LeetCode37. Sudoku Solver

一、题目

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

A sudoku solution must satisfy all of the following rules:

Each of the digits 1-9 must occur exactly once in each row.
Each of the digits 1-9 must occur exactly once in each column.
Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.
The ‘.’ character indicates empty cells.

Example 1:

Input: 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”]]
Output: [[“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”]]
Explanation: The input board is shown above and the only valid solution is shown below:

Constraints:

board.length == 9
board[i].length == 9
board[i][j] is a digit or ‘.’.
It is guaranteed that the input board has only one solution.

二、题解

class Solution {
public:
    bool isValid(int i,int j,char c,vector<vector<char>>& board){
        //行是否重复
        for(int col = 0;col < 9;col++){
            if(board[i][col] == c) return false;
        }
        //列是否重复
        for(int row = 0;row < 9;row++){
            if(board[row][j] == c) return false;
        }
        //判断格子内是否有重复
        int startRow = (i / 3) * 3;
        int startCol = (j / 3) * 3;
        for(int row = startRow;row < startRow + 3;row++){
            for(int col = startCol;col < startCol + 3;col++){
                if(board[row][col] == c) return false; 
            }
        }
        return true;
    }
    bool backtracking(vector<vector<char>>& board){
        for(int i = 0;i < 9;i++){
            for(int j = 0;j < 9;j++){
                if(board[i][j] == '.'){
                    for(char c = '1';c <= '9';c++){
                        if(isValid(i,j,c,board)){
                            board[i][j] = c;
                            bool res = backtracking(board);
                            if(res) return res;
                            board[i][j] = '.';
                        }
                    }
                    return false;
                }
            }
        }
        return true;
    }
    void solveSudoku(vector<vector<char>>& board) {
        backtracking(board);
    }
};