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
class Solution {
int count = 0;
public int totalNQueens(int n) {
boolean[] cols = new boolean[n]; // columns |
boolean[] d1 = new boolean[2 * n]; // diagonals \
boolean[] d2 = new boolean[2 * n]; // diagonals /
backtracking(0, cols, d1, d2, n);
return count;
}
public void backtracking(int row, boolean[] cols, boolean[] d1, boolean []d2, int n) {
if(row == n) count++;
for(int col = 0; col < n; col++) {
int id1 = col - row + n;
int id2 = col + row;
if(cols[col] || d1[id1] || d2[id2]) continue;
cols[col] = true; d1[id1] = true; d2[id2] = true;
backtracking(row + 1, cols, d1, d2, n);
cols[col] = false; d1[id1] = false; d2[id2] = false;
}
}
}