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):
def main():
    import numpy as np
    h,w,k = map(int,input().split())
    l = [list(input()) for i in range(h)]

    def check(lis):
        
        num = np.zeros(len(lis))
        ans = 0
        for i in range(w):
            num2 = np.zeros(len(lis))
            for j in range(h):
                if l[j][i] == "1":
                    num2[d[j]] += 1
            
            if np.max(num2) > k:
                return float("INF")
            else:
                num += num2
            if np.max(num) > k:
                ans += 1
                num = num2
            
        return ans

    ans = 10**9

    for i in range(2**(h-1)):
        count = 0
        lis1 = []
        d = []
        for j in range(h-1):
            d.append(count)
            if (i >> j) & 1:
                lis1.append(j)
                count += 1
        lis1.append(count+1)
        
        ans = min(ans,count+check(lis1))
        
    print(ans)
if __name__ == "__main__":
    main()


def main():
    
    h,w,k = map(int,input().split())
    l = [list(input()) for i in range(h)]

    def check(lis):
        lis.append(h)
        num = [0]*(len(lis))
        ans = 0
        for i in range(w):
            ch = 0
            num2 = [0]*(len(lis))
            for j in range(h):
                
                if l[j][i] == "1":
                    if j <= lis[ch]:
                        num2[ch] += 1
                    else:
                        ch += 1
                        num2[ch] += 1
            if max(num2) > k:
                return float("INF")
            else:
                for i in range(len(num)):
                    num[i] += num2[i]
                    if num[i] > k:
                        ans += 1
                        num = num2
                        break 
            
            
        return ans

    ans = 10**9

    for i in range(2**(h-1)):
        count = 0
        lis1 = []
        for j in range(h-1):
            if (i >> j) & 1:
                lis1.append(j)
                count += 1
        
        ans = min(ans,count+check(lis1))
        
    print(ans)
if __name__ == "__main__":
    main()def main():
    
    h,w,k = map(int,input().split())
    l = [list(input()) for i in range(h)]

    def check(lis):
        lis.append(h)
        num = [0]*(len(lis))
        ans = 0
        for i in range(w):
            ch = 0
            num2 = [0]*(len(lis))
            for j in range(h):
                
                if l[j][i] == "1":
                    if j <= lis[ch]:
                        num2[ch] += 1
                    else:
                        ch += 1
                        num2[ch] += 1
            if max(num2) > k:
                return float("INF")
            else:
                for i in range(len(num)):
                    num[i] += num2[i]
                    if num[i] > k:
                        ans += 1
                        num = num2
                        break 
            
            
        return ans

    ans = 10**9

    for i in range(2**(h-1)):
        count = 0
        lis1 = []
        for j in range(h-1):
            if (i >> j) & 1:
                lis1.append(j)
                count += 1
        
        ans = min(ans,count+check(lis1))
        
    print(ans)
if __name__ == "__main__":
    main()

def main():
    
    h,w,k = map(int,input().split())
    l = [list(input()) for i in range(h)]

    def check(lis):
        
        num = [0]*(len(lis))
        ans = 0
        for i in range(w):
            num2 = [0]*(len(lis))
            for j in range(h):
                
                if l[j][i] == "1":
                    num2[d[j]] += 1
            if max(num2) > k:
                return float("INF")
            else:
                for i in range(len(num)):
                    num[i] += num2[i]
                    if num[i] > k:
                        ans += 1
                        num = num2
                        break 
            
            
        return ans

    ans = 10**9

    for i in range(2**(h-1)):
        count = 0
        lis1 = []
        d = []
        for j in range(h):
            d.append(count)
            if (i >> j) & 1:
                lis1.append(j)
                count += 1
        lis1.append(count+1)
        ans = min(ans,count+check(lis1))
        
    print(ans)
if __name__ == "__main__":
    main()

Verdicts: Runtime Error

Runtime Error

Accepted