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.
- class Solution {
- public:
- void solveSudoku(vector<vector<char>>& board) {
- help(board);
- return;
- }
- // 回溯
- bool help(vector<vector<char>>& board){
- for(int i=0;i<board.size();i++){
- for(int j=0;j<board[i].size();j++){
- // 最后没有数字要填, 退出递归
- if(board[i][j] == '.'){
- for(char k='1';k<='9';k++){
- // 先判定有效再填入
- if(isValid(board,i,j,k)){
- board[i][j] = k;
- if(help(board)) return true;
- else board[i][j] = '.';
- }
- }
- // 所有数字都填了
- return false;
- }
- // 没有数字要填了, 退出返回 true
- }
- }
- return true;
- }
- private:
- // 填入的 c(1-9) 在该行, 该列, 以及该 box 中是否有效, 有效才填入, 无效换下一个数
- bool isValid(vector<vector<char>>& board,int row,int col,char c){
- for(int i=0;i<9;i++){
- if(c == board[row][i]) return false;
- if(c == board[i][col]) return false;
- int x = i/3+row/3*3;
- // 不好想到
- int y = i%3+col/3*3;
- if(c == board[x][y]) return false;
- }
- return true;
- }
- };
来源: http://www.bubuko.com/infodetail-3684208.html