Merge pull request akshitagit#44 from Riyagoel2/master

Added Solution to NQueenProblem using Backtracking

Recursion&Backtracking/NQueenProblem.java

@@ -0,0 +1,102 @@
+// N-Queen Problem using Backtracking
+/*
+The N Queen is the problem of placing N chess queens on an N×N chessboard so that no two queens attack each other.
+The solution uses Backtracking to solve the problem.
+The expected output will contain all possible positions to place the queens.
+           
+*/
+
+import java.util.*;
+
+public class Solution
+{  
+
+public static void main(String [] args){
+
+	Scanner s=new Scanner(System.in);
+  int N=s.nextInt();
+  boolean[][] board=new boolean[N][N];
+	NQueen(board, 0, 0,0, N ,"");
+
+          }
+
+public static void NQueen(boolean[][] board, int row, int col, int queensPlaced, int totalQueens, String ans) {
+
+		if (queensPlaced == totalQueens) {
+			System.out.println(ans);
+			return;
+		}
+
+		if (col == board[0].length) {
+			col = 0;
+			row++;
+		}
+
+		if (row == board.length) {
+			return;
+		}
+
+		if (isItSafeToPlaceQueen(board, row, col)) {
+			board[row][col] = true;
+			NQueen(board, row, col + 1, queensPlaced + 1, totalQueens, ans + "[" + row + "-" + col + "]");
+			board[row][col] = false;
+		}
+		NQueen(board, row, col + 1, queensPlaced, totalQueens, ans);
+
+	}
+
+	private boolean isItSafeToPlaceQueen(boolean[][] board, int row, int col) {
+
+
+		int r = row - 1;
+		int c = col;
+		while (r >= 0) {
+			if (board[r][c]) {
+				return false;
+			}
+			r--;
+		}
+
+		r = row;
+		c = col - 1;
+		while (c >= 0) {
+			if (board[r][c]) {
+				return false;
+			}
+			c--;
+		}
+
+		r = row - 1;
+		c = col - 1;
+		while (r >= 0 && c >= 0) {
+			if (board[r][c]) {
+				return false;
+			}
+			r--;
+			c--;
+		}
+
+		r = row - 1;
+		c = col + 1;
+		while (r >= 0 && c < board[0].length) {
+			if (board[r][c]) {
+				return false;
+			}
+			r--;
+			c++;
+			;
+		}
+		return true;
+	}
+
+}
+
+
+/* Input :
+   4
+
+  Output :
+  [0-1][1-3][2-0][3-2]
+  [0-2][1-0][2-3][3-1]
+
+*/