chore(Java): add N Queen Problem (#570)

algorithms/Java/README.md

@@ -75,3 +75,6 @@
 - [Left View of a Tree](trees/left-view.java)
 - [Right View of a Tree](trees/right-view.java)
 - [Zig-Zag Traversal of a Tree](trees/zig-zag-traversal.java)
+
+## Backtracking
+- [N Queen Problem](backtracking/nqueen.java)

algorithms/Java/backtracking/nqueen.java

@@ -0,0 +1,88 @@
+//The N Queen is the problem of placing N chess queens on an N×N chessboard so that no two queens attack each other.
+
+// Algorithm Type: Backtracking
+// Time Complexity: O(n!)
+
+import java.util.*;
+import java.util.Scanner;
+
+class nqueen
+{
+    //Array to store left diagonal elements to check if queen can be placed in left diagonal
+    static int []LeftDiagonal = new int[50];
+
+    //Array to store right diagonal elements to check if queen can be places in right diagonal
+    static int []RightDiagonal = new int[50];
+
+    //Array to store row-wise elements to check if queen can be placed in row
+    static int []cl = new int[50];
+
+    //Function to return true and print if feasible solution is obtained else return false
+    static boolean solveNQueen()
+    {
+        Scanner sc = new Scanner(System.in);
+        System.out.print("Enter the value of N for NxN chess board:\t");
+        int n = sc.nextInt();
+        int[][] chessBoard = new int[n][n];
+        for(int i=0;i<n;i++){
+            for(int j=0;j<n;j++){
+                chessBoard[i][j]=0;
+            }
+        }
+
+        if (NQueen(chessBoard, 0,n) == false)
+        {
+            System.out.printf("Solution does not exist");
+            return false;
+        }
+
+        printChessBoard(chessBoard,n);
+        return true;
+    }
+    //A recursive approach to solve N queens problem
+    static boolean NQueen(int chessBoard[][], int column,int N)
+    {
+        if (column >= N) //If all queens are placed, then return true
+            return true;
+
+        for (int i = 0; i < N; i++) //placing queens in all rows of that particular column
+        {
+            //Check while placing a queen is not attacked by left and right diagonal elements
+            if ((LeftDiagonal[i - column + N - 1] != 1 &&
+                    RightDiagonal[i + column] != 1) && cl[i] != 1)
+            { //If the above condition is true then place the queen
+                chessBoard[i][column] = 1;
+                LeftDiagonal[i - column + N - 1] =
+                        RightDiagonal[i + column] = cl[i] = 1;
+
+                if (NQueen(chessBoard, column + 1,N))
+                    return true;
+
+                //If placing this queen in chessBoard doesn't lead to a correct & safe position then remove queen from chessBoard
+                //going back through BACKTRACKING
+                chessBoard[i][column] = 0;
+                LeftDiagonal[i - column + N - 1] =
+                        RightDiagonal[i + column] = cl[i] = 0;
+            }
+        }
+        return false; //If queen not placed in any row of this column then return false
+    }
+
+    //Function to print chess board
+    static void printChessBoard(int chessBoard[][],int N)
+    {
+        System.out.printf("\n%d queens can be placed in the following order:\n",N);
+        for (int i = 0; i < N; i++)
+        {
+            for (int j = 0; j < N; j++) {
+                System.out.printf(" %d ", chessBoard[i][j]);
+            }
+            System.out.printf("\n");
+        }
+    }
+    public static void main(String[] args)
+    {
+        nqueen obj = new nqueen();
+        obj.solveNQueen();
+    }
+}