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

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

if S.sum() <= K:
    print(0)
    exit(0)

def satisfy(left, right, S2):
    global K
    for row in S2:
        # if row[left:(right + 1)].sum() > K:
        #     return False
        pass
    return True

# ex. horizons = [0, 0, 1, 0, 0, 1]
def greedy(horizons):
    global W, S
    answer = sum(horizons)
    left = 0
    right = 0
    
    
    # ex.
    # S  = [[1, 1, 1, 0, 0],
    #       [1, 0, 0, 0, 1],
    #       [0, 0, 1, 1, 1]]
    
    # S2 = [[2, 1, 1, 0, 0],
    #       [0, 0, 1, 1, 1]]
    
    top = 0
    bottom = 0
    S2 = []
    for h in horizons:
        if h == 1:
            S2.append(S[:][top:(bottom + 1)].sum(axis=0))
            top = bottom + 1
        bottom += 1
    S2.append(S[:][top:].sum(axis=0))
    while right <= W - 1:
        if not satisfy(left, right, S2):
            
            if left == right:
                return -1
            left = right
            answer += 1
        else:
            right += 1
    return answer

answer = (H - 1) * (W - 1)

# result = greedy([0, 1, 0])

for i in range(0, 2 ** (H - 1)):
    horizons = list(map(int, list(bin(i)[2:].zfill(H - 1))))
    result = greedy(horizons)
    if result > 0 and result < answer:
        answer = result

print(answer)


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

if sum(map(sum, S)) <= K:
    print(0)
    exit(0)

def satisfy(left, right, horizons):
    global K, S
    top = 0
    for idx, h in enumerate(horizons):
        if h == 1:
            bottom = idx
            
            #     row[left:(right + 1)]), S[top:(bottom + 1)]))
            total = 0
            
            if total > K:
                return False
            top = bottom + 1
    row[left:(right + 1)]), S[top:]))
    total = 0
    
    if total > K:
        return False
    return True

# ex. horizons = [0, 0, 1, 0, 0, 1]
def greedy(horizons):
    answer = sum(horizons)
    left = 0
    right = 0
    
    
    while right <= W - 1:
        if not satisfy(left, right, horizons):
            if left == right:
                return -1
            left = right
            answer += 1
        else:
            right += 1
    return answer

answer = (H - 1) * (W - 1)

# result = greedy([0, 1, 0])

for i in range(0, 2 ** (H - 1)):
    horizons = list(map(int, list(bin(i)[2:].zfill(H - 1))))
    result = greedy(horizons)
    if result > 0 and result < answer:
        answer = result

print(answer)


import numpy as np

def main():
    H, W, K = map(int, input().split())
    S = []
    for _ in range(H):
        S.append(list(map(int, list(input()))))
    S = np.array(S)
    if S.sum() <= K:
        print(0)
        exit(0)
    answer = float('INF')
    for i in range(0, 2 ** (H - 1)):
        horizons = list(map(int, list(bin(i)[2:].zfill(H - 1))))
        result = greedy(W, S, K, horizons, answer)
        answer = min(answer, result)
    print(answer)

# ex. horizons = [0, 0, 1, 0, 0, 1]
def greedy(W, S, K, horizons, current_answer):
    answer = sum(horizons)
    # ex.
    # S  = [[1, 1, 1, 0, 0],
    #       [1, 0, 0, 0, 1],
    #       [0, 0, 1, 1, 1]]
    
    # S2 = [[2, 1, 1, 0, 0],
    #       [0, 0, 1, 1, 1]]
    
    top = 0
    bottom = 0
    S2 = []
    for h in horizons:
        if h == 1:
            S2.append(S[:][top:(bottom + 1)].sum(axis=0).tolist())
            top = bottom + 1
        bottom += 1
    S2.append(S[:][top:].sum(axis=0).tolist())
    
    h = len(S2)
    partial_sums = [0] * h
    for right in range(W):
        current = [0] * h
        for idx in range(h):
            current[idx] = S2[idx][right]
            partial_sums[idx] += S2[idx][right]
        
        if max(current) > K:
            return float('INF')
        
        if max(partial_sums) > K:
            answer += 1
            if answer >= current_answer:
                return float('INF')
            partial_sums = current
    return answer

if __name__ == '__main__':
    main()


Verdicts: Wrong Answer

Wrong Answer

Accepted