[LeetCode 36&37] Valid Sudoku & Sudoku Solver (数独问题）

题目链接：valid-sudoku

import java.util.Arrays;

/**
 *
		Determine if a Sudoku is valid, according to: Sudoku Puzzles - The Rules.

		The Sudoku board could be partially filled, where empty cells are filled with the character '.'.

		A partially filled sudoku which is valid.

		Note:
		A valid Sudoku board (partially filled) is not necessarily solvable.
		Only the filled cells need to be validated.
 *
 */

public class ValidSudoku {

	//数度有解的条件
//	Every digit from 1 to 9 must appear:	1-9 这九个数字必须在下面各种情况只出现一次
//		In each of the columns,				每列
//		in each of the rows,				每行
//		and in each of the nine boxes.		每个九宫格

//	501 / 501 test cases passed.
//	Status: Accepted
//	Runtime: 369 ms
//	Submitted: 1 minute ago

	//检查该数独是否有效
	//时间复杂度O(n^2) 空间复杂度O(n)
    public boolean isValidSudoku(char[][] board) {
		boolean[] flag = new boolean[10];//标记
		// 检查九行
		for (int i = 0; i < 9; i++) {
			Arrays.fill(flag, false);
			for (int j = 0; j < 9; j++) {
				if(board[i][j] == '.')
					continue;
				if (!flag[board[i][j] - '0']) {
					flag[board[i][j] - '0'] = true;
				} else {
					return false;
				}
			}
		}

		// 检查九列
		for (int j = 0; j < 9; j++) {
			Arrays.fill(flag, false);
			for (int i = 0; i < 9; i++) {
				if(board[i][j] == '.')
					continue;
				if (!flag[board[i][j] - '0']) {
					flag[board[i][j] - '0'] = true;
				} else {
					return false;
				}
			}
		}

    	//检查九个九宫格
		for (int i = 0; i < 9; i += 3) {
			for (int j = 0; j < 9; j += 3) {
				Arrays.fill(flag, false);
				for (int i1 = 0; i1 < 3; i1++) {
					for (int j1 = 0; j1 < 3; j1++) {
						if(board[i + i1][j + j1] == '.')
							continue;
						if (!flag[board[i + i1][j + j1] - '0']) {
							flag[board[i + i1][j + j1] - '0'] = true;
						} else {
							return false;
						}
					}
				}
			}
		}
    	return true;
    }
	public static void main(String[] args) {
		// TODO Auto-generated method stub

	}

}

题目链接：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.
 *
 */

public class SudokuSolver {

//	6 / 6 test cases passed.
//	Status: Accepted
//	Runtime: 260 ms
//	Submitted: 0 minutes ago

	//输入的数独只有唯一解
	//回溯法
	//时间复杂度O(n^4) 空间复杂度O(1)
    public void solveSudoku(char[][] board) {
        solveSudoku1(board);
    }
    public boolean solveSudoku1(char[][] board) {

    	for (int i = 0; i < 9; i++) {
			for (int j = 0; j < 9; j++) {
				if(board[i][j] == '.') {
					for (int k = 1; k <= 9; k++) {
						board[i][j] = (char) ('0' + k);
						if(isValid(board, i, j) && solveSudoku1(board)) {
							return true;
						} else {
							board[i][j] = '.';	//回溯法
						}
					}
					return false;
				}
			}
		}
    	return true;
    }

    public boolean isValid(char[][] board, int i, int j) {
		//检查所属行
    	for (int k = 0; k < 9; k++) {
			if(i != k && board[i][j] == board[k][j])
				return false;
		}
    	//检查所属列
		for (int k = 0; k < 9; k++) {
			if(j != k && board[i][j] == board[i][k])
				return false;
		}
		//检查所属九宫格
		for (int i1 = 3 * (i / 3); i1 < (i / 3 + 1) * 3; i1 ++) {
			for (int j1 = 3 * (j / 3); j1 < (j / 3 + 1) * 3; j1 ++) {
				if(i1 != i && j1 != j && board[i][j] == board[i1][j1])
					return false;
			}
		}
		return true;
    }

	public static void main(String[] args) {
		// TODO Auto-generated method stub

	}

}