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 i in range(h):
    string = input()
    temp = []
    for j in range(w):
        temp.append(int(string[j]))
    s.append(temp)

s_arr = np.array(s)

ans = 10**9
for i in range(2**(h-1)):
    bin_str = format(i, '0'+str(h-1)+'b')
    kouryo = np.array([[0 for _ in range(w)]])
    cnt = 0
    start = 0
    new = 0
    for j in range(h-1):
        if bin_str[j] == '1':
            cnt += 1
            new = s_arr[start:j+1].sum(axis=0, keepdims=True)
            if np.any(new>k):
                new = -1
                break
            kouryo = np.concatenate((kouryo, new), axis=0)
            start=j+1
    if new == -1: continue
    kouryo = np.concatenate((kouryo, s_arr[start:].sum(axis=0, keepdims=True)), axis=0)

    wa = kouryo[:, 0]
    for j in range(1, w):
        wa = wa + kouryo[:, j]
        if np.any(wa>k):
            cnt += 1
            wa = kouryo[:, j]
    ans = min(ans, cnt)
print(ans)

import numpy as np

h, w, k = map(int, input().split())
s = []
for i in range(h):
    string = input()
    temp = []
    for j in range(w):
        temp.append(int(string[j]))
    s.append(temp)

s_arr = np.array(s)

ans = 10**9
for i in range(2**(h-1)):
    bin_str = format(i, '0'+str(h-1)+'b')
    kouryo = np.array([[0 for _ in range(w)]])
    cnt = 0
    start = 0
    for j in range(h-1):
        if bin_str[j] == '1':
            cnt += 1
            new = s_arr[start:j+1].sum(axis=0, keepdims=True)
            if np.any(new>k):
                new = 0
                break
            kouryo = np.concatenate((kouryo, new), axis=0)
            start=j+1
    if new == 0: continue
    kouryo = np.concatenate((kouryo, s_arr[start:].sum(axis=0, keepdims=True)), axis=0)

    wa = kouryo[:, 0]
    for j in range(1, w):
        wa = wa + kouryo[:, j]
        if np.any(wa>k):
            cnt += 1
            wa = kouryo[:, j]
    ans = min(ans, cnt)
print(ans)

import numpy as np

h, w, k = map(int, input().split())
s = []
for i in range(h):
    string = input()
    temp = []
    for j in range(w):
        temp.append(int(string[j]))
    s.append(temp)

sum_s = [[0 for i in range(w)] for j in range(h)]
if s[0][0] == 1: sum_s[0][0] = 1
for j in range(1, w):
    sum_s[0][j] = sum_s[0][j-1] + s[0][j]
for i in range(1, h):
    sum_s[i][0] = sum_s[i-1][0] + s[i][0]
for i in range(1, h):
    for j in range(1, w):
        sum_s[i][j] = sum_s[i-1][j] + sum_s[i][j-1] - sum_s[i-1][j-1] + s[i][j]
sum_s = np.array(sum_s)

ans = 10**9
for i in range(2**(h-1)):
    bin_str = format(i, '0'+str(h-1)+'b')
    kouryo = []
    temp_s = sum_s[:]
    cnt = 0
    for j in range(h-1):
        if bin_str[j] == '1':
            cnt += 1
            kouryo.append(list(temp_s[j, :]))
            temp_s[j+1:, :] = temp_s[j+1:, :] - temp_s[j, :]
    kouryo.append(list(sum_s[h-1, :]))

    kouryo = np.array(kouryo)
    for j in range(1, w):
        if cnt >= 10**9: break
        for m in range(len(kouryo)):
            if cnt >= 10**9: break
            if kouryo[m, j] > k:
                kouryo[:, j:] = kouryo[:, j:] - kouryo[:, j-1]
                cnt += 1
                break
        for m in range(len(kouryo)):
            if kouryo[m, j-1] > k:
                cnt += 10**9
                break
    ans = min(ans, cnt)
print(ans)

import numpy as np

h, w, k = map(int, input().split())
s = []
for i in range(h):
    string = input()
    temp = []
    for j in range(w):
        temp.append(int(string[j]))
    s.append(temp)

s_arr = np.array(s)

ans = 10**9
for i in range(2**(h-1)):
    bin_str = format(i, '0'+str(h-1)+'b')
    kouryo = np.array([[0 for _ in range(w)]])
    cnt = 0
    start = 0
    for j in range(h-1):
        if bin_str[j] == '1':
            cnt += 1
            kouryo = np.concatenate((kouryo, s_arr[start:j+1].sum(axis=0, keepdims=True)), axis=0)
            start=j+1
    kouryo = np.concatenate((kouryo, s_arr[start:].sum(axis=0, keepdims=True)), axis=0)

    if cnt > ans: continue
    if np.any(kouryo>k): continue

    wa = np.array([0 for _ in range(len(kouryo))])
    for j in range(w):
        wa += kouryo[:, j]
        if np.max(wa)>k:
            cnt += 1
            if cnt > ans: break
            wa = kouryo[:, j]
    ans = min(ans, cnt)
print(ans)

Verdicts: Runtime Error

Runtime Error

Runtime Error

Accepted