n queens using recursion

Author: TonyStark-19

Recursion/nQueens.cpp

@@ -0,0 +1,97 @@
+#include <iostream>
+#include <vector>
+#include <string>
+using namespace std;
+
+bool isSafe(vector<string> &board, int row, int col, int n)
+{
+    // horizontally
+    for (int j = 0; j < n; j++)
+    {
+        if (board[row][j] == 'Q')
+        {
+            return false;
+        }
+    }
+
+    // vertically
+    for (int i = 0; i < n; i++)
+    {
+        if (board[i][col] == 'Q')
+        {
+            return false;
+        }
+    }
+
+    // left diagonal
+    for (int i = row, j = col; i >= 0 && j >= 0; i--, j--)
+    {
+        if (board[i][j] == 'Q')
+        {
+            return false;
+        }
+    }
+
+    // right diagonal
+    for (int i = row, j = col; i >= 0 && j < n; i--, j++)
+    {
+        if (board[i][j] == 'Q')
+        {
+            return false;
+        }
+    }
+
+    return true;
+}
+
+void nQueens(vector<string> &board, int row, int n, vector<vector<string>> &ans)
+{
+    if (row == n)
+    {
+        ans.push_back({board});
+        return;
+    }
+
+    for (int j = 0; j < n; j++)
+    {
+        if (isSafe(board, row, j, n))
+        {
+            board[row][j] = 'Q';
+            nQueens(board, row + 1, n, ans);
+            board[row][j] = '.'; // backtracking
+        }
+    }
+}
+
+vector<vector<string>> solveNQueens(int n)
+{
+    vector<string> board(n, string(n, '.'));
+    vector<vector<string>> ans;
+
+    nQueens(board, 0, n, ans);
+    return ans;
+}
+
+void printBoard(const vector<string> &board)
+{
+    for (const string &row : board)
+    {
+        cout << row << endl;
+    }
+    cout << endl;
+}
+
+int main()
+{
+    int n = 4;
+    vector<vector<string>> solutions = solveNQueens(n);
+
+    cout << "Total solutions for n = " << n << ": " << solutions.size() << endl;
+
+    for (const auto &solution : solutions)
+    {
+        printBoard(solution);
+    }
+
+    return 0;
+}