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):
h,w,k = map(int,input().split())
choco = [list(map(int,list(input()))) for _ in range(h)]

white = [[0]*w for _ in range(h)]
for i in range(h):
    for j in range(w):
        if i != 0:
            white[i][j] += white[i-1][j]
        if j != 0:
            white[i][j] += white[i][j-1]
        if i != 0 and j != 0:
            white[i][j] -= white[i-1][j-1]
        white[i][j] += choco[i][j]
ans = float('inf')
for i in range(2**(h-1)): 
    temp = format(i,'b').count('1') 
    hw = []
    j = i
    cnt = 0
    while j >0:
        if j&1:
            hw.append(cnt)
        cnt += 1
        j = j >> 1
    hw.append(h-1)
    now = -1
    #if w == 1:
    flag = True
    for l in range(len(hw)):
        if l == 0:
            if white[hw[l]][0] > k:
                flag = False
                break
        else:
            if white[hw[l]][0] - white[hw[l-1]][0] > k:
                flag = False
                break
    if not flag:
        continue
    else:
        ans = min(ans,temp)
        continue
    for j in range(w-1):
        flag = True
        if now == -1:
            for l in range(len(hw)):
                if l == 0:
                    if white[hw[l]][j+1] > k:
                        flag = False
                        break
                else:
                    if white[hw[l]][j+1] - white[hw[l-1]][j+1] > k:
                        flag = False
                        break
            if not flag:
                now = j
                temp += 1
        else:
            for l in range(len(hw)):
                if l == 0:
                    if white[hw[l]][j+1] - white[hw[l]][now] > k:
                        flag = False
                        break
                else:
                    if white[hw[l]][j+1] - white[hw[l]][now] - white[hw[l-1]][j+1] + white[hw[l-1]][now]> k:
                        flag = False
                        break
            if not flag:
                now = j
                temp += 1
    ans = min(ans,temp)
print(ans)


h,w,k = map(int,input().split())
choco = [list(map(int,list(input()))) for _ in range(h)]

white = [[0]*w for _ in range(h)]
for i in range(h):
    for j in range(w):
        if i != 0:
            white[i][j] += white[i-1][j]
        if j != 0:
            white[i][j] += white[i][j-1]
        if i != 0 and j != 0:
            white[i][j] -= white[i-1][j-1]
        white[i][j] += choco[i][j]
ans = float('inf')
for i in range(2**(h-1)): 
    temp = format(i,'b').count('1') 
    hw = []
    j = i
    cnt = 0
    while j >0:
        if j&1:
            hw.append(cnt)
        cnt += 1
        j = j >> 1
    hw.append(h-1)
    now = -1
    #if w == 1:
    flag = True
    for l in range(len(hw)):
        if l == 0:
            if white[hw[l]][0] > k:
                flag = False
                break
        else:
            if white[hw[l]][0] - white[hw[l-1]][0] > k:
                flag = False
                break
    if not flag:
        continue
    elif w == 1:
        ans = min(ans,temp)
        continue

    for j in range(w-1):
        flag = True
        if now == -1:
            for l in range(len(hw)):
                if l == 0:
                    if white[hw[l]][j+1] > k:
                        flag = False
                        break
                else:
                    if white[hw[l]][j+1] - white[hw[l-1]][j+1] > k:
                        flag = False
                        break
            if not flag:
                now = j
                temp += 1
        else:
            for l in range(len(hw)):
                if l == 0:
                    if white[hw[l]][j+1] - white[hw[l]][now] > k:
                        flag = False
                        break
                else:
                    if white[hw[l]][j+1] - white[hw[l]][now] - white[hw[l-1]][j+1] + white[hw[l-1]][now]> k:
                        flag = False
                        break
            if not flag:
                now = j
                temp += 1
    ans = min(ans,temp)
print(ans)


Verdicts: Wrong Answer

Accepted