Leetcode 36 Valid Sudoku

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本文介绍了一种高效算法，用于验证9x9数独盘面是否符合数独的基本规则，包括行、列及3x3子网格内数字1-9不重复。通过使用HashSet进行快速查找，确保了算法的时间复杂度为O(n^2)，适用于部分填充的数独盘面。

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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.

这个题的意思是判断目前已知的九宫格中是否符合规则，使用一个HashMap或者是Set即可解决。

1）

class Solution {
    public boolean isValidSudoku(char[][] board) {
        Set seen = new HashSet();
        for (int i=0; i<9; ++i) {
            for (int j=0; j<9; ++j) {
                if (board[i][j] != '.') {
                    String b = "(" + board[i][j] + ")";
                    if (!seen.add(b + i) || !seen.add(j + b) || !seen.add(i/3 + b + j/3))
                        return false;
                }
            }
        }
        return true;
    }
}

时间复杂度O（n2）

2）

class Solution {
    public boolean isValidSudoku(char[][] board) {
    for(int i = 0; i < board.length; i++) {
        if (!isRowValid(board, i) || !isColumnValid(board, i)) {
            return false;
    }		
    } 
    for (int i = 0; i < board.length; i+=3) {
        for(int j = 0; j < board.length; j+=3) {
            if (!isSquareValid(board,i, j)) {
                return false;
            }
        }
    }
    return true;
    }

    public boolean isSquareValid(char[][] board, int iStart, int jStart) {
        Set<Integer> set = new HashSet<>();
        for (int i = iStart; i < iStart + 3; i++) {
            for (int j = jStart; j < jStart + 3; j++) {
            if (board[i][j] != '.' && !set.add(board[i][j] - '.')) {
                return false;
            }
            }
        }
        return true;
    }

    public boolean isRowValid(char[][] board, int index) {
        Set<Integer> set = new HashSet<>();
        for(int i = 0; i < board.length; i++) {
            if (board[index][i] != '.' && !set.add(board[index][i] - '.')) {
                return false;
            }
        }
        return true;
    }
    public boolean isColumnValid(char[][] board, int index) {
        Set<Integer> set = new HashSet<>();
        for(int i = 0; i < board.length; i++) {
            if (board[i][index] != '.' && !set.add(board[i][index] - '.')) {
                return false;
            }
        }
        return true;

    }

}