NQueens.java

package backtracking;

public class NQueens {
    public static void nQueens(char[][] board, int row) {
        // base
        if (row == board.length) {
            printBoard(board);
            return;
        }

        // column loop
        for (int j = 0; j < board.length; j++) {
            if (isSafe(board, row, j)) {
                board[row][j] = 'Q';
                nQueens(board, row + 1); // func call
                board[row][j] = '.'; // backtracking step
            }
        }
    }

    public static boolean isSafe(char[][] board, int row, int col) {
        // vertical up
        for (int i = row - 1; i >= 0; i--) {
            if (board[i][col] == 'Q') {
                return false;
            }
        }

        // diag left up
        for (int i = row - 1, j = col -1; i >= 0 && j >= 0; i--, j--) {
            if (board[i][j] == 'Q') {
                return false;
            }
        }

        // diag right up
        for (int i = row - 1, j = col +1; i >= 0 && j < board.length; i--, j++) {
            if (board[i][j] == 'Q') {
                return false;
            }
        }

        return true;
    }

    public static void printBoard(char[][] board) {
        System.out.println("----- Chess Board -----");
        for (int i = 0; i < board.length; i++) {
            for (int j = 0; j < board.length; j++) {
                System.out.print(board[i][j] + " ");
            }
            System.out.println();
        }
    }

    public static void main(String[] args) {
        int n = 4;
        char[][] board = new char[n][n];

        // init
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                board[i][j] = '.';
            }
        }

        nQueens(board, 0);
    }
}
// TC: O(n!) | SC: O(n^2)

// Place N Queens on a N*N chessboard such that no 2 Queens can attack each other.

/*
N-Queens (LeetCode 51)
https://leetcode.com/problems/n-queens/description/

class Solution {
    public List<List<String>> solveNQueens(int n) {
        List<List<String>> res = new ArrayList<>();
        char[][] board = new char[n][n];
        
        // init
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                board[i][j] = '.';
            }
        }
        
        nQueens(board, 0, res);
        return res;
    }
    
    public static void nQueens(
                               char[][] board,
                               int row,
                               List<List<String>> res) {
        // base
        if (row == board.length) {
            res.add(constructBoard(board));
            return;
        }

        // column loop
        for (int j = 0; j < board.length; j++) {
            if (isSafe(board, row, j)) {
                board[row][j] = 'Q';
                nQueens(board, row + 1, res); // func call
                board[row][j] = '.'; // backtracking step
            }
        }
    }

    public static boolean isSafe(char[][] board, int row, int col) {
        // vertical up
        for (int i = row - 1; i >= 0; i--) {
            if (board[i][col] == 'Q') {
                return false;
            }
        }

        // diag left up
        for (int i = row - 1, j = col - 1; i >= 0 && j >= 0; i--, j--) {
            if (board[i][j] == 'Q') {
                return false;
            }
        }

        // diag right up
        for (int i = row - 1, j = col + 1; i >= 0 && j < board.length; i--, j++) {
            if (board[i][j] == 'Q') {
                return false;
            }
        }

        return true;
    }
    
    public static List<String> constructBoard(char[][] board) {
        List<String> res = new ArrayList<>();
        for (int i = 0; i < board.length; i++) {
            res.add(new String(board[i]));
        }
        return res;
    }
}
*/