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 itertools
H, W, K = map(int,input().split())
S = [list(map(int,list(input()))) for _ in range(H)]
def check(k):
    if k <= K:
        return(True)
    else:
        return(False)
        
noans = 0
def make_lst(i):
    global noans, lst, havelst
    temp = S[0][i]
    for h in range(H-1):
        if y[h]:
            lst.append(temp)
            temp = S[h+1][i]
        else:
            temp += S[h+1][i]
    lst.append(temp)
    if check(max(lst)):
        havelst = 1
    else:
        noans = 1
               
def nocut(i):
    global cutnum, lst, havelst
    prelst = []
    temp = S[0][i]
    j = 0
    for h in range(H-1):
        if y[h]:
            lst[j] += temp
            prelst.append(temp)
            j += 1
            temp = S[h+1][i]
        else:
            temp += S[h+1][i]
    prelst.append(temp)
    lst[-1] += temp
    if check(max(lst)):
        return(True)
    else:
        cutnum += 1
        lst = prelst        
                 
ans = float("inf")
cutlst = []    
for y in itertools.product((0, 1), repeat=H-1):
    havelst = 0
    lst = []
    cutnum = sum(y)
    for x in range(W):
        if noans:
          	noans = 0
            break
        if havelst:
            nocut(x)
        else:
            make_lst(x)
    ans = min(cutnum, ans)
print(ans)
                


import itertools
H, W, K = map(int,input().split())
S = [list(map(int,list(input()))) for _ in range(H)]
def check(k):
    if k <= K:
        return(True)
    else:
        return(False)
        
noans = 0
def make_lst(i):
    global noans, lst, havelst
    temp = S[0][i]
    for h in range(H-1):
        if y[h]:
            lst.append(temp)
            temp = S[h+1][i]
        else:
            temp += S[h+1][i]
    lst.append(temp)
    if check(max(lst)):
        havelst = 1
    else:
        noans = 1
#    print(y,i,lst, "makelst")
               
def nocut(i):
    global cutnum, lst, havelst, noans
    prelst = []
    temp = S[0][i]
    if i == W-1:
        if not check(temp):
            noans = 1
    j = 0
    for h in range(H-1):            
        if y[h]:
            lst[j] += temp
            prelst.append(temp)
            j += 1
            temp = S[h+1][i]
        else:
            temp += S[h+1][i]
        if i == W-1:
            if not check(temp):
                noans = 1
    prelst.append(temp)
    lst[-1] += temp
    if check(max(lst)):

        return(True)
    else:
        cutnum += 1
        lst = prelst        

        
                 
ans = float("inf")    
for y in itertools.product((0, 1), repeat=H-1):
    havelst = 0
    lst = []
    cutnum = sum(y)
    for x in range(W):
        if noans:
            break
        if havelst:
            nocut(x)
        else:
            make_lst(x)
#    print(y,cutnum)
    if noans:
        noans = 0
        continue
    else:
        ans = min(cutnum, ans)
print(ans)

Verdicts: Runtime Error

Accepted