LeetCode刷题day037 (Jieky)

LeetCode第37题 Sudoku Solver

/*
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 '.'.

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.
*/
import java.util.*;
public class SudokuSolver{
	public static void main(String[] args){
		char Sudoku[][] = {
		{'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'}};
		SudokuSolver ss = new SudokuSolver();
		boolean result = ss.solveSudoku(Sudoku);
		System.out.println(result);
	}
	
	public boolean solveSudoku(char[][] board) {
		/*
		解题思想：
		1.填入一个数到方格，检查填入的数是否有效，有效则执行2
		2.当填入一个有效数后，再填入下一个有效数，执行1
		3.当填入一个有效数后，下一个空找不到有效数，则回退，执行1
		4.递归执行1、2、3
		*/
		return solver(board);
	}
	
	private boolean solver(char[][] board) {
		for (int i=0;i<9;i++){
			for(int j=0;j<9;j++){
				// 准备填入数字
				if(board[i][j] == '.'){
					char num = '1';
					// 每个空格尝试0-9，直到找到，或返回false
					while(num <= '9'){
						if (isValid(board,i,j,num)){
							//填入的数字有效，递归方式填入下一个有效数
							board[i][j] = num;
							if(solver(board)){
								// 递归的询问接下来是否能够填入有效数字，若都能返回true
								// break只能跳出当前的循环，两层循环跳出是比较复杂的
								return true;
							}else{
								// 不能一直递归的询问填入有效数字，回退，尝试下一个数
								board[i][j] = '.';
							}
						}
						num += 1;
					}
					// 当前方格不能填入有效数字
					return false;
				}
			}
		}
		// 若数独无解，则在双循环的时候就会返回false
		// 执行到当前位置，则表示最后一个空格不需要填数
		return true;
	}
	
	// 判断输入的数在所在行、列、方框是否存在
	private boolean isValid(char[][] board,int row,int col,char insert){
		for (int i=0;i<9;i++){
			if (board[row][i] == insert) return false;
		}

		for (int i=0;i<9;i++){
			if (board[i][col] == insert) return false;
		}
		
		// 计算出方框的顶点空格坐标，而不是横向、竖向第几个方框
		int rowNum = row/3 * 3;
		int colNum = col/3 * 3;
		for (int i=0;i<3;i++){
			for(int j=0;j<3;j++){
				if (board[rowNum+i][colNum+j]== insert) return false;
			}
		}
		return true;
	}
}