[LeetCode]Sudoku Solver

题目描述

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.

求解数独。

解题思路

用回溯法我们只要检查新加入的值能否在行、列以及小方块里有效即可。

代码

public static void solveSudoku(char[][] board) {
		internalSolveSudoku(board);
	}

	/**
	 * 回溯求解数独问题
	 * 
	 * @param board
	 * @return
	 */
	public static boolean internalSolveSudoku(char[][] board) {
		for (int i = 0; i < board.length; i++) {
			for (int j = 0; j < board[0].length; j++) {
				if (board[i][j] == '.') {
					for (int k = 1; k <= 9; k++) {
						board[i][j] = (char) ('0' + k);
						if (isValid(board, i, j)) {
							// 递归
							if (internalSolveSudoku(board)) {
								return true;
							}
						}
						// 回溯
						board[i][j] = '.';
					}
					return false;
				}
			}
		}
		return true;
	}

	/**
	 * 判断一个数字在当前位置是否合法
	 * 
	 * @param board
	 * @param row
	 * @param column
	 * @return
	 */
	public static boolean isValid(char[][] board, int row, int column) {
		int cellStartX = (row / 3) * 3;
		int cellStartY = (column / 3) * 3;
		char c = board[row][column];

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

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

		for (int i = cellStartX; i < cellStartX + 3; i++) {
			for (int j = cellStartY; j < cellStartY + 3; j++) {
				if (i != row && j != column && board[i][j] == c)
					return false;
			}
		}

		return true;
	}