37. Sudoku Solver

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

Empty cells are indicated by the character ‘.’.

You may assume that there will be only one unique solution.

A sudoku puzzle…

…and its solution numbers marked in red.

解法1： DFS, O(9^N)

N是空格子的总数
就是一个比较直接的dfs的题。对于每一个空格子尝试从１到９，然后检查是否是valid，如果是则继续，如果不是就填回原来的数字。

class Solution {
    public void solveSudoku(char[][] board) {
        if (board == null || board.length == 0 || board[0] == null || board[0].length == 0) {
            return;
        }

        solve(board);

    }

    private boolean solve(char[][] board) {
        for (int i = 0; i < board.length; i++) {
            for (int j = 0; j < board[0].length; j++) {
                if (board[i][j] == '.') {
                    // fill up 1 to 9
                    for (char ch = '1'; ch <= '9'; ch++) {
                        if (isValid(board, i, j, ch)) {
                            board[i][j] = ch;

                            boolean next = solve(board);
                            if (next) {
                                return true;
                            } else {
                                board[i][j] = '.';
                            }
                        }
                    }
                    return false;
                }
            }
        }
        return true;
    }

    private boolean isValid(char[][] board, int row, int col, char ch) {
        for (int i = 0; i < 9; i++) {
            if (board[i][col] != '.' && board[i][col] == ch) return false;
            if (board[row][i] != '.' && board[row][i] == ch) return false;

            // check the small matrix
            int matrixRow = (row / 3) * 3 + i / 3;
            int matrixCol = (col / 3) * 3 + i % 3;
            if (board[matrixRow][matrixCol] != '.' && board[matrixRow][matrixCol] == ch) return false;
        }
        return true;
    }
}