input_text = """
[
[8,0,0,0,0,0,0,0,0],
[0,0,3,6,0,0,0,0,0],
[0,7,0,0,9,0,2,0,0],
[0,5,0,0,0,7,0,0,0],
[0,0,0,0,4,5,7,0,0],
[0,0,0,1,0,0,0,3,0],
[0,0,1,0,0,0,0,6,8],
[0,0,8,5,0,0,0,1,0],
[0,9,0,0,0,0,4,0,0]
]
"""
def copy(li):
li_ = list(range(len(li)))
for i in range(len(li)):
li_[i] = list(range(len(li[i])))
for x in range(len(li)):
for y in range(len(li[x])):
li_[x][y] = li[x][y]
return li_
def insert(num, x, y, board, limit, level=9):
board[x][y] = num
bit = num_to_bit(num)
# row limit
for x_ in range(level):
limit[x_][y] |= bit
for y_ in range(level):
limit[x][y_] |= bit
leftTop_x = x // 3 * 3
leftTop_y = y // 3 * 3
for x_ in range(leftTop_x, leftTop_x + 3):
for y_ in range(leftTop_y, leftTop_y + 3):
limit[x_][y_] |= bit
def num_to_bit(num):
return 1 << (num-1)
def conflict(ul):
rs = False
for x,y,post_list in ul:
if len(post_list) == 0:
rs = True
break
return rs
def list_potential(limit_factor, level=9):
l = limit_factor
result = []
for i in range(1, level + 1):
x = l & 1
if not x:
result.append(i)
l = l >> 1
return result
def fill(board, limit):
bf,lf = copy(board),copy(limit)
continue__ = False
unknown_li = unknown_list(board,limit)
for x, y,pos_list in unknown_li:
if len(pos_list) == 1:
insert(pos_list[0], x, y, bf, lf)
continue__ = True
break
if continue__:
fill(bf, lf)
return bf,lf
def unknown_list(board,limit):
rs = []
for x in range(0, 9):
for y in range(0, 9):
if board[x][y] == 0:
rs.append((x, y,list_potential(limit[x][y])))
return sorted(rs,key=lambda i:len(i[-1]))
## 验证方法
def valid(board):
def square(tlx,tly):
return [board[a][b] for a in range(tlx,tlx+3) for b in range(tly,tly+3)]
def valid__(li):
for i in range(len(li)):
for j in range(i+1,len(li)):
if li[j] == li[i]:return False
return True
rs = True
for r in board:
rs = rs and valid__(r)
for x in [[board[j][i] for i in range(9)] for j in range(9)]:
rs = rs and valid__(x)
xy = [(x,y)for x in range(0,7,3) for y in range(0,7,3)]
for x,y in xy:
rs = rs and valid__(square(x,y))
return rs
def search(board,limit):
rs = []
done = False
def search__(board,limit):
nonlocal done
nonlocal rs
if done == True:
return
bf,lf = fill(board,limit)
ul = unknown_list(bf,lf)
if conflict(ul):
return
elif len(ul) == 0 :
done = True
rs = bf
return
else:
x,y,pos_list = ul[0]
for num in pos_list:
bc__,lc__ = copy(bf),copy(lf)
insert(num,x,y,bc__,lc__)
search__(bc__,lc__)
search__(board,limit)
return rs
def output(input_text):
b = eval(input_text)
board = [
[0 for x in range(9)]
for y in range(9)
]
l =[
[0 for i in range(9)]for j in range(9)
]
for i in range(len(b)):
for j in range(len(b[i])):
if b[i][j]:
insert(b[i][j],i,j,board,l)
rs = search(board,l)
return rs
## 测试并验证
if __name__ == '__main__':
o = output(input_text)
print(o)
print(valid(o))
