[leetcode]37. Sudoku Solver 解数独

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.
3. 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 '.'.

A sudoku puzzle...

...and its solution numbers marked in red.

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.

题意：

解数独

Solution1： Backtracking

code

class Solution {
     public void solveSudoku(char[][] board) {
        if (board == null || board.length != 9 || board[0].length != 9) return;
        boolean tmp = helper(board, 0, 0);
    }

    public boolean helper(char[][] board, int row, int col) {
        if (board == null || board.length != 9 || board[0].length != 9) return false;

        while (row < 9 && col < 9) {
            if (board[row][col] == '.') break; // find the 1st empty spot
            if (col == 8) {// 说明要换行了
                col = 0;
                row++;
            } else {
                col++;
            }
        }
        if (row >= 9) return true;
        int nextRow = row + col / 8;
        int nextCol = (col + 1) % 9;

        for (int num = 1; num <= 9; num++) {
            if (isValid(board, row, col, num)) { // 该num在行，列，box都没出现过
                board[row][col] = (char) (num + '0'); // 试着将num填入cur spot
                boolean result = helper(board, nextRow, nextCol); // 递归调用，下一个
                if (result) return true;
                board[row][col] = '.'; // 如果num在cur spot不合法，回溯。 还原。
            }
        }
        return false;
    }

    // check num is valid at such spot
    // which means in cur row, col or box, this num hasn't appeared before
    public boolean isValid(char[][] board, int row, int col, int num) {
        // check row
        for (int i = 0; i < 9; i++) {
            if (board[row][i] == num + '0')
                return false;
        }
        //check col
        for (int i = 0; i < 9; i++) {
            if (board[i][col] == num + '0')
                return false;
        }
        //check box
        int rowoff = (row / 3) * 3;
        int coloff = (col / 3) * 3;
        for (int i = 0; i < 3; i++) {
            for (int j = 0; j < 3; j++) {
                if (board[rowoff + i][coloff + j] == num + '0') return false;
            }
        }
        return true;
    }
}