdin.readline def dfs(n): if n not in memo: ans = min(n*d, min(dfs(n//2),dfs((n+1)//2)) + a + d*(n % 2)) if n % 3 <= 1: ans = min(ans, dfs(n//3) + b + d*(n % 3)) else: ans = min(ans, dfs((n+2)//3) + b + d*(3 - n % 3)) if n % 5 <= 2: ans = min(ans, dfs(n//5) + c + d*(n % 5)) else: ans = min(ans, dfs((n+4)//5) + c + d*(5 - n % 5)) memo[n] = ans return memo[n] t = int(input()) for _ in range(t): n, a, b, c, d = map(int, input().split()) memo = {0: 0, 1: d} print(dfs(n)) ```
output
1
43,566
10
87,133
Provide a correct Python 3 solution for this coding contest problem. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666
instruction
0
43,567
10
87,134
"Correct Solution: ``` import sys sys.setrecursionlimit(10**9) from collections import defaultdict t = int(input()) for _ in range(t): n,a,b,c,d = map(int,input().split()) dic = defaultdict(int) dic[0] = 0 dic[1] = d def calc(x): if(x==0): return 0 if(dic[x] != 0): return dic[x] tmp = x*d if(x%2==0): tmp = min(tmp, calc(x//2) + a) else: tmp = min(tmp, calc(x//2) + a + d, calc(x//2 + 1) + a + d) if(x%3==0): tmp = min(tmp, calc(x//3) + b) elif(x%3==1): tmp = min(tmp, calc(x//3) + b + d) else: tmp = min(tmp, calc(1 + x//3) + b + d) if(x%5==0): tmp = min(tmp, calc(x//5) + c) elif(x%5 < 3): tmp = min(tmp, calc(x//5) + c + d*(x%5)) else: tmp = min(tmp, calc(1 + x//5) + c + d*(5 - x%5)) dic[x] = tmp return tmp print(calc(n)) ```
output
1
43,567
10
87,135
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666 Submitted Solution: ``` from functools import lru_cache def solve(N, A, B, C, D): @lru_cache(None) def f(N): if N == 0: return 0 if N == 1: return D ret = D * N q, r = divmod(N, 2) if r == 0: ret = min(ret, f(q) + A) else: ret = min(ret, f(q) + A + D, f(q + 1) + A + D) q, r = divmod(N, 3) if r == 0: ret = min(ret, f(q) + B) else: ret = min(ret, f(q) + B + D*r, f(q + 1) + B + D*(3-r)) q, r = divmod(N, 5) if r == 0: ret = min(ret, f(q) + C) else: ret = min(ret, f(q) + C + D*r, f(q + 1) + C + D*(5-r)) return ret return f(N) T = int(input()) for _ in range(T): N, A, B, C, D = map(int, input().split()) print(solve(N, A, B, C, D)) ```
instruction
0
43,568
10
87,136
Yes
output
1
43,568
10
87,137
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666 Submitted Solution: ``` from functools import * from math import * t = int(input()) @lru_cache(maxsize=None) def sol(n, a, b, c, d): if n == 1: return d ans = n * d cn = (n + 1) // 2 fn = n // 2 if cn: ans = min(ans, sol(cn, a, b, c, d) + abs(cn * 2 - n) * d + a) if fn: ans = min(ans, sol(fn, a, b, c, d) + abs(fn * 2 - n) * d + a) cn = (n + 2) // 3 fn = n // 3 if cn: ans = min(ans, sol(cn, a, b, c, d) + abs(cn * 3 - n) * d + b) if fn: ans = min(ans, sol(fn, a, b, c, d) + abs(fn * 3 - n) * d + b) cn = (n + 4) // 5 fn = n // 5 if cn: ans = min(ans, sol(cn, a, b, c, d) + abs(cn * 5 - n) * d + c) if fn: ans = min(ans, sol(fn, a, b, c, d) + abs(fn * 5 - n) * d + c) # print(str(n) + ", " + str(ans)) return ans for _ in range(t): n, a, b, c, d = list(map(int, input().split())) sol.cache_clear() print(min(d * n, sol(n, a, b, c, d))) ```
instruction
0
43,569
10
87,138
Yes
output
1
43,569
10
87,139
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666 Submitted Solution: ``` import sys from functools import lru_cache sys.setrecursionlimit(10 ** 7) rl = sys.stdin.readline def solve(): N, A, B, C, D = map(int, rl().split()) @lru_cache(maxsize=None) def calc(t): if t == 0: return 0 if t == 1: return D res = min( D * t, D * abs(t - t // 5 * 5) + C + calc(t // 5), D * abs(t - (t + 4) // 5 * 5) + C + calc((t + 4) // 5), D * abs(t - t // 3 * 3) + B + calc(t // 3), D * abs(t - (t + 2) // 3 * 3) + B + calc((t + 2) // 3), D * abs(t - t // 2 * 2) + A + calc(t // 2), D * abs(t - (t + 1) // 2 * 2) + A + calc((t + 1) // 2) ) return res return calc(N) if __name__ == '__main__': T = int(rl()) ans = [] for _ in range(T): ans.append(solve()) print(*ans, sep='\n') ```
instruction
0
43,570
10
87,140
Yes
output
1
43,570
10
87,141
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666 Submitted Solution: ``` import sys sys.setrecursionlimit(2147483647) from functools import lru_cache @lru_cache(maxsize=None) def solve(n, a, b, c, d): if n == 0: return 0 if n == 1: return d res = 10**18 res = min(res, d * n) res = min(res, d * (n - n // 2 * 2) + a + solve(n // 2, a, b, c, d)) res = min(res, d * (n - n // 3 * 3) + b + solve(n // 3, a, b, c, d)) res = min(res, d * (n - n // 5 * 5) + c + solve(n // 5, a, b, c, d)) res = min(res, d * ((n + 2 - 1) // 2 * 2 - n) + a + solve((n + 2 - 1) // 2, a, b, c, d)) res = min(res, d * ((n + 3 - 1) // 3 * 3 - n) + b + solve((n + 3 - 1) // 3, a, b, c, d)) res = min(res, d * ((n + 5 - 1) // 5 * 5 - n) + c + solve((n + 5 - 1) // 5, a, b, c, d)) return res T = int(input()) for _ in range(T): N, A, B, C, D = map(int, input().split()) print(solve(N, A, B, C, D)) ```
instruction
0
43,571
10
87,142
Yes
output
1
43,571
10
87,143
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666 Submitted Solution: ``` def dfs(n): global b,check,d #ttfは235、chaはabc #2,3,5の場合それぞれ for ttf,cha in zip([2,3,5],b): #-1ずつしていく場合 if check[0]>check[n]+n*d: check[0]=check[n]+n*d #最寄りまで-してく場合 x1,x2=n//ttf,n%ttf if x1 in check: if check[x1]>check[n]+x2*d+cha: check[x1]=check[n]+x2*d+cha dfs(x1) else: check[x1]=check[n]+x2*d+cha dfs(x1) #最寄りまで+1してく場合 x1,x2=n//ttf+1,ttf-n%ttf if x1 in check: if check[x1]>check[n]+x2*d+cha: check[x1]=check[n]+x2*d+cha dfs(x1) else: check[x1]=check[n]+x2*d+cha dfs(x1) t=int(input()) for i in range(t): N,*b,d=map(int,input().split()) check={N:0,0:N*d} dfs(N) print(check[0]) ```
instruction
0
43,572
10
87,144
No
output
1
43,572
10
87,145
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666 Submitted Solution: ``` DP = {} def solve(n, a, b, c, d, did_plus=False): if n <= 0: return 0 if n == 1: return d if n in DP: return DP[n] ans = float('inf') for i in range(-4, 5): if did_plus: if i > 0: continue num = n + i trash = abs(i)*d if num%5 == 0 and num // 5 < n: ans = min(ans, solve(num//5, a, b, c, d, i>=0) + min(c, d*(num-(num//5))) + trash) if num%3 == 0 and num // 3 < n: ans = min(ans, solve(num//3, a, b, c, d, i>=0) + min(b, d*(num-(num//3))) + trash) if num%2 == 0 and num // 2 < n: ans = min(ans, solve(num//2, a, b, c, d, i>=0) + min(a, d*(num-(num//2))) + trash) # print(str(n) + ' ' + str(ans) + ' ' + str(num) + ' ' + str(i)) DP[n] = int(ans) return int(ans) def solve2(): DP.clear() ans = float('inf') n, a, b, c, d = map(int, input().split()) # for i in range(0, 65): # for j in range(0, 30): # for k in range(0, 10): # val = pow(2, i)*pow(3, j)*pow(5, k) # ans = min(ans, a*i + b*j + c*k + abs(n - val)*(d)) # print(ans) print(solve(n, a, b, c,d)) t = int(input()) for _ in range(t): solve2() ```
instruction
0
43,573
10
87,146
No
output
1
43,573
10
87,147
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666 Submitted Solution: ``` import sys check=dict() N,a,b,c,d=0,0,0,0,0 #ttfは235、chaはabc def dfs_sub(n,ttf,cha): global check,d if 0 in check: check[0]=min(check[n]+n*d,check[0]) else: check[0]=check[n]+n*d x1,x2=n//ttf,n%ttf if ttf-x2>=x2: if x1==0: if x1 in check: if check[x1]>check[n]+x2*d: check[x1]=check[n]+x2*d else: check[x1]=check[n]+x2*d else: if x1 in check: if check[x1]>check[n]+x2*d+cha: check[x1]=check[n]+x2*d+cha dfs(x1) else: check[x1]=check[n]+x2*d+cha dfs(x1) x1,x2=n//ttf+1,ttf-n%ttf if ttf-x2>=x2: if x1 in check: if check[x1]>check[n]+x2*d+cha: check[x1]=check[n]+x2*d+cha dfs(x1) else: check[x1]=check[n]+x2*d+cha dfs(x1) def dfs(n): global check,a,b,c,d dfs_sub(n,2,a) dfs_sub(n,3,b) dfs_sub(n,5,c) t=int(input()) ans=[0]*t for i in range(t): N,a,b,c,d=map(int,input().split()) check={N:0} dfs(N) ans[i]=check[0] for i in range(t): print(ans[i]) ```
instruction
0
43,574
10
87,148
No
output
1
43,574
10
87,149
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You start with the number 0 and you want to reach the number N. You can change the number, paying a certain amount of coins, with the following operations: * Multiply the number by 2, paying A coins. * Multiply the number by 3, paying B coins. * Multiply the number by 5, paying C coins. * Increase or decrease the number by 1, paying D coins. You can perform these operations in arbitrary order and an arbitrary number of times. What is the minimum number of coins you need to reach N? You have to solve T testcases. Constraints * 1 \le T \le 10 * 1 \le N \le 10^{18} * 1 \le A, B, C, D \le 10^9 * All numbers N, A, B, C, D are integers. Input The input is given from Standard Input. The first line of the input is T Then, T lines follow describing the T testcases. Each of the T lines has the format N A B C D Output For each testcase, print the answer on Standard Output followed by a newline. Example Input 5 11 1 2 4 8 11 1 2 2 8 32 10 8 5 4 29384293847243 454353412 332423423 934923490 1 900000000000000000 332423423 454353412 934923490 987654321 Output 20 19 26 3821859835 23441258666 Submitted Solution: ``` import heapq from collections import deque T = int(input()) for t in range(T): N,A,B,C,D = map(int,input().split()) q = [(0,N)] heapq.heapify(q) seen = set() while q: cost, n = heapq.heappop(q) if n in seen: continue seen.add(n) if n == 0: print(cost) break heapq.heappush(q, (cost + N * D, 0)) if n % 2 ==0: heapq.heappush(q, (cost + A, n // 2)) else: # odd number heapq.heappush(q, (cost + D + A, (n + 1) // 2)) heapq.heappush(q, (cost + D + A, (n - 1) // 2)) if n % 3 ==0: heapq.heappush(q, (cost + B, n // 3)) else: rest = n % 3 heapq.heappush(q, (cost + rest * D + B, (n - rest) // 3)) heapq.heappush(q, (cost + (3-rest) * D + B, (n - rest + 3) // 3)) if n % 5 ==0: heapq.heappush(q, (cost + C, n // 5)) else: rest = n % 5 heapq.heappush(q, (cost + rest * D + C, (n - rest) // 5)) heapq.heappush(q, (cost + (5-rest) * D + C, (n - rest + 5) // 5)) ```
instruction
0
43,575
10
87,150
No
output
1
43,575
10
87,151
Provide a correct Python 3 solution for this coding contest problem. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12
instruction
0
43,608
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87,216
"Correct Solution: ``` a, b = map(int, input().split()) print(max([a+(a-1), a+b, b+(b-1)])) ```
output
1
43,608
10
87,217
Provide a correct Python 3 solution for this coding contest problem. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12
instruction
0
43,609
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87,218
"Correct Solution: ``` A, B = map(int, input().split()) print(max(A+B, max(A, B)*2-1)) ```
output
1
43,609
10
87,219
Provide a correct Python 3 solution for this coding contest problem. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12
instruction
0
43,610
10
87,220
"Correct Solution: ``` A,B= [int(x) for x in input().split()] print(max(A+B,2*A-1,2*B-1)) ```
output
1
43,610
10
87,221
Provide a correct Python 3 solution for this coding contest problem. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12
instruction
0
43,611
10
87,222
"Correct Solution: ``` a,b = map(int,input().split()) lst = [a+a-1,a+b,b+b-1] print(max(lst)) ```
output
1
43,611
10
87,223
Provide a correct Python 3 solution for this coding contest problem. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12
instruction
0
43,612
10
87,224
"Correct Solution: ``` a,b=list(map(int,input().split())) print(max(a,b)*2-(a!=b)) ```
output
1
43,612
10
87,225
Provide a correct Python 3 solution for this coding contest problem. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12
instruction
0
43,613
10
87,226
"Correct Solution: ``` #ABC124 a,b = map(int,input().split()) print(max(a+b,a+(a-1),b+(b-1))) ```
output
1
43,613
10
87,227
Provide a correct Python 3 solution for this coding contest problem. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12
instruction
0
43,614
10
87,228
"Correct Solution: ``` a, b = map(int, input().split()) print(max((a+b), (2*a-1), (2*b-1),)) ```
output
1
43,614
10
87,229
Provide a correct Python 3 solution for this coding contest problem. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12
instruction
0
43,615
10
87,230
"Correct Solution: ``` a,b=(map(int,input().split())) print(max(a+(a-1),a+b,b+(b-1))) ```
output
1
43,615
10
87,231
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12 Submitted Solution: ``` A,B=map(int,input().split()) print(sum(sorted([A,B,A-1,B-1])[-2:])) ```
instruction
0
43,616
10
87,232
Yes
output
1
43,616
10
87,233
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12 Submitted Solution: ``` A,B=map(int,input().split()) print(max(A+B,(A*2)-1,(B*2)-1)) ```
instruction
0
43,617
10
87,234
Yes
output
1
43,617
10
87,235
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12 Submitted Solution: ``` A,B = list(map(int,input().split())) print(max((A*2-1,A+B,B*2-1))) ```
instruction
0
43,618
10
87,236
Yes
output
1
43,618
10
87,237
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12 Submitted Solution: ``` A,B =map(int,input().split()) l =[A,A-1,B,B-1] l.sort() print(l[2]+l[3]) ```
instruction
0
43,619
10
87,238
Yes
output
1
43,619
10
87,239
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12 Submitted Solution: ``` p, q = map(int, input().split()) score = max(p, q) * 2 - 1 print(score) ```
instruction
0
43,620
10
87,240
No
output
1
43,620
10
87,241
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12 Submitted Solution: ``` def check_max_coin(a,b): max_coin = 0 for i in range(1:3): if a < b : max_coin += b else: max_coin += a print(max_coin) a, b = map(int, input().split()) check_max_coin(a,b) ```
instruction
0
43,621
10
87,242
No
output
1
43,621
10
87,243
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12 Submitted Solution: ``` a, b = map(int,input()) ma = max(2*a-1, a+b, 2*b-1) print(ma) ```
instruction
0
43,622
10
87,244
No
output
1
43,622
10
87,245
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are two buttons, one of size A and one of size B. When you press a button of size X, you get X coins and the size of that button decreases by 1. You will press a button twice. Here, you can press the same button twice, or press both buttons once. At most how many coins can you get? Constraints * All values in input are integers. * 3 \leq A, B \leq 20 Input Input is given from Standard Input in the following format: A B Output Print the maximum number of coins you can get. Examples Input 5 3 Output 9 Input 3 4 Output 7 Input 6 6 Output 12 Submitted Solution: ``` N,K = map(int,input().split()) s = list(map(int,input())) s.append(2) start = s[0] choku = [0] saka = [0] number = 1 for i in range(N): if s[i] == s[i+1]: number += 1 else: if s[i] == 0: choku.append(number) number = 1 else: saka.append(number) number = 1 choku.append(0) saka.append(0) while(1): max_align = 0 m = len(choku) n = len(saka) if m <= K: print(N) break if start == 0: #最初が直立の場合 for i in range(m-K+1): if max_align <= sum(choku[i:i+K]) + sum(saka[i-1:i+K]): max_align = sum(choku[i:i+K]) + sum(saka[i-1:i+K]) else: for i in range(m-K+1): if max_align <= sum(choku[i:i+K]) + sum(saka[i:i+K+1]): max_align = sum(choku[i:i+K]) + sum(saka[i:i+K+1]) print(max_align) break ```
instruction
0
43,623
10
87,246
No
output
1
43,623
10
87,247
Provide tags and a correct Python 3 solution for this coding contest problem. <image> William is hosting a party for n of his trader friends. They started a discussion on various currencies they trade, but there's an issue: not all of his trader friends like every currency. They like some currencies, but not others. For each William's friend i it is known whether he likes currency j. There are m currencies in total. It is also known that a trader may not like more than p currencies. Because friends need to have some common topic for discussions they need to find the largest by cardinality (possibly empty) subset of currencies, such that there are at least ⌈ n/2 ⌉ friends (rounded up) who like each currency in this subset. Input The first line contains three integers n, m and p (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ p ≤ m ≤ 60, 1 ≤ p ≤ 15), which is the number of trader friends, the number of currencies, the maximum number of currencies each friend can like. Each of the next n lines contain m characters. The j-th character of i-th line is 1 if friend i likes the currency j and 0 otherwise. It is guaranteed that the number of ones in each line does not exceed p. Output Print a string of length m, which defines the subset of currencies of the maximum size, which are liked by at least half of all friends. Currencies belonging to this subset must be signified by the character 1. If there are multiple answers, print any. Examples Input 3 4 3 1000 0110 1001 Output 1000 Input 5 5 4 11001 10101 10010 01110 11011 Output 10001 Note In the first sample test case only the first currency is liked by at least ⌈ 3/2 ⌉ = 2 friends, therefore it's easy to demonstrate that a better answer cannot be found. In the second sample test case the answer includes 2 currencies and will be liked by friends 1, 2, and 5. For this test case there are other currencies that are liked by at least half of the friends, but using them we cannot achieve a larger subset size.
instruction
0
45,624
10
91,248
Tags: bitmasks, brute force, dp, probabilities Correct Solution: ``` import sys import bisect from bisect import bisect_left as lb input_=lambda: sys.stdin.readline().strip("\r\n") from math import log from math import gcd from math import atan2,acos from random import randint sa=lambda :input_() sb=lambda:int(input_()) sc=lambda:input_().split() sd=lambda:list(map(int,input_().split())) sflo=lambda:list(map(float,input_().split())) se=lambda:float(input_()) sf=lambda:list(input_()) flsh=lambda: sys.stdout.flush() #sys.setrecursionlimit(10**6) mod=10**9+7 mod1=998244353 gp=[] cost=[] dp=[] mx=[] ans1=[] ans2=[] special=[] specnode=[] a=0 kthpar=[] def dfs(root,par): if par!=-1: dp[root]=dp[par]+1 for i in range(1,20): if kthpar[root][i-1]!=-1: kthpar[root][i]=kthpar[kthpar[root][i-1]][i-1] for child in gp[root]: if child==par:continue kthpar[child][0]=root dfs(child,root) ans=0 b=[] def hnbhai(tc): n,m,p=sd() a=[] for i in range(n): a.append(sa()) ans="" mx=-1 for _ in range(40): ind=(randint(0,10**6))%n pos=[] num=0 cnt=0 for i in range(m): if a[ind][i]=='1': pos.append(i) num|=(1<<i) cnt+=1 dp=[0]*(1<<cnt) for i in a: nn=0 for j in range(len(pos)): if i[pos[j]]=='1': nn|=1<<j dp[nn]+=1 for i in range(len(pos)): for j in range(1<<cnt): if (j>>i)&1: dp[j^(1<<i)]+=dp[j] for i in range(1<<cnt): if 2*dp[i]>=n and (bin(i)[2:]).count('1')>mx: temp=["0"]*m for j in range(len(pos)): if (i>>j)&1: temp[pos[j]]='1' mx=(bin(i)[2:]).count('1') ans="".join(temp) print(ans) for _ in range(1): hnbhai(_+1) ```
output
1
45,624
10
91,249
Provide tags and a correct Python 3 solution for this coding contest problem. <image> William is hosting a party for n of his trader friends. They started a discussion on various currencies they trade, but there's an issue: not all of his trader friends like every currency. They like some currencies, but not others. For each William's friend i it is known whether he likes currency j. There are m currencies in total. It is also known that a trader may not like more than p currencies. Because friends need to have some common topic for discussions they need to find the largest by cardinality (possibly empty) subset of currencies, such that there are at least ⌈ n/2 ⌉ friends (rounded up) who like each currency in this subset. Input The first line contains three integers n, m and p (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ p ≤ m ≤ 60, 1 ≤ p ≤ 15), which is the number of trader friends, the number of currencies, the maximum number of currencies each friend can like. Each of the next n lines contain m characters. The j-th character of i-th line is 1 if friend i likes the currency j and 0 otherwise. It is guaranteed that the number of ones in each line does not exceed p. Output Print a string of length m, which defines the subset of currencies of the maximum size, which are liked by at least half of all friends. Currencies belonging to this subset must be signified by the character 1. If there are multiple answers, print any. Examples Input 3 4 3 1000 0110 1001 Output 1000 Input 5 5 4 11001 10101 10010 01110 11011 Output 10001 Note In the first sample test case only the first currency is liked by at least ⌈ 3/2 ⌉ = 2 friends, therefore it's easy to demonstrate that a better answer cannot be found. In the second sample test case the answer includes 2 currencies and will be liked by friends 1, 2, and 5. For this test case there are other currencies that are liked by at least half of the friends, but using them we cannot achieve a larger subset size.
instruction
0
45,625
10
91,250
Tags: bitmasks, brute force, dp, probabilities Correct Solution: ``` import random # Python program to compute sum of ranges for different range queries from collections import defaultdict import math import os import sys from io import BytesIO, IOBase from types import GeneratorType from collections import defaultdict BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") n, m, p = map(int, input().split()) b = [] for j in range(n): s = input() c = [] for j in s: c.append(int(j)) b.append(c) tot=0 ans=["0" for i in range(m)] atleast=math.ceil(n/2) for i in range(10): ind = random.randint(-10 ** 18, 10 ** 18) % n req = b[ind] d1 = [] d = defaultdict(lambda:0) l = 0 for j in range(m): if req[j] == 1: d[l] = j d1.append(j) l += 1 ma=1<<l cnt = [0 for i in range(ma)] for j in range(n): req = 0 c = 0 for k in d1: if b[j][k] == 1: req += (1<<c) c += 1 cnt[req]+=1 for i in range(l): for mask in range(ma): if mask&(1<<i): cnt[mask^(1<<i)]+=cnt[mask] for mask in range(ma): if cnt[mask]>=atleast: req=["0" for k in range(m)] total=0 for u in range(16): if (mask & (1<<u)): req[d[u]]="1" total+=1 if total>tot: tot=total ans=req print("".join(ans)) ```
output
1
45,625
10
91,251
Provide tags and a correct Python 3 solution for this coding contest problem. <image> William is hosting a party for n of his trader friends. They started a discussion on various currencies they trade, but there's an issue: not all of his trader friends like every currency. They like some currencies, but not others. For each William's friend i it is known whether he likes currency j. There are m currencies in total. It is also known that a trader may not like more than p currencies. Because friends need to have some common topic for discussions they need to find the largest by cardinality (possibly empty) subset of currencies, such that there are at least ⌈ n/2 ⌉ friends (rounded up) who like each currency in this subset. Input The first line contains three integers n, m and p (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ p ≤ m ≤ 60, 1 ≤ p ≤ 15), which is the number of trader friends, the number of currencies, the maximum number of currencies each friend can like. Each of the next n lines contain m characters. The j-th character of i-th line is 1 if friend i likes the currency j and 0 otherwise. It is guaranteed that the number of ones in each line does not exceed p. Output Print a string of length m, which defines the subset of currencies of the maximum size, which are liked by at least half of all friends. Currencies belonging to this subset must be signified by the character 1. If there are multiple answers, print any. Examples Input 3 4 3 1000 0110 1001 Output 1000 Input 5 5 4 11001 10101 10010 01110 11011 Output 10001 Note In the first sample test case only the first currency is liked by at least ⌈ 3/2 ⌉ = 2 friends, therefore it's easy to demonstrate that a better answer cannot be found. In the second sample test case the answer includes 2 currencies and will be liked by friends 1, 2, and 5. For this test case there are other currencies that are liked by at least half of the friends, but using them we cannot achieve a larger subset size.
instruction
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Tags: bitmasks, brute force, dp, probabilities Correct Solution: ``` import random from math import ceil import os import sys from io import BytesIO, IOBase # region fastio BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") n,m,p = map(int,input().split()) A = [] for _ in range(n): A.append(input()) num_iter = 20 mx_bit_cnt = 0 ans = None def solve(i): global n,m,p,mx_bit_cnt,ans I = [idx for idx in range(m) if A[i][idx] == "1"] L = len(I) C = [0]*(1<<L) for j in range(n): cur = 0 for l in range(L): if A[j][I[l]] == "1": cur += (1<<l) C[cur] += 1 for i in range(L): for mask in range((1<<L)-1,-1,-1): if mask & (1<<i): C[mask^(1<<i)] += C[mask] for mask in range(1<<L): bit_cnt = bin(mask).count("1") if C[mask] < ceil(n/2): continue if bit_cnt >= mx_bit_cnt: mx_bit_cnt = bit_cnt temp = ["0"]*m for l in range(L): if mask & (1<<l): temp[I[l]] = "1" ans = "".join(temp) while num_iter: num_iter -= 1 i = random.randint(0,n-1) solve(i) print(ans) ```
output
1
45,626
10
91,253
Provide tags and a correct Python 3 solution for this coding contest problem. <image> William is hosting a party for n of his trader friends. They started a discussion on various currencies they trade, but there's an issue: not all of his trader friends like every currency. They like some currencies, but not others. For each William's friend i it is known whether he likes currency j. There are m currencies in total. It is also known that a trader may not like more than p currencies. Because friends need to have some common topic for discussions they need to find the largest by cardinality (possibly empty) subset of currencies, such that there are at least ⌈ n/2 ⌉ friends (rounded up) who like each currency in this subset. Input The first line contains three integers n, m and p (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ p ≤ m ≤ 60, 1 ≤ p ≤ 15), which is the number of trader friends, the number of currencies, the maximum number of currencies each friend can like. Each of the next n lines contain m characters. The j-th character of i-th line is 1 if friend i likes the currency j and 0 otherwise. It is guaranteed that the number of ones in each line does not exceed p. Output Print a string of length m, which defines the subset of currencies of the maximum size, which are liked by at least half of all friends. Currencies belonging to this subset must be signified by the character 1. If there are multiple answers, print any. Examples Input 3 4 3 1000 0110 1001 Output 1000 Input 5 5 4 11001 10101 10010 01110 11011 Output 10001 Note In the first sample test case only the first currency is liked by at least ⌈ 3/2 ⌉ = 2 friends, therefore it's easy to demonstrate that a better answer cannot be found. In the second sample test case the answer includes 2 currencies and will be liked by friends 1, 2, and 5. For this test case there are other currencies that are liked by at least half of the friends, but using them we cannot achieve a larger subset size.
instruction
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Tags: bitmasks, brute force, dp, probabilities Correct Solution: ``` import random import sys from sys import stdin def popcnt(x): ret = 0 while x > 0: ret += x % 2 x //= 2 return ret n,m,p = map(int,stdin.readline().split()) s = [stdin.readline()[:-1] for i in range(n)] ans = 0 anslis = ["0"] * m for loop in range(20): v = random.randint(0,n-1) vbits = [] for i in range(m): if s[v][i] == "1": vbits.append(i) dp = [0] * (2**len(vbits)) vbits.reverse() for i in range(n): now = 0 for j in vbits: now *= 2 if s[i][j] == "1": now += 1 dp[now] += 1 vbits.reverse() #print (v,dp) for j in range(len(vbits)): for i in range(len(dp)): if i & 2**j == 0: dp[i] += dp[i | 2**j] #print (v,dp) for i in range(len(dp)): if dp[i] >= (n+1)//2: pc = popcnt(i) if ans < pc: #print ("change!") ans = pc anslis = [0] * m for j in range(len(vbits)): if 2**j & i > 0: anslis[vbits[j]] = 1 print ("".join(map(str,anslis))) ```
output
1
45,627
10
91,255
Provide tags and a correct Python 3 solution for this coding contest problem. <image> William is hosting a party for n of his trader friends. They started a discussion on various currencies they trade, but there's an issue: not all of his trader friends like every currency. They like some currencies, but not others. For each William's friend i it is known whether he likes currency j. There are m currencies in total. It is also known that a trader may not like more than p currencies. Because friends need to have some common topic for discussions they need to find the largest by cardinality (possibly empty) subset of currencies, such that there are at least ⌈ n/2 ⌉ friends (rounded up) who like each currency in this subset. Input The first line contains three integers n, m and p (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ p ≤ m ≤ 60, 1 ≤ p ≤ 15), which is the number of trader friends, the number of currencies, the maximum number of currencies each friend can like. Each of the next n lines contain m characters. The j-th character of i-th line is 1 if friend i likes the currency j and 0 otherwise. It is guaranteed that the number of ones in each line does not exceed p. Output Print a string of length m, which defines the subset of currencies of the maximum size, which are liked by at least half of all friends. Currencies belonging to this subset must be signified by the character 1. If there are multiple answers, print any. Examples Input 3 4 3 1000 0110 1001 Output 1000 Input 5 5 4 11001 10101 10010 01110 11011 Output 10001 Note In the first sample test case only the first currency is liked by at least ⌈ 3/2 ⌉ = 2 friends, therefore it's easy to demonstrate that a better answer cannot be found. In the second sample test case the answer includes 2 currencies and will be liked by friends 1, 2, and 5. For this test case there are other currencies that are liked by at least half of the friends, but using them we cannot achieve a larger subset size.
instruction
0
45,628
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91,256
Tags: bitmasks, brute force, dp, probabilities Correct Solution: ``` import random import sys from sys import stdin def popcnt(x): ret = 0 while x > 0: ret += x % 2 x //= 2 return ret n,m,p = map(int,stdin.readline().split()) s = [stdin.readline()[:-1] for i in range(n)] ans = 0 anslis = ["0"] * m for loop in range(8): v = random.randint(0,n-1) vbits = [] for i in range(m): if s[v][i] == "1": vbits.append(i) dp = [0] * (2**len(vbits)) vbits.reverse() for i in range(n): now = 0 for j in vbits: now *= 2 if s[i][j] == "1": now += 1 dp[now] += 1 vbits.reverse() #print (v,dp) for j in range(len(vbits)): for i in range(len(dp)): if i & 2**j == 0: dp[i] += dp[i | 2**j] #print (v,dp) for i in range(len(dp)): if dp[i] >= (n+1)//2: pc = popcnt(i) if ans < pc: #print ("change!") ans = pc anslis = [0] * m for j in range(len(vbits)): if 2**j & i > 0: anslis[vbits[j]] = 1 print ("".join(map(str,anslis))) ```
output
1
45,628
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91,257
Provide tags and a correct Python 3 solution for this coding contest problem. <image> William is hosting a party for n of his trader friends. They started a discussion on various currencies they trade, but there's an issue: not all of his trader friends like every currency. They like some currencies, but not others. For each William's friend i it is known whether he likes currency j. There are m currencies in total. It is also known that a trader may not like more than p currencies. Because friends need to have some common topic for discussions they need to find the largest by cardinality (possibly empty) subset of currencies, such that there are at least ⌈ n/2 ⌉ friends (rounded up) who like each currency in this subset. Input The first line contains three integers n, m and p (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ p ≤ m ≤ 60, 1 ≤ p ≤ 15), which is the number of trader friends, the number of currencies, the maximum number of currencies each friend can like. Each of the next n lines contain m characters. The j-th character of i-th line is 1 if friend i likes the currency j and 0 otherwise. It is guaranteed that the number of ones in each line does not exceed p. Output Print a string of length m, which defines the subset of currencies of the maximum size, which are liked by at least half of all friends. Currencies belonging to this subset must be signified by the character 1. If there are multiple answers, print any. Examples Input 3 4 3 1000 0110 1001 Output 1000 Input 5 5 4 11001 10101 10010 01110 11011 Output 10001 Note In the first sample test case only the first currency is liked by at least ⌈ 3/2 ⌉ = 2 friends, therefore it's easy to demonstrate that a better answer cannot be found. In the second sample test case the answer includes 2 currencies and will be liked by friends 1, 2, and 5. For this test case there are other currencies that are liked by at least half of the friends, but using them we cannot achieve a larger subset size.
instruction
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45,629
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Tags: bitmasks, brute force, dp, probabilities Correct Solution: ``` import sys import bisect from bisect import bisect_left as lb input_=lambda: sys.stdin.readline().strip("\r\n") from math import log from math import gcd from math import atan2,acos from random import randint sa=lambda :input_() sb=lambda:int(input_()) sc=lambda:input_().split() sd=lambda:list(map(int,input_().split())) sflo=lambda:list(map(float,input_().split())) se=lambda:float(input_()) sf=lambda:list(input_()) flsh=lambda: sys.stdout.flush() #sys.setrecursionlimit(10**6) mod=10**9+7 mod1=998244353 gp=[] cost=[] dp=[] mx=[] ans1=[] ans2=[] special=[] specnode=[] a=0 kthpar=[] def dfs(root,par): if par!=-1: dp[root]=dp[par]+1 for i in range(1,20): if kthpar[root][i-1]!=-1: kthpar[root][i]=kthpar[kthpar[root][i-1]][i-1] for child in gp[root]: if child==par:continue kthpar[child][0]=root dfs(child,root) ans=0 b=[] def hnbhai(tc): n,m,p=sd() a=[] for i in range(n): a.append(sa()) ans="" mx=-1 for _ in range(40): ind=randint(0,n-1) pos=[] num=0 cnt=0 for i in range(m): if a[ind][i]=='1': pos.append(i) num|=(1<<i) cnt+=1 dp=[0]*(1<<cnt) for i in a: nn=0 for j in range(len(pos)): if i[pos[j]]=='1': nn|=1<<j dp[nn]+=1 for i in range(len(pos)): for j in range(1<<cnt): if (j>>i)&1: dp[j^(1<<i)]+=dp[j] for i in range(1<<cnt): if 2*dp[i]>=n and (bin(i)[2:]).count('1')>mx: temp=["0"]*m for j in range(len(pos)): if (i>>j)&1: temp[pos[j]]='1' mx=(bin(i)[2:]).count('1') ans="".join(temp) print(ans) for _ in range(1): hnbhai(_+1) ```
output
1
45,629
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91,259