The n-queens puzzle is the problem of placing n
queens on an n x n
chessboard such that no two queens attack each other.
Given an integer n
, return the number of distinct solutions to the n-queens puzzle.
Example 1:
Input: n = 4 Output: 2 Explanation: There are two distinct solutions to the 4-queens puzzle as shown.
Example 2:
Input: n = 1 Output: 1
Constraints:
1 <= n <= 9
Related Topics:
Backtracking
Similar Questions:
// OJ: https://leetcode.com/problems/n-queens-ii/
// Author: github.com/lzl124631x
// Time: O(N!)
// Space: O(N)
class Solution {
vector<bool> col, hill, dale;
int n;
int dfs(int i) {
if (i == n) {
return 1;
}
int ans = 0;
for (int j = 0; j < n; ++j) {
int h = i + j, d = i + n - 1 - j;
if (col[j] || hill[h] || dale[d]) continue;
col[j] = hill[h] = dale[d] = true;
ans += dfs(i + 1);
col[j] = hill[h] = dale[d] = false;
}
return ans;
}
public:
int totalNQueens(int n) {
this->n = n;
col.assign(n, false);
hill.assign(2 * n - 1, false);
dale.assign(2 * n - 1, false);
return dfs(0);
}
};