From 8dc9f4da842dfef3eeed616ce649bf248fd4856e Mon Sep 17 00:00:00 2001
From: purrvax <ppsingh_b24@et.vjti.ac.in>
Date: Thu, 23 Oct 2025 15:31:37 +0530
Subject: [PATCH] 51 solution added

---
 51.N-Queens.cpp | 64 +++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 64 insertions(+)
 create mode 100644 51.N-Queens.cpp

diff --git a/51.N-Queens.cpp b/51.N-Queens.cpp
new file mode 100644
index 0000000..dd26bcb
--- /dev/null
+++ b/51.N-Queens.cpp
@@ -0,0 +1,64 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+class Solution {
+public:
+    // Function to check if placing a queen at (row, col) is safe
+    bool isSafe(int row, int col, vector<string> &temp, int n) {
+        int duprow = row;
+        int dupcol = col;
+        // Check all columns to the left in the same row
+        for (int j = 0; j < col; j++) {
+            if (temp[row][j] == 'Q') return false;
+        }
+
+        // Check upper-left diagonal
+        while(row >= 0 && col >= 0){
+            if(temp[row][col] == 'Q') return false;
+            row--;
+            col--;
+        }
+        row = duprow;
+        col = dupcol;
+        // Check lower-left diagonal
+        while(row < n && col >= 0){
+            if(temp[row][col] == 'Q') return false;
+            row++;
+            col--;
+        }
+
+        return true;
+    }
+
+    // Backtracking function to place queens column by column
+    void solve(int col, vector<string> temp, vector<vector<string>> &ans, int n) {
+        // If all columns are filled, add current board to answer
+        if (col == n) {
+            ans.push_back(temp);
+            return;
+        }
+
+        for (int row = 0; row < n; row++) {
+            if (isSafe(row, col, temp, n)) {
+                // Place queen
+                temp[row][col] = 'Q';
+                // Recurse for next column
+                solve(col + 1, temp, ans, n); 
+                // Backtrack and remove queen
+                temp[row][col] = '.';        
+            }
+        }
+    }
+
+    // Main function to call backtracking
+    vector<vector<string>> solveNQueens(int n) {
+    vector<vector<string>> ans;
+    vector<string> temp;
+    string s(n, '.');
+    for(int i = 0 ; i < n ; i++) temp.push_back(s); // FIXED
+
+    solve(0, temp, ans, n);
+    return ans;
+}
+
+};
\ No newline at end of file