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Copy path0037.解数独.cpp
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0037.解数独.cpp
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/*
* @lc app=leetcode.cn id=37 lang=cpp
*
* [37] 解数独
*
* https://leetcode-cn.com/problems/sudoku-solver/description/
*
* algorithms
* Hard (55.87%)
* Likes: 265
* Dislikes: 0
* Total Accepted: 13.7K
* Total Submissions: 23.8K
* Testcase Example: '[["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"]]'
*
* 编写一个程序，通过已填充的空格来解决数独问题。
*
* 一个数独的解法需遵循如下规则：
*
*
* 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。
*
*
* 空白格用 '.' 表示。
*
*
*
* 一个数独。
*
*
*
* 答案被标成红色。
*
* Note:
*
*
* 给定的数独序列只包含数字 1-9 和字符 '.' 。
* 你可以假设给定的数独只有唯一解。
* 给定数独永远是 9x9 形式的。
*
*
*/
// @lc code=start
#include <map>
#include <vector>
using namespace std;
class Solution {
public:
void backtrace(vector<int>* row, vector<int>* col, vector<int>* mat, bool& is_done,
vector<vector<char>>& board, int n_row, int n_col)
{
if (is_done)
return;
if (n_row == 9) {
is_done = true;
return;
}
int next_row = n_col == 8 ? (n_row + 1) : n_row;
int next_col = n_col == 8 ? 0 : n_col + 1;
if (board[n_row][n_col] != '.') {
backtrace(row, col, mat, is_done, board, next_row, next_col);
return;
}
for (int i = 1; i < 10; i++) {
if (row[n_row][i - 1] != 1 && col[n_col][i - 1] != 1 && mat[(n_col / 3) + (n_row / 3) * 3][i - 1] != 1) {
board[n_row][n_col] = '0' + i;
row[n_row][i - 1] = 1;
col[n_col][i - 1] = 1;
mat[(n_col / 3) + (n_row / 3) * 3][i - 1] = 1;
backtrace(row, col, mat, is_done, board, next_row, next_col);
if (is_done) {
return;
}
board[n_row][n_col] = '.';
row[n_row][i - 1] = 0;
col[n_col][i - 1] = 0;
mat[(n_col / 3) + (n_row / 3) * 3][i - 1] = 0;
}
}
}
void solveSudoku(vector<vector<char>>& board)
{
// 用 vector 而不是 map 来加快速度
vector<int> row[9] = {
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
};
vector<int> col[9] = {
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
};
vector<int> mat[9] = {
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
vector<int>(9, 0),
};
for (int i = 0; i < 9; ++i) {
for (int j = 0; j < 9; ++j) {
if (board[i][j] != '.') {
row[i][board[i][j] - '0' - 1] = 1;
col[j][board[i][j] - '0' - 1] = 1;
mat[(j / 3) + (i / 3) * 3][board[i][j] - '0' - 1] = 1;
}
}
}
bool is_done = false;
backtrace(row, col, mat, is_done, board, 0, 0);
}
};
// @lc code=end