From 20f2c97aad056132bc8abb1666a0587405ab0dd2 Mon Sep 17 00:00:00 2001
From: Haripriya <93302077+Haripriya-1212@users.noreply.github.com>
Date: Fri, 6 Oct 2023 10:40:52 +0530
Subject: [PATCH] Create nQueens.cpp

n queens problem with steps
---
 backtracking/nQueens.cpp | 124 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 124 insertions(+)
 create mode 100644 backtracking/nQueens.cpp

diff --git a/backtracking/nQueens.cpp b/backtracking/nQueens.cpp
new file mode 100644
index 000000000..01b6a3326
--- /dev/null
+++ b/backtracking/nQueens.cpp
@@ -0,0 +1,124 @@
+#include<iostream>
+using namespace std;
+
+bool isSafe(int arr[][4],int x,int y,int n){
+
+    // in column
+    for(int i=0;i<n;i++){
+        if(arr[i][y]==1){
+            return false;
+        }
+    }
+    // in row
+    for(int j=0;j<n;j++){
+        if(arr[x][j]==1){
+            return false;
+        }
+    }
+
+    int row = x;
+    int col = y;
+    
+    //left diagonal
+    while(row>=0 && col>=0){
+        if(arr[row][col]==1){
+            return false;
+        }
+        row--;
+        col--;
+    }
+    
+    row = x;
+    col = y;
+    
+    
+    // right diagonal
+    while(row>=0 && col<n){
+        if(arr[row][col]==1){
+            return false;
+        }
+        row--;
+        col++;
+    }
+
+    return true;
+}
+
+void printMatrix(int arr[][4],int n){
+    for(int i=0;i<n;i++){
+        for(int j=0;j<n;j++){
+            if(arr[i][j] == 0)
+                cout<<"_"<<" ";
+            else
+                cout<<"Q"<<" ";
+        }
+        cout<<endl;
+    }
+    cout<<endl;
+}
+
+// row = starting row
+bool nQueen(int arr[][4],int n,int row){
+
+    // base case = if row > n ==> done
+    if(row>=n){
+        return true;
+    }
+    
+    // columns - elements in a particular row
+    for(int j=0;j<n;j++){
+        for(int k=0;k<n;k++){
+            arr[row][k]=0;
+        }
+        if(isSafe(arr,row,j,n)){
+            arr[row][j]=1;
+            
+            printMatrix(arr,n);
+
+            if(nQueen(arr,n,row+1)){
+                return true;
+            }
+
+            arr[n][j]=0;   // backtracking
+        }
+    }
+
+    return false;
+}
+
+
+
+int main(){
+
+    int n = 4;
+
+    int arr[4][4];
+
+    // initializing all to 0
+    for(int i=0;i<n;i++){
+        for(int j=0;j<n;j++){
+            arr[i][j]=0;
+        }
+    }
+    cout<<"\nSTEPS : \n";
+    printMatrix(arr,n);
+
+    for(int i=0;i<n;i++){
+        // giving starting row i
+        bool ans = nQueen(arr,n,i);
+
+        if(ans){
+            cout<<"\nSolution : \n\n";
+            printMatrix(arr,n);
+            break;
+        }
+        else{
+            cout<<"Solution doesn't exist\n";
+            printMatrix(arr,n);
+            cout<<endl<<endl;
+            break;
+        }
+
+    }
+    return 0;
+}