class harvey_box:
  def __init__(self, p):
    self.brd = [list(i) for i in p.splitlines()]
    self._row, self._clm = len(self.brd), len(self.brd[0])
    self.x = [(i, j) for i in range(self._row) for j in range(self._clm) if self.brd[i][j] == '-']

  def solve(self):
    stc = [self._solver(*self.x[0])]
    while stc:
      try:
        if next(stc[-1]): continue
        if len(stc) == len(self.x): self.print_brd(); continue
        stc.append(self._solver(*self.x[len(stc)]))
      except:
        stc.pop()

  def print_brd(self):
    for i in self.brd: print(''.join(i))
    print()

  def _solver(self, px, py):
    for i in range(2):
      self.brd[px][py] = str(i)
      tmp1 = ''.join(self.brd[px])
      tmp2 = ''.join(self.brd[i][py] for i in range(self._row))
      yield tmp1.count('111')>0 or tmp1.count('000')>0 or tmp2.count('111')>0 or tmp2.count('000')>0\
      or tmp1.count('0')>3 or tmp1.count('1')>3 or tmp2.count('0')>3 or tmp2.count('1')>3
    self.brd[px][py] = '-'

if __name__ == '__main__':
  test = '''\
--0-1-
------
11--0-
-1----
-----0
-10---'''
  harvey_box(test).solve()

100110
001011
110100
011001
101010
010101

def find(board, i, j):
    # 파리, 구더기
    for m in ('0', '1'):
        board[i][j] = m
        # 가로, 세로
        for l in ('col', 'row'):
            s = ''
            for k in range(6):
                if l == 'col':
                    s += board[i][k]
                else:
                    s += board[k][j]
            # 불가능하면, 반대가 정답
            if s.count('1') > 3 or s.count('0') > 3 or s.count('111') > 0 or s.count('000') > 0:
                if board[i][j] == '0':
                    board[i][j] = '1'
                else:
                    board[i][j] = '0'
                return 1
    # 둘 다 가능하면 원복
    board[i][j] = '-'
    return 0


def print_board(board):
    for i in range(6):
        print(''.join(board[i]))
    print()




input = '''\
--0-1-
------
11--0-
-1----
-----0
-10---'''

empty_cnt = input.count('-')
board = [[j for j in i] for i in input.splitlines()]
print_board(board)

while empty_cnt > 0:
    for i in range(6):
        for j in range(6):
            if board[i][j] == '-':
                # 파리나 구더기를 넣어보고 불가능하면, 반대가 정답
                empty_cnt -= find(board, i, j)

print_board(board)

가로 또는 세로 한 줄에 대해서

3마리씩 놓아아 하므로, '1' 세 개인 줄은 '0'을 채운다.

'1'이 세 개 연속될 수 없으므로, '11-' => '110', '-11' => '011' , '1-1' => '101'

'0'에 대해서도 똑같이 처리한다.

import numpy as np


# line(1행 또는 1열)에서 x('1' 또는 '0')에 대해 검사한다.
def check(line, x):
    global changed

    y = {'1':'0', '0':'1'}[x]
    res = line[:]
    if res.count(x) == 3:
        res = res.replace('-', y)
    else:
        res = res.replace('-'+x+x, y+x+x)
        res = res.replace(x+x+'-', x+x+y)
        res = res.replace(x+'-'+x, x+y+x)

    if line != res:
        changed = True

    return res


inp_str = '''--0-1-
------
11--0-
-1----
-----0
-10---'''

arr = np.array([list(x) for x in inp_str.splitlines()])
changed = True
while changed:
    changed = False
    for k in range(6):
        arr[k,:] = list(check(check(''.join(arr[k,:]), '1'), '0')) # k번 행
        arr[:,k] = list(check(check(''.join(arr[:,k]), '1'), '0')) # k번 열

for i in range(6):
    print(''.join(arr[i,:]))

from random import *

inp1='''--0-1-
------
11--0-
-1----
-----0
-10---'''
print ('<input>\n',inp1,'\n\n<output>')
inp1=inp1.split('\n')

for i in range (len(inp1)):
    while (1):
        temp=list(inp1[i])
        for j in range (len(temp)):
            if temp[j]=='-':
                if temp.count('0')<3 and temp.count('1')<3:
                    temp[j]=str(randint(0,1))
                elif temp.count('0')==3 and temp.count('1')<3:
                    temp[j]='1'
                elif temp.count('0')<3 and temp.count('1')==3:
                    temp[j]='0'

        temp=''.join(temp)
        if '000' not in temp and '111' not in temp:
            print (temp)
            break

import numpy as np
inp="""--0-1-
------
11--0-
-1----
-----0
-10---"""
lst=[list(ln) for ln in inp.split("\n")]  #print(np.matrix(lst))
def check(y,x,cmp):
    global lst
    if lst[y].count(cmp)==3:  #한줄(같은 y축)에 동일한 요소가 3개 있으면 False
        return False
    if [lst[j][x] for j in range(6)].count(cmp)==3:  #한줄(같은 x축)에 동일한 요소가 3개 있으면 False
        return False
    for i in range(4):  #동일한 요소가 3개 이상 반복되면 False
        if lst[y][i]==lst[y][i+1]==lst[y][i+2] and lst[y][i]!="-":
            return False
        if lst[i][x]==lst[i+1][x]==lst[i+2][x] and lst[i][x]!="-":
            return False
    return True
def solve():
    global lst
    for y in range(6):
        for x in range(6):
            if lst[y][x]=="-":
                for cmp in range(2):
                    if check(y,x,str(cmp)):
                        lst[y][x]=str(cmp)
                        solve()
                        lst[y][x]="-"
                return
    for ln in lst:  #그냥 이렇게 4줄 말고 print(np.matrix(lst))로 써도 무방
        for cmp in ln:
            print("%2s"%cmp, end="")
        print()
solve()

정답:

 1 0 0 1 1 0
 0 0 1 0 1 1
 1 1 0 1 0 0
 0 1 1 0 0 1
 1 0 1 0 1 0
 0 1 0 1 0 1