Add N Queen problem algorithm file

c++/nqueen.cpp

@@ -0,0 +1,45 @@
+#include <bits/stdc++.h>
+using namespace std;
+int n;
+
+bool safe(vector<vector<int>> &board, int r, int c) {
+    for (int i = 0; i < c; i++) if (board[r][i] == 1) return false;
+    for (int i = r, j = c; i >= 0 && j >= 0; i--,j--) if (board[i][j] == 1) return false;
+    for (int i = r, j = c; i < n && j >= 0; i++,j--) if (board[i][j] == 1) return false;
+    return true;
+}
+
+bool solve(vector<vector<int>> &board, int c) {
+    if (c >= n) return true;
+    else {
+        for (int i = 0; i < n; i++)
+        {
+            if (safe(board, i,c)) {
+                board[i][c] = 1;
+                if (solve(board, c+1)) return true;
+                board[i][c] = 0;
+            }
+        }
+        return false;
+    }
+}
+
+signed main()
+{
+    cout << "Enter the value of N\n";
+    cin >> n;
+    vector<vector<int>> board(100, vector<int> (100, 0));
+    if (!solve(board, 0)) cout << "No Solution exists!\n";
+    else {
+        for (int i = 0; i < n; i++)
+        {
+            for (int j = 0; j < n; j++)
+            {
+                cout << board[i][j] << " ";
+            }
+            cout << endl;
+        }
+
+    }
+    return 0;
+}