LeetCode 37: Sudoku Solver

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.

A sudoku puzzle, and its solution numbers marked in red.

解题思路

采用回溯法（Backtracking）求解，代码如下：

class Solution {
private:
// 检测第 x 行，第 y 列是否有效
bool isValidSudoku(vector<vector<char>>& board, int row, int col) {
// 行
for(int j = 0; j < 9; j++)
if(j != col && board[row][j] == board[row][col])
return false;
// 列
for(int i = 0; i < 9; i++)
if(i != row && board[i][col] == board[row][col])
return false;
// 九宫格
int gridRow = row/3*3, gridCol = col/3*3;
for(int i = 0; i < 3; i++)
for(int j = 0; j < 3; j++)
if(gridRow + i != row && gridCol + j != col &&
board[gridRow + i][gridCol + j] == board[row][col])
return false;

return true;
}

bool internalSolver(vector<vector<char>>& board) {
for (int i = 0; i < 9; ++i) {
for (int j = 0; j < 9; ++j) {
if (board[i][j] == '.') {
// 若board[i][j] == '.'，则尝试填入数字1-9
for (int k = 0; k < 9; ++k) {
board[i][j] = '1' + k;

// 当前填入的数字有效，递归解决余下部分
if (isValidSudoku(board, i, j)) {
if (internalSolver(board)) {
// 余下部分成功解决，则board已填充完全
return true;
}
}
}

//该空格无论设置什么数字都无法达到合法状态，回溯
board[i][j] = '.';
return false;
}
}
}
return true;
}

public:
void solveSudoku(vector<vector<char>>& board) {
internalSolver(board);
}
};

这里提供了一个JavaScript实现的 Sudoku puzzle solver 和一些相关链接。