adding nqueen problem

Author: Muskan-goyal6

nQueen/Question.txt

@@ -0,0 +1,10 @@
+The N Queen is the problem of placing N chess queens on an N×N chessboard so
+that no two queens attack each other. For example, following is a solution 
+for 4 Queen problem.
+The expected output is a binary matrix which has Qs for the blocks where 
+queens are placed and Xs where queens are not placed. 
+EXAMPLE:
+X  X  Q  X 
+Q  X  X  X
+X  X  X  Q
+X  Q  X  X  

nQueen/nQueen.cpp

@@ -0,0 +1,90 @@
+
+#include <iostream>
+using namespace std;
+
+char board[30][30];
+
+void printBoard(char arr[][30], int n) {
+    for (int r = 0; r < n; ++r) {
+        for (int c = 0; c < n; ++c) {
+            cout << arr[r][c] << " " ;
+        }
+        cout << endl;
+    }
+}
+
+void initialiseBoard(int n) {
+    for (int r = 0; r < n; ++r) {
+        for (int c = 0; c < n; ++c) {
+            board[r][c] = 'X';
+        }
+    }
+}
+
+bool canPlace(char board[][30], int N, int x, int y)
+{
+    //check the row if aqueen already exists
+    for (int r = 0; r < N; ++r)
+    {
+        if (board[r][y] == 'Q') 
+            return false;
+    }
+
+    int rInc[] = { -1, +1, +1, -1};
+    int cInc[] = { -1, +1, -1, +1};
+     //check diagonal if queen already exists
+    for (int dir = 0; dir < 4; ++dir)
+    {
+        int rowAdd = rInc[dir];
+        int colAdd = cInc[dir];
+        int r = x + rowAdd;
+        int c = y + colAdd;
+        //check that r c is within the board
+        while (r >= 0 && r < N && c >= 0 && c < N)
+        {
+            if (board[r][c] == 'Q')
+             return false;
+            r = r + rowAdd;
+            c = c + colAdd;
+        }
+    }
+    return true;
+}
+
+bool nqueen(int r, int n)
+{
+    if (r == n)//base case if all queens are placed 
+    {
+        return true;
+    }
+    //for every column, use hit and trial by placing a queen in the each cell of curr Row
+    for (int c = 0; c < n; ++c)
+    {
+        int x = r;
+        int y = c;
+        //check if queen can be placed on board[i][c]
+        if (canPlace(board, n, x, y)==true)
+        {
+            board[x][y] = 'Q'; //place queen in each column
+            bool isSuccessful = nqueen(r + 1, n);   //recursion to place rest of queens
+            if (isSuccessful == true)
+             return true;
+            board[x][y] = 'X';   //else unmark the cell or backtrack
+        }
+    }
+    return false; //if queen cannot be placed in any row in this column then return false
+}
+
+int main()
+{
+    int n;
+    cin >> n;
+
+    initialiseBoard(n);//initialse all the board with X
+    bool isSuccessful = nqueen(0, n);
+
+    if (isSuccessful) printBoard(board, n);
+    else cout << "Sorry man! You need to have a larger board!\n";
+
+    return 0;
+}