Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np

h, w, k = [int(i) for i in input().split()]
s = np.zeros([h,w])
ans = (w-1)*(h-1)

for i in range(h):
    st = [int(j) for j in list(input())]
    s[i,:] = st
idx = []
for i in range(1<<h-1):
    tmp = []
    g = []
    for j in range(h-1):
        if ((i>>j)&1):
            tmp.append(j+1)

    n = len(tmp)
    choco = np.zeros([n+1,w])
    for j in range(n+1):
        if n == 0:
            choco = np.sum(s,axis=0)
        elif n > 0:
            if j == n:
                choco[j] = np.sum(s[tmp[j-1]:,:],axis=0)
            elif j == 0:
                choco[j] = np.sum(s[:tmp[j],:], axis=0)
            else:
                choco[j] = np.sum(s[tmp[j-1]:tmp[j],:], axis=0)
    w_div = 0
    w_div0 = 0
    nn = 0
    ans0 = (w-1)*(h-1)
    
    while w_div < w+1:
        if w_div == 0:
            num_choco = np.zeros((1,1))
            num_choco[0,0] = np.array(np.sum(choco))
        else:
            if n == 0:
                num_choco = np.zeros((1, 2))
                if w_div0 == 0:
                    num_choco[:,0] = np.sum(choco[:w_div])
                else:
                    num_choco[:,0] = np.sum(choco[w_div0:w_div])
                num_choco[:,1] = np.sum(choco[w_div:])
                
            else:
                num_choco = np.zeros((n+1,2))
                if w_div0 == 0:
                    num_choco[:,0] = np.sum(choco[:,:w_div],axis=1).T
                else:
                    num_choco[:,0] = np.sum(choco[:,w_div0:w_div],axis=1).T
                num_choco[:,1] = np.sum(choco[:,w_div:],axis=1).T
                
        if np.any(num_choco > k):
            if np.any(num_choco[:,0] > k) and w_div != 0:
                if w_div - w_div0 == 1:
                    break
                w_div0 = w_div-1
                nn += 1
                w_div += 0
            else:
                w_div +=1
        else:
            if w_div == w:
                ans0 = n + nn
                ans = min(ans,ans0)
            w_div += 1
print(ans)

Fixed submission:
import numpy as np
import itertools
H, W, K = [int(_) for _ in input().split()]
S = np.zeros((H + 1, W + 1), dtype=int)
S[1:, 1:] = [[int(_) for _ in input()] for _ in range(H)]
cum = S.cumsum(axis=0).cumsum(axis=1)
# print(cum)

ans = 10**10
for bs in itertools.product([True, False], repeat=H - 1):
    bs = [True] + list(bs) + [True]
#     print(bs)
    idxs = []
    for i, b in enumerate(bs):
        if b:
            idxs += [i]
    cum2 = np.array([cum[i2] - cum[i1] for i1, i2 in zip(idxs, idxs[1:])])
    i = 0
    cnt = sum(bs) - 3
    while i < W:
        di = min(
            np.searchsorted(c[i + 1:] - c[i], K, side='right') for c in cum2)
        if di == 0:
            cnt = 10**10
            break
        i += di
        cnt += 1
    ans = min(ans, cnt)
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np

h, w, k = [int(i) for i in input().split()]
s = np.zeros([h,w])
ans = (w-1)*(h-1)

for i in range(h):
    st = [int(j) for j in list(input())]
    s[i,:] = st
idx = []
for i in range(1<<h-1):
    tmp = []
    g = []
    for j in range(h-1):
        if ((i>>j)&1):
            tmp.append(j+1)

    n = len(tmp)
    choco = np.zeros([n+1,w])
    for j in range(n+1):
        if n == 0:
            choco = np.sum(s,axis=0)
        elif n > 0:
            if j == n:
                choco[j] = np.sum(s[tmp[j-1]:,:],axis=0)
            elif j == 0:
                choco[j] = np.sum(s[:tmp[j],:], axis=0)
            else:
                choco[j] = np.sum(s[tmp[j-1]:tmp[j],:], axis=0)
    w_div = 0
    w_div0 = 0
    nn = 0
    ans0 = (w-1)*(h-1)
    
    while w_div < w+1:
        if w_div == 0:
            num_choco = np.zeros((1,1))
            num_choco[0,0] = np.array(np.sum(choco))
        else:
            if n == 0:
                num_choco = np.zeros((1, 2))
                if w_div0 == 0:
                    num_choco[:,0] = np.sum(choco[:w_div])
                else:
                    num_choco[:,0] = np.sum(choco[w_div0:w_div])
                num_choco[:,1] = np.sum(choco[w_div:])
                
            else:
                num_choco = np.zeros((n+1,2))
                if w_div0 == 0:
                    num_choco[:,0] = np.sum(choco[:,:w_div],axis=1).T
                else:
                    num_choco[:,0] = np.sum(choco[:,w_div0:w_div],axis=1).T
                num_choco[:,1] = np.sum(choco[:,w_div:],axis=1).T
                
        if np.any(num_choco > k):
            if np.any(num_choco[:,0] > k) and w_div != 0:
                w_div0 = w_div-1
                nn += 1
                w_div += 0
            else:
                w_div +=1
        else:
            if w_div == w:
                ans0 = n + nn

                ans = min(ans,ans0)
            w_div += 1
print(ans)

Fixed submission:
import numpy as np
import itertools
H, W, K = [int(_) for _ in input().split()]
S = np.zeros((H + 1, W + 1), dtype=int)
S[1:, 1:] = [[int(_) for _ in input()] for _ in range(H)]
cum = S.cumsum(axis=0).cumsum(axis=1)
# print(cum)

ans = 10**10
for bs in itertools.product([True, False], repeat=H - 1):
    bs = [True] + list(bs) + [True]
#     print(bs)
    idxs = []
    for i, b in enumerate(bs):
        if b:
            idxs += [i]
    cum2 = np.array([cum[i2] - cum[i1] for i1, i2 in zip(idxs, idxs[1:])])
    i = 0
    cnt = sum(bs) - 3
    while i < W:
        di = min(
            np.searchsorted(c[i + 1:] - c[i], K, side='right') for c in cum2)
        if di == 0:
            cnt = 10**10
            break
        i += di
        cnt += 1
    ans = min(ans, cnt)
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
# bit全探索を意識して書いてみる
import numpy as np

h, w, k = [int(i) for i in input().split()]
s = np.zeros([h,w])
ans = (w-1)*(h-1) # 区切りの最大値

for i in range(h):
    st = [int(j) for j in list(input())]
    s[i,:] = st
idx = []
for i in range(1<<h-1):
    tmp = []
    g = []
    for j in range(h-1):
        if ((i>>j)&1):
            tmp.append(j+1)

    n = len(tmp)
    choco = np.zeros([n+1,w])
    for j in range(n+1):
        if n == 0:
            choco = np.sum(s,axis=0)
        elif n > 0:
            if j == n:
                choco[j] = np.sum(s[tmp[j-1]:,:],axis=0)
            elif j == 0:
                choco[j] = np.sum(s[:tmp[j],:], axis=0)
            else:
                choco[j] = np.sum(s[tmp[j-1]:tmp[j],:], axis=0)
#     print(choco)
    w_div = 0
    w_div0 = 0
    nn = 0
    ans0 = (w-1)*(h-1)
    
    # 分割した行列の列方向の合計が来ている状態
    while w_div < w+1:
         # 縦に分割している回数
        # chocoを分割した時の各領域のwhiteChoco合計数
        if w_div == 0:
            num_choco = np.zeros((1,1))
            num_choco[0,0] = np.array(np.sum(choco))
        else:
            if n == 0:
                num_choco = np.zeros((1, 2))
                if w_div0 == 0:
                    num_choco[:,0] = np.sum(choco[:w_div])
                else:
                    num_choco[:,0] = np.sum(choco[w_div0:w_div])
                num_choco[:,1] = np.sum(choco[w_div:])
                
            else:
                num_choco = np.zeros((n+1,2))
                if w_div0 == 0:
                    num_choco[:,0] = np.sum(choco[:,:w_div],axis=1).T # 分割点の左側の合計を計算
                else:
                    num_choco[:,0] = np.sum(choco[:,w_div0:w_div],axis=1).T # 分割点の左側の合計を計算
                num_choco[:,1] = np.sum(choco[:,w_div:],axis=1).T # 分割点の右側の合計を計算
        
#         print(num_choco)
        # それぞれの領域はchocoがk個以下か判定
        if np.any(num_choco > k): # 多いものがあった場合，前回のところで区切る
            if np.any(num_choco[:,0] > k) and w_div != 0:
                w_div0 = w_div-1
                nn += 1
#                 print('nn += 1 : w_div0=',w_div0)
                w_div += 0
            else:
                w_div +=1
        else: # 条件を超えているものがない場合，それはいい感じなのでansと比較する．
            if w_div == w:
                ans0 = n + nn
#                 print('n:', n, 'nn:', nn, 'ans', ans0)
                ans = min(ans,ans0)
            w_div += 1
#     print('---')
print(ans)

Fixed submission:
import numpy as np
import itertools
H, W, K = [int(_) for _ in input().split()]
S = np.zeros((H + 1, W + 1), dtype=int)
S[1:, 1:] = [[int(_) for _ in input()] for _ in range(H)]
cum = S.cumsum(axis=0).cumsum(axis=1)
# print(cum)

ans = 10**10
for bs in itertools.product([True, False], repeat=H - 1):
    bs = [True] + list(bs) + [True]
#     print(bs)
    idxs = []
    for i, b in enumerate(bs):
        if b:
            idxs += [i]
    cum2 = np.array([cum[i2] - cum[i1] for i1, i2 in zip(idxs, idxs[1:])])
    i = 0
    cnt = sum(bs) - 3
    while i < W:
        di = min(
            np.searchsorted(c[i + 1:] - c[i], K, side='right') for c in cum2)
        if di == 0:
            cnt = 10**10
            break
        i += di
        cnt += 1
    ans = min(ans, cnt)
print(ans)