Leetcode 036 有效的数独

地址 https://leetcode-cn.com/problems/valid-sudoku/

判断一个 9x9 的数独是否有效。只需要根据以下规则，验证已经填入的数字是否有效即可。

数字 1-9 在每一行只能出现一次。
数字 1-9 在每一列只能出现一次。
数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。
上图是一个部分填充的有效的数独。

数独部分空格内已填入了数字，空白格用 '.' 表示。

示例 1:

输入:
[
  ["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"]
]
输出: true
示例 2:

输入:
[
  ["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"]
]
输出: false
解释: 除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。
     但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。
说明:

一个有效的数独（部分已被填充）不一定是可解的。
只需要根据以上规则，验证已经填入的数字是否有效即可。
给定数独序列只包含数字 1-9 和字符 '.' 。
给定数独永远是 9x9 形式的。

解答

使用 三个数组 标记 各个方块 各行各列 已经使用的数字 ，放置重复使用即可

块的IDX索引计算需要一点小转折 其他没什么问题

class Solution {
public:
    int rec[9][10] = { 0 };
    int row[9][10] = { 0 };
    int col[9][10] = { 0 };
    bool isValidSudoku(vector<vector<char>>& board) {
        for (int x = 0; x < 9; x++) {
            for (int y = 0; y < 9; y++) {
                if (board[x][y] != '.') {
                    int n = board[x][y] - '0';
                    int recX = x / 3; int recY = y / 3;
                    int recIdx = recX * 3 + recY;
                    if (rec[recIdx][n] == 1) 
                        return false;
                    else rec[recIdx][n] = 1;

                    if (row[x][n] == 1) 
                        return false;
                    else row[x][n] = 1;

                    if (col[y][n] == 1) 
                        return false;
                    else col[y][n] = 1;
                }
            }
        }


        return true;
    }
};

// 11232345675.cpp : 此文件包含 'main' 函数。程序执行将在此处开始并结束。
//

#include <iostream>
#include <vector>

using namespace std;

/*
判断一个 9x9 的数独是否有效。只需要根据以下规则，验证已经填入的数字是否有效即可。

数字 1-9 在每一行只能出现一次。
数字 1-9 在每一列只能出现一次。
数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。


数独部分空格内已填入了数字，空白格用 '.' 表示。

示例 1:

输入:
[
  ["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"]
]
输出: true
示例 2:

输入:
[
  ["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"]
]
输出: false
解释: 除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。
     但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。
说明:

一个有效的数独（部分已被填充）不一定是可解的。
只需要根据以上规则，验证已经填入的数字是否有效即可。
给定数独序列只包含数字 1-9 和字符 '.' 。
给定数独永远是 9x9 形式的。
*/

class Solution {
public:
    int row[10][10];
    int col[10][10];
    int box[10][10];

    bool check(int n, int r, int c)
    {
        if (row[r][n] == 1 || col[c][n] == 1 || box[r / 3 * 3 + c / 3][n] == 1) {
            return false;
        }

        return true;
    }

    bool isValidSudoku(vector<vector<char>>& board) {
        //初始化行列宫的数组
        memset(row, 0, sizeof(row));
        memset(col, 0, sizeof(col));
        memset(box, 0, sizeof(box));

        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                if (board[i][j] != '.') {
                    int n = board[i][j] - '0';
                    if (check(n, i, j) == false) 
                        return false;
                    row[i][n] = 1;
                    col[j][n] = 1;
                    box[i / 3 * 3 + j / 3][n] = 1;
                }
            }
        }

        return true;
    }
};

/*
[
['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']
]
*/
int main()
{
    Solution s;
    vector<vector<char>> vv{
        {'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'}
    };
    cout << s.isValidSudoku(vv);
}