From 7cd2b2dc086e038c966950a39f65d11722d560fb Mon Sep 17 00:00:00 2001
From: Natwar Gopal <natwar.gopal2001@gmail.com>
Date: Wed, 19 Oct 2022 20:57:44 +0530
Subject: [PATCH] Added N_Queens

---
 Backtracking/N-Queens.cpp | 104 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 104 insertions(+)
 create mode 100644 Backtracking/N-Queens.cpp

diff --git a/Backtracking/N-Queens.cpp b/Backtracking/N-Queens.cpp
new file mode 100644
index 0000000..686834c
--- /dev/null
+++ b/Backtracking/N-Queens.cpp
@@ -0,0 +1,104 @@
+/*
+https://leetcode.com/problems/n-queens/description/
+51. N-Queens
+Leetcode Hard
+*/
+class Solution {
+
+    bool isPossible(vector<string>& partialAns, int row, int col, int n) {
+
+
+        int len = partialAns.size();
+
+        for(int i = 0;i<len;i++) {
+
+            if(partialAns[i][col] == 'Q') return 0;
+
+        }
+
+        int i=row-1, j = col + 1;
+
+        while(i>=0 and j<n) {
+
+            if(partialAns[i][j]=='Q') return 0;
+
+            i--;j++;
+
+        }
+
+        i=row - 1, j = col -1;
+
+        while(i>=0 and j>=0) {
+
+            if(partialAns[i][j]=='Q') return 0;
+
+            i--;j--;
+
+        }
+
+        
+
+        return 1;
+
+    }
+
+    void helper(vector<vector<string>>& ans, int n, int row, vector<string>& partialAns) {
+
+        
+
+        if(row >= n) {
+
+            ans.push_back(partialAns);
+
+            return;
+
+        }
+
+        string s = "";
+
+        for(int col=0;col < n;col++) {
+
+            if(isPossible(partialAns,row,col,n)) {
+
+                string temp = s;
+
+                temp+='Q';
+
+                int i = col;
+
+                while(i<n-1){
+
+                    temp+='.';
+
+                    i++;
+
+				}
+                partialAns.push_back(temp);
+
+                helper(ans,n,row+1,partialAns);
+
+                partialAns.pop_back();
+
+            }
+
+            s+=".";
+
+        }
+
+    }
+
+public:
+
+    vector<vector<string>> solveNQueens(int n) {
+
+        vector<vector<string>> ans;
+
+        vector<string> partialAns;
+
+        helper(ans,n,0,partialAns);
+
+        return ans;
+
+    }
+
+};