Solution.java

class Solution {
    private List<List<String>> solutions;
    private char[][] nQueens;
    private boolean[] colUsed;
    private boolean[] diagonals45Used;
    private boolean[] diagonals135Used;
    private int n;

    public List<List<String>> solveNQueens(int n) {
        solutions = new ArrayList<>();
        nQueens = new char[n][n];
        for (int i = 0; i < n; i++) Arrays.fill(nQueens[i], '.');
        colUsed = new boolean[n];
        diagonals45Used = new boolean[(2 * n) - 1];
        diagonals135Used = new boolean[(2 * n) - 1];
        this.n = n;
        backtracking(0);
        return solutions;
    }

    private void backtracking(int row) {
        if (row == n) {
            List<String> list = new ArrayList<>();
            for (char[] chars : nQueens) list.add(new String(chars));
            solutions.add(list);
            return;
        }
        for (int col = 0; col < n; col++) {
            int diagonals45Idx = row + col;
            int diagonals135Idx = n - 1 - (row - col);
            if (colUsed[col] || diagonals45Used[diagonals45Idx] || diagonals135Used[diagonals135Idx]) continue;
            nQueens[row][col] = 'Q';
            colUsed[col] = diagonals45Used[diagonals45Idx] = diagonals135Used[diagonals135Idx] = true;
            backtracking(row + 1);
            colUsed[col] = diagonals45Used[diagonals45Idx] = diagonals135Used[diagonals135Idx] = false;
            nQueens[row][col] = '.';
        }
    }
}