Problem: We have a chocolate bar partitioned into H horizontal rows and W vertical columns of squares.  The square (i, j) at the i-th row from the top and the j-th column from the left is dark if S_{i,j} is `0`, and white if S_{i,j} is `1`.  We will cut the bar some number of times to divide it into some number of blocks. In each cut, we cut the whole bar by a line running along some boundaries of squares from end to end of the bar.  How many times do we need to cut the bar so that every block after the cuts has K or less white squares?

Submission attempts (in order):
import numpy as np
from itertools import product

H,W,K = map(int, input().split())
S = np.array(([list(map(int,list(input()))) for _ in range(H)])).T

if sum(sum(s) for s in S)<=K:
    print(0)
else:
    answer = (H-1) * (W-1)
    for X in product([False,True], repeat=H-1):
        ans = np.sum(X)
        if ans >= answer:
            continue
        M = [[0]]
        for i, x in enumerate(X):
            if x:
                M.append([])
            M[-1].append(i+1)
        D = np.array([0]*len(M))
        for s in S:
            D[:] += [sum(s[i] for i in m) for m in M]
            if any(d > K  for d in D):
                ans += 1
                if ans >= answer:
                    break
                D[:] = [sum(s[i] for i in m) for m in M]
                if any(d > K for d in D):
                    ans = answer + 1
                    break

        answer = min(answer,ans)

    print(answer

import numpy as np
from itertools import product

H,W,K = map(int, input().split())
S = np.array([list(map(int,list(input()))) for _ in range(H)]).T
"""
H,W,K = 3,5,2

S = [[1,1,1,0,0],
     [1,0,0,0,1],
     [0,0,1,1,1]]
"""


S = np.array(S).T

if np.sum(S)<=K:
    print(0)
else:
    answer = H * W
    for X in product([False,True], repeat=H-1):
        ans = np.sum(X)
        #print(ans)
        M = [[0]]
        for i, x in enumerate(X):
            if x:
                M.append([])
            M[-1].append(i+1)
        #print(M)
        D = [0]*len(M)
        #print(D)
        for s in S:
            for k, m in enumerate(M):
                D[k] += np.sum(s[i] for i in m)
                #print("D",D)
            if any(d > K  for d in D):
                ans += 1
                #print("ans",ans)
                D[:] = [np.sum(s[i] for i in m) for m in M]
                
        if answer > ans:
            answer = ans

    print(min(answer,ans))

import numpy as np
from itertools import product

H,W,K = map(int, input().split())
S = np.array(([list(map(int,list(input()))) for _ in range(H)])).T
print(S)

if np.sum(S)<=K:
    print(0)
else:
    answer = H * W
    for X in product([False,True], repeat=H-1):
        ans = np.sum(X)
        M = [[0]]
        for i, x in enumerate(X):
            if x:
                M.append([])
            M[-1].append(i+1)
        #print(M)
        D = np.zeros(len(M))
        #print(D)
        for s in S:
            D[:] += [np.sum(s[i] for i in m) for m in M]
            if any(d > K  for d in D):
                ans += 1
                #print("ans",ans)
                D[:] = [np.sum(s[i] for i in m) for m in M]
                
        if answer > ans:
            answer = ans

    print(min(answer,ans))


def main():
    from itertools import product

    H,W,K = map(int, input().split())
    S = [list(input()) for _ in range(H)]
    
    i = 0
    while i < len(S):
        if '1' in S[i]:
            i += 1
        else:
            del S[i]
    H = len(S)
 
    S = [[int(s[i]) for s in S] for i in range(W)]

    if sum(sum(s) for s in S)<=K:
        print(0)
    else:
        answer = (H-1) * (W-1)
        for X in product([False,True], repeat=H-1):
            ans = np.sum(X)
            if ans >= answer:
                continue
            M = [[0]]
            for i, x in enumerate(X):
                if x:
                    M.append([])
                M[-1].append(i+1)
            D = [0]*len(M)
            for s in S:
                for k, m in enumerate(M):
                    D[k] += sum(s[i] for i in m)
                if any(d > K  for d in D):
                    ans += 1
                    if ans >= answer:
                        break
                    for k, m in enumerate(M):
                        D[k] = sum(s[i] for i in m)
                    
                    if any(d > K for d in D):
                        ans = answer + 1
                        break

            answer = min(answer,ans)

        print(answer)

main()

import numpy as np
from itertools import product

H,W,K = map(int, input().split())
S = np.array(([list(map(int,list(input()))) for _ in range(H)])).T

if np.sum(S)<=K:
    print(0)
else:
    answer = H * W
    for X in product([False,True], repeat=H-1):
        ans = np.sum(X)
        M = [[0]]
        for i, x in enumerate(X):
            if x:
                M.append([])
            M[-1].append(i+1)
        D = [0]*len(M)
        for s in S:
            D[:] += [sum(s[i] for i in m) for m in M]
            if any(d > K  for d in D):
                ans += 1
                D[:] = [sum(s[i] for i in m) for m in M]
                
        if answer > ans:
            answer = ans

    print(min(answer,ans))

import numpy as np
from itertools import product

H,W,K = map(int, input().split())
S = np.array(([list(map(int,list(input()))) for _ in range(H)])).T

if np.sum(S)<=K:
    print(0)
else:
    answer = H * W
    D = []
    for X in product([False,True], repeat=H-1):
        ans = np.sum(X)
        if ans > answer:
            continue
        M = [[0]]
        for i, x in enumerate(X):
            if x:
                M.append([])
            M[-1].append(i+1)
        D = [0]*len(M)
        for s in S:
            D[:] += [sum(s[i] for i in m) for m in M]
            print(D)
            if any(d > K  for d in D):
                ans += 1
                D[:] = [sum(s[i] for i in m) for m in M]

    if answer > ans:
        answer = ans

    print(min(answer,ans))

import numpy as np
from itertools import product

H,W,K = map(int, input().split())
S = np.array(([list(map(int,list(input()))) for _ in range(H)])).T

if np.sum(S)<=K:
    print(0)
else:
    answer = H * W
    for X in product([False,True], repeat=H-1):
        ans = np.sum(X)
        if ans >= answer:
            continue
        M = [[0]]
        for i, x in enumerate(X):
            if x:
                M.append([])
            M[-1].append(i+1)
        D = np.zeros(len(M))
        for s in S:
            D[:] += [sum(s[i] for i in m) for m in M]
            print(D)
            if any(d > K  for d in D):
                ans += 1
                if ans >= answer:
                    break
                D[:] = [sum(s[i] for i in m) for m in M]

    if answer > ans:
        answer = ans

    print(min(answer,ans))


def main():
    from itertools import product

    H,W,K = map(int, input().split())
    S = [list(input()) for _ in range(H)]
    
    i = 0
    while i < len(S):
        if '1' in S[i]:
            i += 1
        else:
            del S[i]
    H = len(S)
 
    S = [[int(s[i]) for s in S] for i in range(W)]

    if sum(sum(s) for s in S)<=K:
        print(0)
    else:
        answer = (H-1) * (W-1)
        for X in product([False,True], repeat=H-1):
            ans = np.sum(X)
            if ans >= answer:
                continue
            M = [[0]]
            for i, x in enumerate(X):
                if x:
                    M.append([])
                M[-1].append(i+1)
            D = np.array([0]*len(M))
            for s in S:
                D[:] += [sum(s[i] for i in m) for m in M]
                if any(d > K  for d in D):
                    ans += 1
                    if ans >= answer:
                        break
                    D[:] = [sum(s[i] for i in m) for m in M]
                    if any(d > K for d in D):
                        ans = answer + 1
                        break

            answer = min(answer,ans)

        print(answer)

main()


def main():
    from itertools import product
    import numpy as np

    H,W,K = map(int, input().split())
    S = (np.array([list(map(int,list(input()))) for _ in range(H)]).T).tolist()

    if sum(sum(s) for s in S)<=K:
        print(0)
    else:
        answer = (H-1) * (W-1)
        for X in product([False,True], repeat=H-1):
            ans = np.sum(X)
            if ans >= answer:
                continue
            M = [[0]]
            for i, x in enumerate(X):
                if x:
                    M.append([])
                M[-1].append(i+1)
            D = [0]*len(M)
            for s in S:
                for k, m in enumerate(M):
                    D[k] += sum(s[i] for i in m)
                if any(d > K  for d in D):
                    ans += 1
                    if ans >= answer:
                        break
                    for k, m in enumerate(M):
                        D[k] = sum(s[i] for i in m)
                    
                    if any(d > K for d in D):
                        ans = answer + 1
                        break

            answer = min(answer,ans)

        print(answer)

main()

Verdicts: Runtime Error

Wrong Answer

Wrong Answer

Runtime Error

Wrong Answer

Wrong Answer

Wrong Answer

Runtime Error

Accepted