Add implementation for the N-Queens problem using backtracking

Author: gourabofficial

Backtracking/nQueensProblem.java

@@ -0,0 +1,112 @@
+public class nQueensProblem {
+    public static void main(String[] args) {
+        int n = 4;
+        char[][] board = new char[n][n];
+
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < n; j++) {
+                board[i][j] = 'X';
+            }
+
+        }
+
+        nqueen(board, 0);
+    }
+
+    static void nqueen(char[][] board, int row) {
+        int n = board.length;
+
+        // base case
+        if (n == row) {
+            for (int i = 0; i < n; i++) {
+                for (int j = 0; j < n; j++) {
+                    System.out.print(board[i][j]);
+                }
+                System.out.println();
+            }
+            System.out.println();
+            return;
+        }
+
+        for (int j = 0; j < n; j++) {
+
+            if (isSafe(board, row, j)) {
+                board[row][j] = 'Q';
+                nqueen(board, row + 1); // resursive callll
+                board[row][j] = 'X';
+
+            }
+        }
+
+    }
+
+    static boolean isSafe(char[][] board, int row, int col) {
+
+        int n = board.length;
+
+        // check row
+        for (int j = 0; j < n; j++) {
+            if (board[row][j] == 'Q') {
+                return false;
+            }
+        }
+
+        // check coloum
+        for (int i = 0; i < n; i++) {
+            if (board[i][col] == 'Q') { // neds to change [i][col]
+                return false;
+            }
+        }
+
+        // check right top diagonal
+        int i = row;
+        int j = col;
+
+        while (i >= 0 && j < n) {
+            if (board[i][j] == 'Q')
+                return false;
+
+            i--;
+            j++;
+        }
+
+        // check the right buttom diagonal
+        i = row;
+        j = col;
+
+        while (i < n && j < n) {
+            if (board[i][j] == 'Q')
+                return false;
+
+            i++;
+            j++;
+        }
+
+        // check the left buttom diagonal
+
+        i = row;
+        j = col;
+
+        while (i < n && j >= 0) {
+            if (board[i][j] == 'Q')
+                return false;
+
+            i++;
+            j--;
+        }
+
+        // check the left top diaonal
+        i = row;
+        j = col;
+
+        while (i >= 0 && j >= 0) {
+            if (board[i][j] == 'Q')
+                return false;
+
+            i--;
+            j--;
+        }
+
+        return true;
+    }
+}