51. N-Queens

class Solution {
    public List<List<String>> solveNQueens(int n) {
        List<List<String>> list = new ArrayList<>();

        char[][] board = new char[n][n];
        for (int i = 0; i < n; i++) {
            Arrays.fill(board[i], '.');
        }

        backtrack(list, board, 0);
        return list;
    }

    private void backtrack(List<List<String>> list, char[][] board, int rowIndex) {
        if (rowIndex == board.length) {
            List<String> rowList = new ArrayList<>(board.length);
            for (char[] line : board) {
                rowList.add(new String(line));
            }
            list.add(rowList);
            return;
        }

        for (int j = 0; j < board.length; j++) {
            if (canFill(board, rowIndex, j)) {
                board[rowIndex][j] = 'Q';
                backtrack(list, board, rowIndex + 1);
                board[rowIndex][j] = '.';
            }
        }
    }

    private boolean canFill(char[][] used, int i, int j) {
        for (int k = 0; k < i; k++) {
            if (used[k][j] == 'Q') {
                return false;
            }
        }

        for (int x = i - 1, y = j - 1; x >= 0 && y >= 0; x--, y--) {
            if (used[x][y] == 'Q') {
                return false;
            }
        }
        for (int x = i - 1, y = j + 1; x >= 0 && y < used.length; x--, y++) {
            if (used[x][y] == 'Q') {
                return false;
            }
        }

        return true;
    }
}

Reference

51. N-Queens