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):
H,W,K = map(int,input().split())
import numpy as np
from collections import deque
ans = 10000
S = np.array([list(map(int,list(input()))) for _ in range(H)])
cum = [[0]*W for _ in range(H+1)]
for j in range(W):
  for i in range(1,H+1):
    cum[i][j] = cum[i-1][j]+S[i-1][j]
    
cum = np.array(cum)
for i in range(2**(H-1)):
  q = deque([0])
  for h in range(H):
    if (i>>h)&1:
      q.append(h+1)
  q.append(H)
  p = deque()
  judge = False
  for a in range(len(q)-1):
    x = cum[q[a+1]]-cum[q[a]]
    if (x>K).any():
      judge = True
      break
    else:
      p.append(x)

  if judge:
    continue
  

    
print(ans)

H,W,K = map(int,input().split())
import numpy as np
from collections import deque
ans = 10000
S = np.array([list(map(int,list(input()))) for _ in range(H)])
cum = [[0]*W for _ in range(H+1)]
for j in range(W):
  for i in range(1,H+1):
    cum[i][j] = cum[i-1][j]+S[i-1][j]
    
cum = np.array(cum)
for i in range(2**(H-1)):
  q = deque([0])
  for h in range(H):
    if (i>>h)&1:
      q.append(h+1)
  q.append(H)
  p = deque()
  judge = False
  for a in range(len(q)-1):
    x = cum[q[a+1]]-cum[q[a]]
    if (x>K).any():
      judge = True
      break
    else:
      p.append(x)

  if judge:
    continue
  
  t_a = len(q)-2
  n = len(p)
  l = [0]*n
  for w in range(W):
    for x,a in enumerate(p):
      continue
  ans = min(ans,t_a)
    
print(ans)

H,W,K = map(int,input().split())
import numpy as np
from collections import deque
ans = 10000
S = np.array([list(map(int,list(input()))) for _ in range(H)])
cum = [[0]*W for _ in range(H+1)]
for j in range(W):
  for i in range(1,H+1):
    cum[i][j] = cum[i-1][j]+S[i-1][j]
    
cum = np.array(cum)
for i in range(2**(H-1)):
  q = deque([0])
  for h in range(H):
    if (i>>h)&1:
      q.append(h+1)
  q.append(H)
  p = deque()
  judge = False
  for a in range(len(q)-1):
    x = cum[q[a+1]]-cum[q[a]]
    if (x>K).any():
      judge = True
      break
    else:
      p.append(x)

  if judge:
    continue
  
  t_a = len(q)-2
  n = len(p)
  l = [0]*n
  for w in range(W):
    for x,a in enumerate(p):
      y = l[x]+a[w]
      if y>K:
        t_a+=1
        l = [0]*n
        for z,b in enumerate(p):
          l[z] = b[w]
        break
  ans = min(ans,t_a)
    
print(ans)

H,W,K = map(int,input().split())
import numpy as np
from collections import deque
ans = 10000
S = np.array([list(map(int,list(input()))) for _ in range(H)])
cum = [[0]*W for _ in range(H+1)]
for j in range(W):
  for i in range(1,H+1):
    cum[i][j] = cum[i-1][j]+S[i-1][j]
    
cum = np.array(cum)
for i in range(2**(H-1)):
  q = deque([0])
  for h in range(H):
    if (i>>h)&1:
      q.append(h+1)
  q.append(H)
  q = list(q)
  p = deque()
  judge = False
  for a in range(len(q)-1):
    x = cum[q[a+1]]-cum[q[a]]
    if (x>K).any():
      judge = True
      break
    else:
      p.append(list(x))

  if judge:
    continue
  p = list(p)
  t_a = len(q)-2
  n = len(p)
  l = [0]*n
  for w in range(W):
    for x,a in enumerate(p):
      y = l[x]
      if y>K:
        t_a+=1
        l = [0]*n
        for z,b in enumerate(p):
          l[z] = b[w]
        break
      else:
        l[x]=y
  ans = min(ans,t_a)
    
print(ans)

H,W,K = map(int,input().split())
import numpy as np
from collections import deque
ans = 10000
S = np.array([list(map(int,list(input()))) for _ in range(H)])
cum = [[0]*W for _ in range(H+1)]
for j in range(W):
  for i in range(1,H+1):
    cum[i][j] = cum[i-1][j]+S[i-1][j]
    
cum = np.array(cum)
for i in range(2**(H-1)):
  q = deque([0])
  for h in range(H):
    if (i>>h)&1:
      q.append(h+1)
  q.append(H)
  p = deque()
  judge = False
  for a in range(len(q)-1):
    x = cum[q[a+1]]-cum[q[a]]
    if (x>K).any():
      judge = True
      break
    else:
      p.append(x)

  if judge:
    continue
  
  t_a = len(q)-2
  n = len(p)
  l = [0]*n
  for w in range(W):
    for x,a in enumerate(p):
      if l[x]>K:
        t_a+=1
        l = [0]*n
        for z,b in enumerate(p):
          l[z] = b[w]
        break
  ans = min(ans,t_a)
    
print(ans)

def main()
  H,W,K = map(int,input().split())
  from collections import deque
  ans = 10000
  S = [list(map(int,list(input()))) for _ in range(H)]
  cum = [[0]*W for _ in range(H+1)]
  for j in range(W):
    for i in range(1,H+1):
      cum[i][j] = cum[i-1][j]+S[i-1][j]

  for i in range(2**(H-1)):
    q = deque([0])
    for h in range(H):
      if (i>>h)&1:
        q.append(h+1)
    q.append(H)
    q = list(q)
    p = deque()
    judge = False
    for a in range(len(q)-1):
      x = [x-y for x in cum[q[a+1]] for y in cum[q[a]]]
      for j in x:
        if j>K:
          judge = True
          break
      if judge:
        break
      else:
        p.append(list(x))

    if judge:
      continue
    p = list(p)
    t_a = len(q)-2
    n = len(p)
    l = [0]*n
    for w in range(W):
      for x,a in enumerate(p):
        y = l[x]+a[w]
        if y>K:
          t_a+=1
          l = [0]*n
          for z,b in enumerate(p):
            l[z] = b[w]
          break
        else:
          l[x]=y
    ans = min(ans,t_a)

  print(ans)
  
main()

H,W,K = map(int,input().split())
import numpy as np
import math
S = np.array([list(map(int,list(input()))) for _ in range(H)])
total = np.sum(S)
if total==K:
  print(0)
else:
  print(math.ceil(total/K)//2)

H,W,K = map(int,input().split())
import numpy as np
from collections import deque
ans = 10000
S = np.array([list(map(int,list(input()))) for _ in range(H)])
cum = [[0]*W for _ in range(H+1)]
for j in range(W):
  for i in range(1,H+1):
    cum[i][j] = cum[i-1][j]+S[i-1][j]
    
cum = np.array(cum)

H,W,K = map(int,input().split())
import numpy as np
from collections import deque
ans = 10000
S = np.array([list(map(int,list(input()))) for _ in range(H)])
cum = [[0]*W for _ in range(H+1)]
for j in range(W):
  for i in range(1,H+1):
    cum[i][j] = cum[i-1][j]+S[i-1][j]
    
cum = np.array(cum)
for i in range(2**(H-1)):
  q = deque([0])
  for h in range(H):
    if (i>>h)&1:
      q.append(h+1)
  q.append(H)
  p = deque()
  for a in range(len(q)-1):
    x = cum[q[a+1]]-cum[q[a]]
    if (x>K).any():
      judge = True
      break
    else:
      p.append(x)

  if judge:
    continue
  
  t_a = len(q)-2
  l = [0]*len(p)
  judge = False
  for w in range(W):
    for x,a in enumerate(p):
      l[x]+=a[w]
      if l[x]>K:
        t_a+=1
        l = [0]*len(p)
        for z,b in enumerate(p):
          l[z] = b[w]
        break
  ans = min(ans,t_a)
    
print(ans)

H,W,K = map(int,input().split())
import numpy as np
from collections import deque
ans = 10000
S = np.array([list(map(int,list(input()))) for _ in range(H)])
cum = [[0]*W for _ in range(H+1)]
for j in range(W):
  for i in range(1,H+1):
    cum[i][j] = cum[i-1][j]+S[i-1][j]
    
cum = np.array(cum)
for i in range(2**(H-1)):
  q = deque([0])
  for h in range(H):
    if (i>>h)&1:
      q.append(h+1)
  q.append(H)
  q = list(q)
  p = deque()
  judge = False
  for a in range(len(q)-1):
    x = list(cum[q[a+1]]-cum[q[a]])
    if (x>K).any():
      judge = True
      break
    else:
      p.append(x)

  if judge:
    continue
  p = list(p)
  t_a = len(q)-2
  n = len(p)
  l = [0]*n
  for w in range(W):
    for x,a in enumerate(p):
      y = l[x]+a[w]
      if y>K:
        t_a+=1
        l = [0]*n
        for z,b in enumerate(p):
          l[z] = b[w]
        break
      else:
        l[x]=y
  ans = min(ans,t_a)
    
print(ans)

def main():
  H,W,K = map(int,input().split())
  import numpy as np
  from collections import deque
  ans = 10000
  S = np.array([list(map(int,list(input()))) for _ in range(H)])
  cum = [[0]*W for _ in range(H+1)]
  for j in range(W):
    for i in range(1,H+1):
      cum[i][j] = cum[i-1][j]+S[i-1][j]

  cum = np.array(cum)
  for i in range(2**(H-1)):
    j = 0
    q = deque([0])
    for h in range(H):
      if (i>>h)&1:
        q.append(h+1)
    q.append(H)
    t_a = len(q)-2
    if t_a>=ans:
      continue
    p = deque()
    judge = False
    for a in range(len(q)-1):
      x = cum[q[a+1]]-cum[q[a]]
      if (x>K).any():
        judge = True
        break
      else:
        p.append(list(x))

    if judge:
      continue
    n = len(p)
    l = [0]*n
    for w in range(W):
      y = [l[j]+p[j][w] for j in range(n)]
      if max(y)>K:
        t_a+=1
        l = [p[j][w] for j in range(n)]
        if t_a>=ans:
          judge = True
          break
      else:
        l = y
    if judge:
      continue
    ans = min(ans,t_a)

  print(ans)
  
main()

Verdicts: Wrong Answer

Wrong Answer

Wrong Answer

Wrong Answer

Wrong Answer

Runtime Error

Wrong Answer

Wrong Answer

Runtime Error

Runtime Error

Accepted