37 Sudoku Solver

1. Question

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.

2. Implementation

(1) Backtracking
class Solution {
public void solveSudoku(char[][] board) {
if (board == null || board.length == 0) {
return;
}
recSolveSudoku(board);
}
public boolean recSolveSudoku(char[][] board) {
for (int i = 0; i < board.length; i++) {
for (int j = 0; j < board[0].length; j++) {
if (board[i][j] == '.') {
for (char c = '1'; c <= '9'; c++) {
if (isValid(board, i, j, c)) {
board[i][j] = c;
if (recSolveSudoku(board)) {
return true;
}
board[i][j] = '.';
}
}
return false;
}
}
}
return true;
}
public boolean isValid(char[][] board, int row, int col, char num) {
for (int i = 0; i < 9; i++) {
if (board[i][col] == num || board[row][i] == num) {
return false;
}
if (board[3 * (row / 3) + i / 3][3 * (col / 3) + i % 3] == num) {
return false;
}
}
return true;
}
}

3. Time & Space Complexity

Backtracking: 时间复杂度O(9^n),n是board为空格的个数, 空间复杂度O(n), 递归的深度最多为n