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题目🦀

37. 解数独

难度困难

编写一个程序，通过填充空格来解决数独问题。

数独的解法需 遵循如下规则：

数字 1-9 在每一行只能出现一次。
数字 1-9 在每一列只能出现一次。
数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）

数独部分空格内已填入了数字，空白格用 '.' 表示。

示例 1：

输入：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"]]
输出：[["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
解释：输入的数独如上图所示，唯一有效的解决方案如下所示：

提示：

board.length == 9
board[i].length == 9
board[i][j] 是一位数字或者 '.'
题目数据保证输入数独仅有一个解

解题思路🌵

有出路、有死路。
考虑使用回溯算法。

解题步骤🌟

经典回溯套路

//初始化result path
const result = []
const path = []
// [1,2,3,4]
//循环
push
backtrac()
pop
//return

循环行和列，尝试在每个位置放置1-9，并检验合法性
包括行、列、3 * 3方块的合法性
如果合法继续循环，直到找到一个合法的解，如果不合法，则回溯状态，并继续尝试其他的可能性

源码🔥

/**
 * @param {character[][]} board
 * @return {void} Do not return anything, modify board in-place instead.
 */
var solveSudoku = function(board) {
    function isValid(row, col, val, board) {
        let len = board.length
        // 行不能重复
        for(let i = 0; i < len; i++) {
            if(board[row][i] === val) {
                return false
            }
        }
        // 列不能重复
        for(let i = 0; i < len; i++) {
            if(board[i][col] === val) {
                return false
            }
        }
        let startRow = Math.floor(row / 3) * 3
        let startCol = Math.floor(col / 3) * 3

        for(let i = startRow; i < startRow + 3; i++) {
            for(let j = startCol; j < startCol + 3; j++) {
                if(board[i][j] === val) {
                    return false
                }
            }
        }

        return true
    }

    function backTracking() {
      for(let row=0;row<9;row++){
          for(let col=0;col<9;col++){
              if(board[row][col]!=='.'){
                  continue
              }
              //从1-9选取数字能不能放入
              for(let i=1;i<=9;i++){
                  if(isValid(row,col,`${i}`,board)){
                      board[row][col]=`${i}`
                      if(backTracking()){
                          return true
                      }
                      board[row][col]=`.`
                  }
              }
              return false
          }
      }
      return true
    }
    backTracking(board)
    
};

时间复杂度:O(N^2)

空间复杂度:O(1)

结束语🌞

那么鱼鱼的LeetCode算法篇的「leetCode」37-解数独⚡️就结束了，虽然前端对算法要求没有后端高，但是算法是编程基础，程序=数据结构➕算法，所以算法这个东西没有捷径，只能多写多练，多总结，文章的目的其实很简单，就是督促自己去完成算法练习并总结和输出，菜不菜不重要，但是热爱🔥，喜欢大家能够喜欢我的短文，也希望通过文章认识更多志同道合的朋友，如果你也喜欢折腾，欢迎加我好友，一起沙雕，一起进步。

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写在最后

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