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):
from itertools import combinations, chain

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


def h_divide(Sss, div_is):
    result = []
    for s, e in zip(chain([0], div_is), chain(div_is, [len(Sss)])):
        result.append(Sss[s:e])
    return result


def _v_end(Sss, start, K):
    count = 0
    for i in range(start, len(Sss[0])):
        s = sum(map(lambda Ss: Ss[i], Sss))
        if count + s > K:
            return i - 1
        count += s
    return len(Sss[0]) - 1


def v_end(Ssss, start, K):
    result = -1
    for Sss in Ssss:
        end = _v_end(Sss, start, K)
        if end < start:
            return -1
        if result < 0 or result > end:
            result = end
    return result


def v_div_count(Ssss, K):
    start, result = 0, 0
    while True:
        end = v_end(Ssss, start, K)
        if end < 0:
            return -1
        if end == len(Ssss[0][0]) - 1:
            break
        result += 1
        start = end + 1
    return result


h_cands = list(range(1, len(Sss)))
ans = -1
for n in range(len(h_cands) + 1):
    for comb in combinations(h_cands, n):
        if n >= ans:
            continue
        Ssss = h_divide(Sss, list(comb))
        cnt = v_div_count(Ssss, K)
        if cnt < 0:
            continue
        if ans < 0 or ans > n + cnt:
            ans = n + cnt
print(ans)


from itertools import combinations, chain

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


def h_divide(Sss, div_is):
    result = []
    for s, e in zip(chain([0], div_is), chain(div_is, [len(Sss)])):
        result.append(Sss[s:e])
    return result


def _v_end(Sss, start, K):
    count = 0
    for i in range(start, len(Sss[0])):
        s = sum(map(lambda Ss: Ss[i], Sss))
        if count + s > K:
            return i - 1
        count += s
    return len(Sss[0]) - 1


def v_end(Ssss, start, K):
    result = -1
    for Sss in Ssss:
        end = _v_end(Sss, start, K)
        if end < start:
            return -1
        if result < 0 or result > end:
            result = end
    return result


def v_div_count(Ssss, K):
    start, result = 0, 0
    while True:
        end = v_end(Ssss, start, K)
        if end < 0:
            return -1
        if end == len(Ssss[0][0]) - 1:
            break
        result += 1
        start = end + 1
    return result


h_cands = list(range(1, len(Sss)))
ans = -1
for n in range(len(h_cands) + 1):
    for comb in combinations(h_cands, n):
        if ans > 0 and n >= ans:
            continue
        Ssss = h_divide(Sss, list(comb))
        cnt = v_div_count(Ssss, K)
        if cnt < 0:
            continue
        if ans < 0 or ans > n + cnt:
            ans = n + cnt
print(ans)


Verdicts: Wrong Answer

Accepted