说明

算法：Valid Sudoku
LeetCode地址：https://leetcode.com/problems/valid-sudoku/

题目：
Determine if a 9x9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

Each row must contain the digits 1-9 without repetition.
Each column must contain the digits 1-9 without repetition.
Each of the 9 3x3 sub-boxes of the grid must contain the digits 1-9 without repetition.

A partially filled sudoku which is valid.

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

Example 1:

Input:
[["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"]
]
Output: true

Example 2:

Input:
[["8","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"]
]
Output: false
Explanation: Same as Example 1, except with the 5 in the top left corner being modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.

Note:

A Sudoku board (partially filled) could be valid but is not necessarily solvable.
Only the filled cells need to be validated according to the mentioned rules.
The given board contain only digits 1-9 and the character ‘.’.
The given board size is always 9x9.

解题思路

数独问题是个二维的图，实际是有三个条件下都没有重复的数据，
很明显用Set来过滤，如果数据加入失败，那么表示数据已经存在。
接下来降维解决，把二维图化解为三个条件的一维处理。

row横向方向
column纵向方向
cube方框内是否重复，横向/3 - 纵向/3 , 实际就是cube的唯一标识，
比如index[0, 1, 2]的横向纵向都是0-0.

时间复杂度 O(9*9)

代码实现

import java.util.HashSet;
import java.util.Set;public class ValidSudoku {public boolean isValidSudoku(char[][] board) {Set<String> visitSet = new HashSet<>(81);for (int row = 0; row < 9; row++) {for (int column = 0; column < 9; column++) {char data = board[row][column];if (data == '.') {continue;}if (!visitSet.add(data + " row " + row)) {System.out.println("duplicate board[" + row + "][" + column + "]" + " ;data: " + data+ " row " + row);return false;}if (!visitSet.add(data + " column " + column)) {System.out.println("duplicate board[" + row + "][" + column + "]" + " ;data: " + data+ " column " + column);return false;}if (!visitSet.add(data + " cube " + row/3 + '-' + column/3) ) {System.out.println("duplicate board[" + row + "][" + column + "]" + " ;data: " + data+ " cube " + row/3 + '-' + column/3);return false;}}}return true;}public static void main(String[] args) {char[][] board1 = {{'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'}};char[][] board2 = {{'8','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'}};ValidSudoku obj = new ValidSudoku();System.out.println("Output 1: " + obj.isValidSudoku(board1));System.out.println("Output 2: " + obj.isValidSudoku(board2));}
}

运行结果

Output 1: true
duplicate board[2][2] ;data: 8 cube 0-0
Output 2: false

代码执行效率

Runtime: 15 ms, faster than 65.36% of Java online submissions for Valid Sudoku.
Memory Usage: 46.9 MB, less than 5.15% of Java online submissions for Valid Sudoku.

总结

二维图问题降维为三个条件的非重复数据解决。

代码下载：
https://github.com/zgpeace/awesome-java-leetcode/blob/master/code/LeetCode/src/popular/ValidSudoku.java

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算法:Valid Sudoku(有效的数独)

说明

解题思路

代码实现

运行结果

代码执行效率

总结

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