Buggy python submission (verdict: Time Limit Exceeded):
h, w, k = map(int, input().split())
s = [input() for _ in range(h)]

cum_s = [[0 for _ in range(w+1)] for _ in range(h)]
for i in range(1, w+1):
    for j in range (h):
        cum_s[j][i] += (s[j][i-1] == '1') + cum_s[j][i-1]
#print(cum_s)

ans = 10 ** 6
for i in range(2 ** (h-1)):
    sep = []
    tmp = [0]
    for j in range(h-1):
        if (i >> j) & 1:
            tmp.append(j+1)
        else:
            if tmp != []:
                sep.append(tmp)
            tmp = [j+1]
    sep.append(tmp)
    #print(sep)
    
    idx = 0
    cnt = 0
    for j in range(1,w+1):
        flg = False
        for l in sep:
            tmp_sum = sum([cum_s[x][j] - cum_s[x][idx] for x in l])
            if tmp_sum > k:
                if j - idx == 1:
                    cnt = 10 ** 6
                flg = True
        
        if flg:
            cnt += 1
            idx = j-1 
    #print(len(sep)-1, cnt)
    ans = min(ans, len(sep)-1 + cnt)

if w == 1:
    x = sum([s[i] == '1' for i in range(h)])
    print(max(0, -(-x // k)-1))
elif h == 1:
    x = sum([s[0][i] == '1' for i in range(w)])
    print(max(0, -(-x // k)-1))
else:
    print(ans)

Fixed submission:
h, w, k = map(int, input().split())
s = [input() for _ in range(h)]

cum_s = [[0 for _ in range(w+1)] for _ in range(h)]
for i in range(1, w+1):
    for j in range (h):
        cum_s[j][i] += (s[j][i-1] == '1') + cum_s[j][i-1]
#print(cum_s)

ans = 10 ** 6
for i in range(2 ** (h-1)):
    sep = []
    tmp = [0]
    for j in range(h-1):
        if (i >> j) & 1:
            tmp.append(j+1)
        else:
            if tmp != []:
                sep.append(tmp)
            tmp = [j+1]
    sep.append(tmp)
    #print(sep)
    
    idx = 0
    cnt = 0
    for j in range(1,w+1):
        flg = False
        for l in sep:
            tmp_sum = sum([cum_s[x][j] - cum_s[x][idx] for x in l])
            if tmp_sum > k:
                if j - idx == 1:
                    cnt = 10 ** 6
                flg = True
        
        if flg:
            cnt += 1
            idx = j-1 
    #print(len(sep)-1, cnt)
    ans = min(ans, len(sep)-1 + cnt)

if w == 1:
    x = sum([s[i] == '1' for i in range(h)])
    print(max(0, -(-x // k)-1))
elif h == 1:
    x = sum([s[0][i] == '1' for i in range(w)])
    print(max(0, -(-x // k)-1))
else:
    print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
h, w, k = map(int, input().split())
s = [input() for _ in range(h)]
cum_s = [[0 for _ in range(w+1)] for _ in range(h)]
for i in range(1, w+1):
    for j in range (h):
        cum_s[j][i] += (s[j][i-1] == '1') + cum_s[j][i-1]
#print(cum_s)

ans = 10 ** 6
for i in range(2 ** (h-1)):
    sep = []
    tmp = [0]
    for j in range(h-1):
        if (i >> j) & 1:
            tmp.append(j+1)
        else:
            if tmp != []:
                sep.append(tmp)
            tmp = [j+1]
    sep.append(tmp)
    #print(sep)
    
    idx = 0
    cnt = 0
    for j in range(1,w+1):
        flg = False
        for l in sep:
            tmp_sum = sum([cum_s[x][j] - cum_s[x][idx] for x in l])
            if tmp_sum > k:
                flg = True
        
        if flg:
            cnt += 1
            idx = j-1 
    #print(len(sep)-1, cnt)
    ans = min(ans, len(sep)-1 + cnt)
        
print(ans)

Fixed submission:
h, w, k = map(int, input().split())
s = [input() for _ in range(h)]

cum_s = [[0 for _ in range(w+1)] for _ in range(h)]
for i in range(1, w+1):
    for j in range (h):
        cum_s[j][i] += (s[j][i-1] == '1') + cum_s[j][i-1]
#print(cum_s)

ans = 10 ** 6
for i in range(2 ** (h-1)):
    sep = []
    tmp = [0]
    for j in range(h-1):
        if (i >> j) & 1:
            tmp.append(j+1)
        else:
            if tmp != []:
                sep.append(tmp)
            tmp = [j+1]
    sep.append(tmp)
    #print(sep)
    
    idx = 0
    cnt = 0
    for j in range(1,w+1):
        flg = False
        for l in sep:
            tmp_sum = sum([cum_s[x][j] - cum_s[x][idx] for x in l])
            if tmp_sum > k:
                if j - idx == 1:
                    cnt = 10 ** 6
                flg = True
        
        if flg:
            cnt += 1
            idx = j-1 
    #print(len(sep)-1, cnt)
    ans = min(ans, len(sep)-1 + cnt)

if w == 1:
    x = sum([s[i] == '1' for i in range(h)])
    print(max(0, -(-x // k)-1))
elif h == 1:
    x = sum([s[0][i] == '1' for i in range(w)])
    print(max(0, -(-x // k)-1))
else:
    print(ans)