LeetCode-in-All
51. N-Queens
Hard
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 all distinct solutions to the n-queens puzzle. You may return the answer in any order.
Each solution contains a distinct board configuration of the n-queens’ placement, where 'Q' and '.' both indicate a queen and an empty space, respectively.
Example 1:
Input: n = 4
Output: [[“.Q..”,”…Q”,”Q…”,”..Q.”],[”..Q.”,”Q…”,”…Q”,”.Q..”]]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above
Example 2:
Input: n = 1
Output: [[“Q”]]
Constraints:
1 <= n <= 9
Solution
impl Solution {
pub fn solve_n_queens(n: i32) -> Vec<Vec<String>> {
let mut pos = vec![false; n as usize + 2 * n as usize - 1 + 2 * n as usize - 1];
let mut pos2 = vec![0; n as usize];
let mut ans = Vec::new();
Solution::helper(n as usize, 0, &mut pos, &mut pos2, &mut ans);
ans
}
fn helper(
n: usize,
row: usize,
pos: &mut Vec<bool>,
pos2: &mut Vec<usize>,
ans: &mut Vec<Vec<String>>,
) {
if row == n {
Solution::construct(n, pos2, ans);
return;
}
for i in 0..n {
let index = n + 2 * n - 1 + n - 1 + i - row;
if pos[i] || pos[n + i + row] || pos[index] {
continue;
}
pos[i] = true;
pos[n + i + row] = true;
pos[index] = true;
pos2[row] = i;
Solution::helper(n, row + 1, pos, pos2, ans);
pos[i] = false;
pos[n + i + row] = false;
pos[index] = false;
}
}
fn construct(n: usize, pos2: &Vec<usize>, ans: &mut Vec<Vec<String>>) {
let mut sol = Vec::new();
for r in 0..n {
let mut queen_row = vec!['.'; n];
queen_row[pos2[r]] = 'Q';
sol.push(queen_row.into_iter().collect());
}
ans.push(sol);
}
}