N-Queens

• https://leetcode.com/problems/n-queens/

Given an integer n, return all distinct solutions to the n-queens puzzle.

Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space respectively.

For example, There exist two distinct solutions to the 4-queens puzzle:

[ [".Q..", // Solution 1 "...Q", "Q...", "..Q."],

["..Q.", // Solution 2 "Q...", "...Q", ".Q.."] ]

Time complexity: O(n!)

Note: this solution is left the room for improvement.

public List<List<String>> solveNQueens(int n) {
    char[][] board = new char[n][n];
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            board[i][j] = '.';
        }
    }
    List<List<String>> result = new ArrayList<>();
    helperNQueens(board, 0, result);
    return result;
}


private void helperNQueens(char[][] board, int row, List<List<String>> result) {
    if (row == board.length) {
        List<String> current = new ArrayList();
        for (int i = 0; i < board.length; i++) {
            StringBuilder sb = new StringBuilder();
            for (int j = 0; j < board[0].length; j++) {
                sb.append(board[i][j]);
            }
            current.add(sb.toString());
        }
        result.add(current);
    } else {
        // check each cells in column
        for (int j = 0; j < board[0].length; j++) {
            if (isSafe(board, row, j)) {
                board[row][j] = 'Q';
                helperNQueens(board, row + 1, result);
                board[row][j] = '.';
            }
        }
    }
}


private boolean isSafe(char[][] board, int m, int n) {
    // check all rows above
    for (int i = 0; i < m; i++) {
        if (board[i][n] == 'Q')
            return false;
    }

    // check left diagonal
    int i = m -1;
    int j = n - 1;
    while (i >= 0 && j >= 0) {
        if (board[i][j] == 'Q') {
            return false;
        }
        i--;
        j--;
    }

    // check right diagonal
    i = m -1;
    j = n + 1;
    while (i >= 0 && j < board[0].length) {
        if (board[i][j] == 'Q') {
            return false;
        }
        i--;
        j++;
    }
    return true;
}