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

def main():
    h,w,k = tuple([int(t)for t in input().split()])

    s = [[int(i) for i in list(input())] for _ in range(h)]
    
    cusum = np.array([accumelist(s_) for s_ in s])

    candidates = []

    for i in range(1<<(h-1)):
        subcu = divide(cusum,i)
        subcusum = np.empty((0,w),int)

        for sub_ in subcu:
            subcusum = np.append(subcusum,np.sum(sub_,axis=0,keepdims=True),axis=0)

        cutnum = 0
        j=0
        temp = [0]*subcusum.shape[0]

        for j in range(w):
            for l in range(subcusum.shape[0]):
                if subcusum[l][j]-temp[l]>k:
                    temp = subcusum.T[j-1]
                    cutnum+=1
                    break
        
        candidates.append(cutnum+bin(i).count('1'))

    print(min(candidates))
            
def divide(s,i):
    subs = []
    counter = 0
    pos = 0
    while i!= 0:
        counter +=1
        if i%2==1:
            subs.append(s[pos:counter])
            pos = counter
        i >>=1
 
    subs.append(s[pos:])
    return subs

def accumelist(s):
    if s == []:
        return []
    res = [s[0]]
    for i in range(1,len(s)):
        res.append(res[i-1]+s[i])

    return res
    
if __name__ == "__main__":
    main()

Fixed submission:
import math
import functools
from operator import add

def main():
    h,w,k = tuple([int(t)for t in input().split()])

    s = [[int(i) for i in list(input())] for _ in range(h)]
    
    cusum = [accumelist(s_) for s_ in s]

    candidates = []

    for i in range(1<<(h-1)):
        subcu = divide(cusum,i)
        subs = divide(s,i)

        subcusum = []

        rowsum = []

        for sub_ in subcu:
            subcusum.append(functools.reduce((lambda a,b:list(map(add,a,b))),sub_))

        for sub_ in subs:
            rowsum.append(functools.reduce((lambda a,b:list(map(add,a,b))),sub_))


        cutnum = 0

        temp = [0]*len(subcusum)

        for j in range(w):
            for l in range(len(subcusum)):
                if subcusum[l][j]-temp[l]>k:
                    if rowsum[l][j]>k:
                        cutnum+=10000
                    temp = [x[j-1] for x in subcusum]
                    cutnum+=1
                    break
        
        candidates.append(cutnum+bin(i).count('1'))

    print(min(candidates))
            
def divide(s,i):
    subs = []
    counter = 0
    pos = 0
    while i!= 0:
        counter +=1
        if i%2==1:
            subs.append(s[pos:counter])
            pos = counter
        i >>=1
 
    subs.append(s[pos:])
    return subs

def accumelist(s):
    if s == []:
        return []
    res = [s[0]]
    for i in range(1,len(s)):
        res.append(res[i-1]+s[i])

    return res

def _add_(a,b):
    return map(add,a,b)
    
if __name__ == "__main__":
    main()

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

def main():
    h,w,k = tuple([int(t)for t in input().split()])

    s = [[int(i) for i in list(input())] for _ in range(h)]
    
    cusum = [accumelist(s_) for s_ in s]

    candidates = []

    for i in range(1<<(h-1)):
        subcu = divide(cusum,i)
        subcusum = []
        for sub_ in subcu:
            subcusum.append(np.sum(np.array(sub_),axis=0))

        subcusum = np.array(subcusum)

        cutnum = 0
        j=0
        temp = 0
        for j in range(w):
            subsum = subcusum[:,j]-temp
            if np.any(subsum>k):
                temp = subcusum[:,j-1]
                cutnum+=1
        
        candidates.append(cutnum+bin(i).count('1'))

    print(min(candidates))
            
def divide(s,i):
    subs = []
    counter = 0
    pos = 0
    while i!= 0:
        counter +=1
        if i%2==1:
            subs.append(s[pos:counter])
            pos = counter
        i >>=1
 
    subs.append(s[pos:])
    return subs

def accumelist(s):
    if s == []:
        return []
    res = [s[0]]
    for i in range(1,len(s)):
        res.append(res[i-1]+s[i])

    return res
    
if __name__ == "__main__":
    main()

Fixed submission:
import math
import functools
from operator import add

def main():
    h,w,k = tuple([int(t)for t in input().split()])

    s = [[int(i) for i in list(input())] for _ in range(h)]
    
    cusum = [accumelist(s_) for s_ in s]

    candidates = []

    for i in range(1<<(h-1)):
        subcu = divide(cusum,i)
        subs = divide(s,i)

        subcusum = []

        rowsum = []

        for sub_ in subcu:
            subcusum.append(functools.reduce((lambda a,b:list(map(add,a,b))),sub_))

        for sub_ in subs:
            rowsum.append(functools.reduce((lambda a,b:list(map(add,a,b))),sub_))


        cutnum = 0

        temp = [0]*len(subcusum)

        for j in range(w):
            for l in range(len(subcusum)):
                if subcusum[l][j]-temp[l]>k:
                    if rowsum[l][j]>k:
                        cutnum+=10000
                    temp = [x[j-1] for x in subcusum]
                    cutnum+=1
                    break
        
        candidates.append(cutnum+bin(i).count('1'))

    print(min(candidates))
            
def divide(s,i):
    subs = []
    counter = 0
    pos = 0
    while i!= 0:
        counter +=1
        if i%2==1:
            subs.append(s[pos:counter])
            pos = counter
        i >>=1
 
    subs.append(s[pos:])
    return subs

def accumelist(s):
    if s == []:
        return []
    res = [s[0]]
    for i in range(1,len(s)):
        res.append(res[i-1]+s[i])

    return res

def _add_(a,b):
    return map(add,a,b)
    
if __name__ == "__main__":
    main()

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

def main():
    h,w,k = tuple([int(t)for t in input().split()])

    s = [[int(i) for i in list(input())] for _ in range(h)]
    
    s = np.array(s)

    candidates = []

    for i in range(1<<h-1):
        s_subs = divide(s,i)
        cutnum = 0
        pos = 0
        subsum = np.array([0]*len(s_subs))
        j = 0
        while j<w:
            temp = np.array([np.sum(s_[:,j]) for s_ in s_subs])
            if any([s_>k for s_ in temp]):
                cutnum = -1-bin(i).count('1')
                break

            subsum = subsum+temp
            if any([s_>k for s_ in subsum]):
                cutnum+=1
                subsum = np.array([0]*len(s_subs))
                j-=1
            
            j+=1

        candidates.append((bin(i).count('1')+cutnum))

    print(min([t for t in candidates if t>=0]))

def divide(s,i):
    subs = []
    counter = 0
    pos = 0
    while i!= 0:
        counter +=1
        if i%2==1:
            subs.append(s[pos:counter])
            pos = counter
        i >>=1

    subs.append(s[pos:])
    return subs
    
if __name__ == "__main__":
    main()

Fixed submission:
import math
import functools
from operator import add

def main():
    h,w,k = tuple([int(t)for t in input().split()])

    s = [[int(i) for i in list(input())] for _ in range(h)]
    
    cusum = [accumelist(s_) for s_ in s]

    candidates = []

    for i in range(1<<(h-1)):
        subcu = divide(cusum,i)
        subs = divide(s,i)

        subcusum = []

        rowsum = []

        for sub_ in subcu:
            subcusum.append(functools.reduce((lambda a,b:list(map(add,a,b))),sub_))

        for sub_ in subs:
            rowsum.append(functools.reduce((lambda a,b:list(map(add,a,b))),sub_))


        cutnum = 0

        temp = [0]*len(subcusum)

        for j in range(w):
            for l in range(len(subcusum)):
                if subcusum[l][j]-temp[l]>k:
                    if rowsum[l][j]>k:
                        cutnum+=10000
                    temp = [x[j-1] for x in subcusum]
                    cutnum+=1
                    break
        
        candidates.append(cutnum+bin(i).count('1'))

    print(min(candidates))
            
def divide(s,i):
    subs = []
    counter = 0
    pos = 0
    while i!= 0:
        counter +=1
        if i%2==1:
            subs.append(s[pos:counter])
            pos = counter
        i >>=1
 
    subs.append(s[pos:])
    return subs

def accumelist(s):
    if s == []:
        return []
    res = [s[0]]
    for i in range(1,len(s)):
        res.append(res[i-1]+s[i])

    return res

def _add_(a,b):
    return map(add,a,b)
    
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Runtime Error):
import math
import numpy as np

def main():
    h,w,k = tuple([int(t)for t in input().split()])

    s = [[int(i) for i in list(input())] for _ in range(h)]
    
    s = np.array(s)

    candidates = []

    for i in range(1<<h):
        s_subs = divide(s,i)
        cutnum = 0
        pos = 0
        subsum = np.array([0]*len(s_subs))
        j = 0
        while j<w:
            temp = np.array([np.sum(s_[:,j]) for s_ in s_subs])
            if any([s_>k for s_ in temp]):
                cutnum = -1-bin(i).count('1')
                break

            subsum = subsum+temp
            if any([s_>k for s_ in subsum]):
                cutnum+=1
                subsum = np.array([0]*len(s_subs))
                j-=1
            
            j+=1

        candidates.append((bin(i).count('1')+cutnum))

    print(min([t for t in candidates if t>=0]))

def divide(s,i):
    subs = []
    counter = 0
    pos = 0
    while i!= 0:
        counter +=1
        if i%2==1:
            subs.append(s[pos:counter])
            pos = counter
        i >>=1

    subs.append(s[pos:])
    return subs
    
if __name__ == "__main__":
    main()

Fixed submission:
import math
import functools
from operator import add

def main():
    h,w,k = tuple([int(t)for t in input().split()])

    s = [[int(i) for i in list(input())] for _ in range(h)]
    
    cusum = [accumelist(s_) for s_ in s]

    candidates = []

    for i in range(1<<(h-1)):
        subcu = divide(cusum,i)
        subs = divide(s,i)

        subcusum = []

        rowsum = []

        for sub_ in subcu:
            subcusum.append(functools.reduce((lambda a,b:list(map(add,a,b))),sub_))

        for sub_ in subs:
            rowsum.append(functools.reduce((lambda a,b:list(map(add,a,b))),sub_))


        cutnum = 0

        temp = [0]*len(subcusum)

        for j in range(w):
            for l in range(len(subcusum)):
                if subcusum[l][j]-temp[l]>k:
                    if rowsum[l][j]>k:
                        cutnum+=10000
                    temp = [x[j-1] for x in subcusum]
                    cutnum+=1
                    break
        
        candidates.append(cutnum+bin(i).count('1'))

    print(min(candidates))
            
def divide(s,i):
    subs = []
    counter = 0
    pos = 0
    while i!= 0:
        counter +=1
        if i%2==1:
            subs.append(s[pos:counter])
            pos = counter
        i >>=1
 
    subs.append(s[pos:])
    return subs

def accumelist(s):
    if s == []:
        return []
    res = [s[0]]
    for i in range(1,len(s)):
        res.append(res[i-1]+s[i])

    return res

def _add_(a,b):
    return map(add,a,b)
    
if __name__ == "__main__":
    main()

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

def main():
    h,w,k = tuple([int(t)for t in input().split()])

    s = [[int(i) for i in list(input())] for _ in range(h)]
    
    s = np.array(s)

    candidates = []

    for i in range(1<<h):
        s_subs = divide(s,i)
        cutnum = 0
        pos = 0
        subsum = np.array([0]*len(s_subs))
        j = 0
        while j<w:
            temp = np.array([np.sum(s_[:,j]) for s_ in s_subs])
            if any([s_>k for s_ in temp]):
                cutnum = -1-bin(i).count('1')
                break

            subsum = subsum+temp
            if any([s_>k for s_ in subsum]):
                cutnum+=1
                subsum = np.array([0]*len(s_subs))
                j-=1
            
            j+=1

        candidates.append((bin(i).count('1')+cutnum))

    print(min([t for t in candidates if t>=0]))

def divide(s,i):
    subs = []
    counter = 0
    pos = 0
    while i!= 0:
        counter +=1
        if i%2==1:
            subs.append(s[pos:counter])
            pos = counter
        i >>=1

    subs.append(s[pos:])
    return subs
    
if __name__ == "__main__":
    main()

Fixed submission:
import math
import functools
from operator import add

def main():
    h,w,k = tuple([int(t)for t in input().split()])

    s = [[int(i) for i in list(input())] for _ in range(h)]
    
    cusum = [accumelist(s_) for s_ in s]

    candidates = []

    for i in range(1<<(h-1)):
        subcu = divide(cusum,i)
        subs = divide(s,i)

        subcusum = []

        rowsum = []

        for sub_ in subcu:
            subcusum.append(functools.reduce((lambda a,b:list(map(add,a,b))),sub_))

        for sub_ in subs:
            rowsum.append(functools.reduce((lambda a,b:list(map(add,a,b))),sub_))


        cutnum = 0

        temp = [0]*len(subcusum)

        for j in range(w):
            for l in range(len(subcusum)):
                if subcusum[l][j]-temp[l]>k:
                    if rowsum[l][j]>k:
                        cutnum+=10000
                    temp = [x[j-1] for x in subcusum]
                    cutnum+=1
                    break
        
        candidates.append(cutnum+bin(i).count('1'))

    print(min(candidates))
            
def divide(s,i):
    subs = []
    counter = 0
    pos = 0
    while i!= 0:
        counter +=1
        if i%2==1:
            subs.append(s[pos:counter])
            pos = counter
        i >>=1
 
    subs.append(s[pos:])
    return subs

def accumelist(s):
    if s == []:
        return []
    res = [s[0]]
    for i in range(1,len(s)):
        res.append(res[i-1]+s[i])

    return res

def _add_(a,b):
    return map(add,a,b)
    
if __name__ == "__main__":
    main()

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

def main():
    h,w,k = tuple([int(t)for t in input().split()])

    s = [[int(i) for i in list(input())] for _ in range(h)]
    
    s = np.array(s)

    candidates = []

    for i in range(1<<h):
        s_subs = divide(s,i)
        cutnum = 0
        pos = 0

        for j in range(w):

            subsum = [np.sum(s_[:,pos:j])>k for s_ in s_subs]
            if any(subsum):
                pos = j-1
                cutnum+=1
        
        if any([np.sum(s_[:,pos:])>k for s_ in s_subs]):
            cutnum+=1


        candidates.append((bin(i).count('1')+cutnum))

    print(min(candidates))

def divide(s,i):
    subs = []
    counter = 0
    pos = 0
    while i!= 0:
        counter +=1
        if i%2==1:
            subs.append(s[pos:counter])
            pos = counter
        i >>=1

    subs.append(s[pos:])
    return subs
    
if __name__ == "__main__":
    main()

Fixed submission:
import math
import functools
from operator import add

def main():
    h,w,k = tuple([int(t)for t in input().split()])

    s = [[int(i) for i in list(input())] for _ in range(h)]
    
    cusum = [accumelist(s_) for s_ in s]

    candidates = []

    for i in range(1<<(h-1)):
        subcu = divide(cusum,i)
        subs = divide(s,i)

        subcusum = []

        rowsum = []

        for sub_ in subcu:
            subcusum.append(functools.reduce((lambda a,b:list(map(add,a,b))),sub_))

        for sub_ in subs:
            rowsum.append(functools.reduce((lambda a,b:list(map(add,a,b))),sub_))


        cutnum = 0

        temp = [0]*len(subcusum)

        for j in range(w):
            for l in range(len(subcusum)):
                if subcusum[l][j]-temp[l]>k:
                    if rowsum[l][j]>k:
                        cutnum+=10000
                    temp = [x[j-1] for x in subcusum]
                    cutnum+=1
                    break
        
        candidates.append(cutnum+bin(i).count('1'))

    print(min(candidates))
            
def divide(s,i):
    subs = []
    counter = 0
    pos = 0
    while i!= 0:
        counter +=1
        if i%2==1:
            subs.append(s[pos:counter])
            pos = counter
        i >>=1
 
    subs.append(s[pos:])
    return subs

def accumelist(s):
    if s == []:
        return []
    res = [s[0]]
    for i in range(1,len(s)):
        res.append(res[i-1]+s[i])

    return res

def _add_(a,b):
    return map(add,a,b)
    
if __name__ == "__main__":
    main()