本文共 5246 字，大约阅读时间需要 17 分钟。

36. 有效的数独

from typing import Listclass Solution:    def isValidSudoku(self, board):        """        :type board: List[List[str]]        :rtype: bool        """        # init data        rows = [{   } for i in range(9)] # 字典 哈希表 列表第一个字典：rows[0]这个字典是第一行的键值信息        columns = [{   } for i in range(9)] # 字典 哈希表        boxes = [{   } for i in range(9)] # 字典 哈希表        # validate a board        for i in range(9):            for j in range(9):                num = board[i][j]  # 第i行  第j列  的元素                if num != '.':                    num = int(num)                    box_index = (i // 3) * 3 + j // 3    # 在一个3*3方格里的index                    # keep the current cell value                    rows[i][num] = rows[i].get(num, 0) + 1  # 第i行的rows字典里找这个元素，找不到就是0，加1后变成1. 找得到加上1后就会大于1                    columns[j][num] = columns[j].get(num, 0) + 1                    boxes[box_index][num] = boxes[box_index].get(num, 0) + 1                    # check if this value has been already seen before                    if rows[i][num] > 1 or columns[j][num] > 1 or boxes[box_index][num] > 1:                        return False        return Trueprint(Solution().isValidSudoku([  ["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"]  ]))

运行完毕后：

rows = [{   } for i in range(9)]print(rows)rows[0][1]=1rows[0][3]=1rows[1][1]=1print(rows)

结果

C:\Users\xd_du\Anaconda3\envs\py37\python.exe C:/Users/xd_du/PycharmProjects/wave/gendata.py[{   }, {   }, {   }, {   }, {   }, {   }, {   }, {   }, {   }][{   1: 1, 3: 1}, {   1: 1}, {   }, {   }, {   }, {   }, {   }, {   }, {   }]Process finished with exit code 0

37. 解数独

https://leetcode-cn.com/problems/sudoku-solver/solution/jie-shu-du-by-leetcode-solution/

from typing import Listclass Solution:    def solveSudoku(self, board: List[List[str]]) -> None:        def dfs(pos: int):            nonlocal valid            if pos == len(spaces):                valid = True                return            i, j = spaces[pos]            for digit in range(9):                if line[i][digit] == column[j][digit] == block[i // 3][j // 3][digit] == False:                    line[i][digit] = column[j][digit] = block[i // 3][j // 3][digit] = True                    board[i][j] = str(digit + 1)                    dfs(pos + 1)   #递归                    line[i][digit] = column[j][digit] = block[i // 3][j // 3][digit] = False                if valid:                    return        line = [[False] * 9 for _ in range(9)]        column = [[False] * 9 for _ in range(9)]        block = [[[False] * 9 for _a in range(3)] for _b in range(3)]        valid = False        spaces = list()        for i in range(9):            for j in range(9):                if board[i][j] == ".":                    spaces.append((i, j))                else:                    digit = int(board[i][j]) - 1                    line[i][digit] = column[j][digit] = block[i // 3][j // 3][digit] = True        dfs(0)board = [    ["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"]]Solution().solveSudoku(board)for i in range(9):    print(board[i])

def check(matrix, row, col, value):    """    检测在(row,col)放value是否合适    1.每行含1-9,不含重复值value    2.每列含1-9,不含重复值value    3.3*3区块含1-9,不含重复值value    """    # 检测每行    for j in range(9):        if matrix[row][j] == value:            return False    # 检测每列    for i in range(9):        if matrix[i][col] == value:            return False    # 检测元素所在3*3区域    area_row = (row // 3) * 3    area_col = (col // 3) * 3    for i in range(area_row, area_row + 3):        for j in range(area_col, area_col + 3):            if matrix[i][j] == value:                return False    return True  def solveSudoku(matrix, count=0):    """    遍历每一个未填元素，遍历1-9替换为合适的数字    """    if (count == 81):  # 递归出口        return True    #行优先遍历    row = count // 9  # 行标    col = count % 9  # 列标    if matrix[row][col] != 0:  # 已填充        return solveSudoku(matrix, count=count + 1)    else:  # 未填充        for i in range(1, 10):            if check(matrix, row, col, i):  # 找到可能的填充数                matrix[row][col] = i                if solveSudoku(matrix, count=count + 1):  # 是否可完成                    return True  # 可完成                # 不可完成                matrix[row][col] = 0  # 回溯        return False  # 不可完成 while True:    try:        matrix = []        for i in range(9):            matrix.append([int(i) for i in  input().split(' ')])#多维列表输入        solveSudoku(matrix)        for i in range(9):            print( ' '.join(map(str, matrix[i])))    except:        break

生成一张标准数独地图

标准数独地图有17个数字提示，且是有唯一解的。

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