[leetcode] 37. Sudoku Solver

Description

Write a program to solve a Sudoku puzzle by filling the empty cells.

A sudoku solution must satisfy all of the following rules:

1. Each of the digits 1-9 must occur exactly once in each row.
2. Each of the digits 1-9 must occur exactly once in each column.
4. Each of the the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.
   Empty cells are indicated by the character ‘.’.



5. A sudoku puzzle…



6. Note:

• The given board contain only digits 1-9 and the character ‘.’.
• You may assume that the given Sudoku puzzle will have a single unique solution.
• The given board size is always 9x9.

分析

题目的意思是：求解数独。

• 思路很直接，一个深度优先搜索的问题。是一个hard类型的题目，所以比一般的dfs类型的题目要难，数组是一个矩阵，所以要双重循环遍历所有的位置，在每个位置填写数字后，要判断这个数字是否符合题目要求的三个限制。

代码

class Solution {
public:
    void solveSudoku(vector<vector<char>>& board) {
        solve(board);
    }
    bool solve(vector<vector<char>>& board){
        int n=board.size();
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(board[i][j]=='.'){
                    for(char c='1';c<='9';c++){
                        if(isValid(board,i,j,c)){
                            board[i][j]=c;
                            if(solve(board)){
                                return true;
                            }else{
                                board[i][j]='.';
                            }
                        }
                    }
                    return false;
                }
            }
        }
        return true;
    }
    bool isValid(vector<vector<char>>& board,int row,int col,char num){
        int n=board.size();
        for(int i=0;i<n;i++){
            if(board[i][col]==num||board[row][i]==num){
                return false;
            }
            if(board[3*(row/3)+i/3][3*(col/3)+i%3]==num){
                return false;
            }
        }
        return true;
    }
};

参考文献

​​[编程题]sudoku-solver​​