37. Sudoku Solver

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LeetCode

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Problem

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

A sudoku solution must satisfy all 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.

Code

class Solution {
    public void solveSudoku(char[][] board) {
        solve(board);
    }

    private boolean solve(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(board, i, j, c)){
                            board[i][j] = c;
                            if(solve(board)){
                                return true;
                            } else {
                                board[i][j] = '.';
                            }
                        }
                    }
                    // 试了所有的组合都不行
                    return false;
                }
            }
        }
        // 没有.的位置，也就是有效的解
        return true;
    }

    private boolean isValid(char[][] board, int row, int col, char c){
        for(int j = 0; j < 9; j++){
            if(col != j && board[row][j] == c) return false;
        }

        for(int i = 0; i < 9; i++){
            if(row != i && board[i][col] == c) return false;
        }


        int rowIndex = 3 * (row / 3);
        int colIndex = 3 * (col / 3);

        for(int i = rowIndex; i < rowIndex + 3; i++){
            for(int j = colIndex; j < colIndex + 3; j++){
                if(i != row && j != col && board[i][j] == c) return false;
            }
        }
        return true;
    }
}