37.解數獨

編寫一個程式，通過已填充的空格來解決數獨問題。
一個數獨的解法需遵循如下規則：

1. 數字1-9在每一行只能出現一次。
2. 數字1-9在每一列只能出現一次。
3. 數字1-9在每一個以粗實線分隔的3x3宮內只能出現一次。

空白格用'.'表示。（左側為題目，右側為一個解答）

Note:

• 給定的數獨序列只包含數字1-9和字元'.'。
• 你可以假設給定的數獨只有唯一解。
• 給定數獨永遠是9x9形式的。

解題思路

9×9：看作3×3，然後每個單元又是一個3×3小塊
Solution：初始化小塊
big_permutations：大塊中挑選組合數最少的小塊，
    原因在於，一旦小塊確定下來，周邊的小塊的組合數會下降（由於限定條件增加），
    加快搜索速度，確定某個組合數最少的小塊，就把數字填入board，
    再從剩餘小塊篩選組合數最少的小塊，以此類推。
possible_blk：每個候選小塊（有些小塊已經確定，就不在候選範圍內）的可能組合，
    取其中組合數最少的返回，為了不浪費，生成n個生成器，不用馬上那個取回所有結果，
    而是先定義生成器，然後用next(生成器)來取，誰先取完，就是組合數最少的一個
 

small_permutations：小塊的組合
    比如小塊中有4個空白，
    每個空白可選值如下（由於塊，行，列已經填入數字的限制）
        [['4'], ['2', '7'], ['2', '7'], ['1']]
    那麼可能的組合如下：
        ['4', '2', '7', '1']
        ['4', '7', '2', '1']

程式碼

class Solution37(object):
    def solveSudoku(self, board):
        blk = [[board[b//3 * 3+ i//3][(b%3)*3+i%3] for
 
 i in range(9)]for b in range(9)]
        blank_pos = [[i for i in range(9) if blk[k][i]=='.'] for k in range(9)]
        blank_val = [[str(i) for i in range(1,10) if not str(i) in blk[no]] for no in range(9)]
        for res in self.big_permutations(board,blank_pos,blank_val):
            return res
            
    
 
def big_permutations(self,board,blank_pos,blank_val,b_no=[]):
        no,pp = self.possible_blk(board,blank_pos,blank_val,b_no)
        for p3 in pp:
            for i in range(len(p3)):
                board[no//3*3 + blank_pos[no][i]//3][(no%3)*3 + blank_pos[no][i]%3] = p3[i]
            if len(b_no) == 8:
                yield board[:]
            else:
                for res in self.big_permutations(board,blank_pos,blank_val,b_no + [no]):
                    yield res
            for i in range(len(p3)):
                board[no//3*3 + blank_pos[no][i]//3][(no%3)*3 + blank_pos[no][i]%3] = '.'

    def possible_blk(self,board,blank_pos,blank_val,b_no):
        pno_other = [i for i in range(9) if not i in b_no]
        p3 = [[] for i in range(9-len(b_no))]
        y3 = []
        row = [[board[y][x] for x in range(9) if board[y][x]!='.'] for y in range(9)]
        col = [[board[y][x] for y in range(9) if board[y][x]!='.'] for x in range(9)]
        for k in range(len(p3)):
            no = pno_other[k]
            p = [0] * len(blank_pos[no])
            for i in range(len(p)):
                y,x = no//3*3 + blank_pos[no][i]//3,(no%3)*3 + blank_pos[no][i]%3
                p[i] = [m for m in blank_val[no] if not m in (row[y]+col[x])]
            y3.append(self.small_permutations(p))
        while True:
            for k in range(len(p3)):
                try:
                    res = next(y3[k])
                    p3[k].append(res)
                except StopIteration as e:
                    return [pno_other[k],p3[k]]

    def small_permutations(self,p,per=[]):
        cur_floor = len(per)
        for pos in range(len(p[cur_floor])):
            t = per + [p[cur_floor][pos]]
            if len(set(t)) == len(t):
                if len(t) == len(p):
                        yield [p[cur_floor][pos]]
                else:
                        for result in self.small_permutations(p,per + [p[cur_floor][pos]]):
                                yield [p[cur_floor][pos]] + result

result = Solution37().solveSudoku([["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]])
for r in result:
    print(r)
print("-------------------------------")

在速度提高上下了功夫：