Buggy python submission (verdict: Runtime Error):
# coding: utf-8
import sys
#from operator import itemgetter
sysread = sys.stdin.buffer.readline
read = sys.stdin.buffer.read
#from heapq import heappop, heappush
#from collections import defaultdict
sys.setrecursionlimit(10**7)
#import math
from itertools import product, accumulate, combinations, product
#import bisect# lower_bound etc
#import numpy as np
#from copy import deepcopy
#from collections import deque
def run():
    H,W,K = map(int, sysread().split())
    S = []
    for i in range(H):
        S.append(list(accumulate(list(map(int, list(input()))), lambda x,y:x+y)))
    for h in range(1, H):
        for w in range(W):
            S[h][w] += S[h-1][w]

    ret = float('inf')

    for idxes_ in product((0,1), repeat=H-1):
        l = 0
        r = 1
        idxes = [0]
        for i, val in enumerate(idxes_, 1):
            if val == 1:
                idxes.append(i)
        idxes.append(H)
        min_cut = len(idxes) - 2
        while r <= W:
            for i in range(len(idxes)-1):
                if idxes[i] == 0 and l == 0:
                    cri = S[idxes[i+1]-1][r-1]
                elif l == 0:
                    cri = S[idxes[i+1]-1][r-1] - S[idxes[i]-1][r-1]
                elif idxes[i] == 0:
                    cri = S[idxes[i+1]-1][r-1] - S[idxes[i+1]-1][l-1]
                else:
                    cri = S[idxes[i+1]-1][r-1] - S[idxes[i]-1][r-1] - S[idxes[i+1]-1][l-1] + S[idxes[i]-1][l-1]

                if cri > K:
                    r -= 1
                    if l == r:
                        min_cut = float('inf')
                        r = W+1
                        break
                    l = r
                    min_cut += 1
                    break
            r += 1
        ret = min(ret, min_cut)

    print(ret)




if __name__ == "__main__":
    run()


Fixed submission:
# coding: utf-8
from itertools import combinations as combs

H,W,K = list(map(int, input().split()))
arr = []
for i in range(H):
  arr.append(list(map(int, list(input()))))

def cut_sum(arr, x1, x2, y):
  ret = 0
  for i in range(x1, x2):
    ret += arr[i][y]
  return ret

row_idxes = list(range(1,H))
min_val = float('inf')

for n_rows in range(H):
  for row_set in combs(row_idxes, n_rows):
    count = len(row_set)
    row_lines = [0] + list(row_set)+ [H]
    col1, col2 = 0, 1
    sums = [0] * (len(row_lines) - 1)
    while col2 <= W:
      row1 = 0
      for box, row2 in enumerate(row_lines[1:]):
        sums[box] += cut_sum(arr, row1, row2, col2-1)
        if sums[box] > K:
          if (col2 - col1) == 1:
            count = float('inf')
            break
          count += 1
          col1 = col2 - 1
          col2 -= 1
          sums = [0] * (len(row_lines) - 1)
          break
        row1 = row2
      if count >= min_val:
        break
      col2 += 1
    
    if min_val > count:
      min_val = count
print(min_val)

Buggy python submission (verdict: Time Limit Exceeded):
# coding: utf-8
import sys
#from operator import itemgetter
sysread = sys.stdin.buffer.readline
read = sys.stdin.buffer.read
#from heapq import heappop, heappush
#from collections import defaultdict
sys.setrecursionlimit(10**7)
#import math
from itertools import product#accumulate, combinations, product
#import bisect# lower_bound etc
import numpy as np
#from copy import deepcopy
#from collections import deque
def run():
    H,W,K = map(int, sysread().split())
    S = []
    for i in range(H):
        S.append(list(map(int, list(input()))))
    S = np.array(S)
    ret = float('inf')
    for w in range(1, W):
        S[:,w] += S[:,w-1]
    for h in range(1, H):
        S[h,:] += S[h-1,:]

    for idxes_ in product((0,1), repeat=H-1):
        l = 0
        r = 1
        idxes = [0]
        for i, val in enumerate(idxes_, 1):
            if val == 1:
                idxes.append(i)
        idxes.append(H)
        min_cut = len(idxes) - 2
        while r <= W:
            for i in range(len(idxes)-1):
                if idxes[i] == 0 and l == 0:
                    cri = S[idxes[i+1]-1, r-1]
                elif l == 0:
                    cri = S[idxes[i+1]-1, r-1] - S[idxes[i]-1, r-1]
                elif idxes[i] == 0:
                    cri = S[idxes[i+1]-1, r-1] - S[idxes[i+1]-1, l-1]
                else:
                    cri = S[idxes[i+1]-1, r-1] - S[idxes[i]-1, r-1] - S[idxes[i+1]-1, l-1] + S[idxes[i]-1, l-1]

                if cri > K:
                    r -= 1
                    if l == r:
                        min_cut = float('inf')
                        r = W+1
                        break
                    l = r
                    min_cut += 1
                    break
            r += 1
        ret = min(ret, min_cut)

    print(ret)




if __name__ == "__main__":
    run()


Fixed submission:
# coding: utf-8
from itertools import combinations as combs

H,W,K = list(map(int, input().split()))
arr = []
for i in range(H):
  arr.append(list(map(int, list(input()))))

def cut_sum(arr, x1, x2, y):
  ret = 0
  for i in range(x1, x2):
    ret += arr[i][y]
  return ret

row_idxes = list(range(1,H))
min_val = float('inf')

for n_rows in range(H):
  for row_set in combs(row_idxes, n_rows):
    count = len(row_set)
    row_lines = [0] + list(row_set)+ [H]
    col1, col2 = 0, 1
    sums = [0] * (len(row_lines) - 1)
    while col2 <= W:
      row1 = 0
      for box, row2 in enumerate(row_lines[1:]):
        sums[box] += cut_sum(arr, row1, row2, col2-1)
        if sums[box] > K:
          if (col2 - col1) == 1:
            count = float('inf')
            break
          count += 1
          col1 = col2 - 1
          col2 -= 1
          sums = [0] * (len(row_lines) - 1)
          break
        row1 = row2
      if count >= min_val:
        break
      col2 += 1
    
    if min_val > count:
      min_val = count
print(min_val)

Buggy python submission (verdict: Time Limit Exceeded):
# coding: utf-8
import sys
#from operator import itemgetter
sysread = sys.stdin.buffer.readline
read = sys.stdin.buffer.read
#from heapq import heappop, heappush
#from collections import defaultdict
sys.setrecursionlimit(10**7)
#import math
from itertools import product#accumulate, combinations, product
#import bisect# lower_bound etc
import numpy as np
#from copy import deepcopy
#from collections import deque
def run():
    H,W,K = map(int, sysread().split())
    S = []
    for i in range(H):
        S.append(list(map(int, list(input()))))
    S = np.array(S)
    ret = float('inf')
    for w in range(1, W):
        S[:,w] += S[:,w-1]
    for idxes_ in product((0,1), repeat=H-1):
        l = 0
        r = 1
        idxes = [0]
        for i, val in enumerate(idxes_, 1):
            if val == 1:
                idxes.append(i)
        idxes.append(H)
        min_cut = len(idxes) - 2
        while r <= W:
            for i in range(len(idxes)-1):
                cri = S[idxes[i]:idxes[i+1], r-1].sum()
                if l > 0:
                    cri -= S[idxes[i]:idxes[i+1], l-1].sum()
                if cri > K:
                    r -= 1
                    if l == r:
                        min_cut = float('inf')
                        r = W+1
                        break
                    l = r
                    min_cut += 1
                    break
            r += 1
        ret = min(ret, min_cut)

    print(ret)




if __name__ == "__main__":
    run()


Fixed submission:
# coding: utf-8
from itertools import combinations as combs

H,W,K = list(map(int, input().split()))
arr = []
for i in range(H):
  arr.append(list(map(int, list(input()))))

def cut_sum(arr, x1, x2, y):
  ret = 0
  for i in range(x1, x2):
    ret += arr[i][y]
  return ret

row_idxes = list(range(1,H))
min_val = float('inf')

for n_rows in range(H):
  for row_set in combs(row_idxes, n_rows):
    count = len(row_set)
    row_lines = [0] + list(row_set)+ [H]
    col1, col2 = 0, 1
    sums = [0] * (len(row_lines) - 1)
    while col2 <= W:
      row1 = 0
      for box, row2 in enumerate(row_lines[1:]):
        sums[box] += cut_sum(arr, row1, row2, col2-1)
        if sums[box] > K:
          if (col2 - col1) == 1:
            count = float('inf')
            break
          count += 1
          col1 = col2 - 1
          col2 -= 1
          sums = [0] * (len(row_lines) - 1)
          break
        row1 = row2
      if count >= min_val:
        break
      col2 += 1
    
    if min_val > count:
      min_val = count
print(min_val)

Buggy python submission (verdict: Time Limit Exceeded):
# coding: utf-8
import sys
#from operator import itemgetter
sysread = sys.stdin.buffer.readline
read = sys.stdin.buffer.read
#from heapq import heappop, heappush
#from collections import defaultdict
sys.setrecursionlimit(10**7)
#import math
from itertools import product#accumulate, combinations, product
#import bisect# lower_bound etc
import numpy as np
#from copy import deepcopy
#from collections import deque
def run():
    H,W,K = map(int, sysread().split())
    S = []
    for i in range(H):
        S.append(list(map(int, list(input()))))
    S = np.array(S)
    ret = float('inf')
    for idxes_ in product((0,1), repeat=H-1):
        l = 0
        r = 1
        idxes = [0]
        for i, val in enumerate(idxes_, 1):
            if val == 1:
                idxes.append(i)
        idxes.append(H)
        min_cut = len(idxes) - 2
        while r <= W:
            for i in range(len(idxes)-1):
                cri = S[idxes[i]:idxes[i+1], l:r].sum()
                if cri > K:
                    r -= 1
                    if l == r:
                        min_cut = float('inf')
                        r = W+1
                        break
                    l = r
                    min_cut += 1
                    break
            r += 1
        ret = min(ret, min_cut)

    print(ret)




if __name__ == "__main__":
    run()


Fixed submission:
# coding: utf-8
from itertools import combinations as combs

H,W,K = list(map(int, input().split()))
arr = []
for i in range(H):
  arr.append(list(map(int, list(input()))))

def cut_sum(arr, x1, x2, y):
  ret = 0
  for i in range(x1, x2):
    ret += arr[i][y]
  return ret

row_idxes = list(range(1,H))
min_val = float('inf')

for n_rows in range(H):
  for row_set in combs(row_idxes, n_rows):
    count = len(row_set)
    row_lines = [0] + list(row_set)+ [H]
    col1, col2 = 0, 1
    sums = [0] * (len(row_lines) - 1)
    while col2 <= W:
      row1 = 0
      for box, row2 in enumerate(row_lines[1:]):
        sums[box] += cut_sum(arr, row1, row2, col2-1)
        if sums[box] > K:
          if (col2 - col1) == 1:
            count = float('inf')
            break
          count += 1
          col1 = col2 - 1
          col2 -= 1
          sums = [0] * (len(row_lines) - 1)
          break
        row1 = row2
      if count >= min_val:
        break
      col2 += 1
    
    if min_val > count:
      min_val = count
print(min_val)

Buggy python submission (verdict: Time Limit Exceeded):
# coding: utf-8
import numpy as np
from itertools import combinations as combs

H,W,K = list(map(int, input().split()))
arr = []
for i in range(H):
  arr.append(list(map(int, list(input()))))
arr = np.array(arr)

def cut_sum(arr, x1, x2, y1, y2):
  return arr[x1:x2, y1:y2].sum()

row_idxes = list(range(1,H))
min_val = 10 ** 9

for n_rows in range(H):
  for row_set in combs(row_idxes, n_rows):
    count = len(row_set)
    row_lines = [0] + list(row_set)+ [H]
    col1, col2 = 0, 1
    while col2 <= W:
      row1 = 0
      for row2 in row_lines[1:]:
        val = cut_sum(arr, row1, row2, col1, col2)
        if val > K:
          if (col2 - col1) == 1:
            count = 10 ** 9
            break
          count +=1
          col1 = col2 - 1
          col2 -= 1 
          break
        row1 = row2
      if count >= min_val:
        break
      col2 += 1
    
    if min_val > count:
      min_val = count
print(min_val)

Fixed submission:
# coding: utf-8
from itertools import combinations as combs

H,W,K = list(map(int, input().split()))
arr = []
for i in range(H):
  arr.append(list(map(int, list(input()))))

def cut_sum(arr, x1, x2, y):
  ret = 0
  for i in range(x1, x2):
    ret += arr[i][y]
  return ret

row_idxes = list(range(1,H))
min_val = float('inf')

for n_rows in range(H):
  for row_set in combs(row_idxes, n_rows):
    count = len(row_set)
    row_lines = [0] + list(row_set)+ [H]
    col1, col2 = 0, 1
    sums = [0] * (len(row_lines) - 1)
    while col2 <= W:
      row1 = 0
      for box, row2 in enumerate(row_lines[1:]):
        sums[box] += cut_sum(arr, row1, row2, col2-1)
        if sums[box] > K:
          if (col2 - col1) == 1:
            count = float('inf')
            break
          count += 1
          col1 = col2 - 1
          col2 -= 1
          sums = [0] * (len(row_lines) - 1)
          break
        row1 = row2
      if count >= min_val:
        break
      col2 += 1
    
    if min_val > count:
      min_val = count
print(min_val)

Buggy python submission (verdict: Time Limit Exceeded):
# coding: utf-8
import numpy as np
from itertools import combinations as combs

H,W,K = list(map(int, input().split()))
arr = []
for i in range(H):
  arr.append(list(map(int, list(input()))))
arr = np.array(arr)

def cut_sum(arr, x1, x2, y1, y2):
  return arr[x1:x2, y1:y2].sum()

row_idxes = list(range(1,H))
min_val = 10 ** 9

for n_rows in range(H):
  for row_set in combs(row_idxes, n_rows):
    count = len(row_set)
    row_lines = [0] + list(row_set)+ [H]
    col1, col2 = 0, 1
    while col2 <= W:
      row1 = 0
      for row2 in row_lines[1:]:
        val = cut_sum(arr, row1, row2, col1, col2)
        if val > K:
          if (col2 - col1) == 1:
            count = 10 ** 9
            break
          count +=1
          col1 = col2 - 1
          col2 -= 1 
          break
        row1 = row2
      if count == 10 **9:
        break
      col2 += 1
    
    if min_val > count:
      min_val = count
print(min_val)

Fixed submission:
# coding: utf-8
from itertools import combinations as combs

H,W,K = list(map(int, input().split()))
arr = []
for i in range(H):
  arr.append(list(map(int, list(input()))))

def cut_sum(arr, x1, x2, y):
  ret = 0
  for i in range(x1, x2):
    ret += arr[i][y]
  return ret

row_idxes = list(range(1,H))
min_val = float('inf')

for n_rows in range(H):
  for row_set in combs(row_idxes, n_rows):
    count = len(row_set)
    row_lines = [0] + list(row_set)+ [H]
    col1, col2 = 0, 1
    sums = [0] * (len(row_lines) - 1)
    while col2 <= W:
      row1 = 0
      for box, row2 in enumerate(row_lines[1:]):
        sums[box] += cut_sum(arr, row1, row2, col2-1)
        if sums[box] > K:
          if (col2 - col1) == 1:
            count = float('inf')
            break
          count += 1
          col1 = col2 - 1
          col2 -= 1
          sums = [0] * (len(row_lines) - 1)
          break
        row1 = row2
      if count >= min_val:
        break
      col2 += 1
    
    if min_val > count:
      min_val = count
print(min_val)