From 0bbfbb60c1b6b3c060d464be0acb848be87e006e Mon Sep 17 00:00:00 2001
From: perfectdash <116922021+perfectdash@users.noreply.github.com>
Date: Sat, 28 Oct 2023 11:14:29 +0530
Subject: [PATCH] Added  Cycle_detection_using_DSU.cpp

Cycle_detection_using_DSU
---
 Coding/C++/Cycle_detection_using_D.cpp | 83 ++++++++++++++++++++++++++
 1 file changed, 83 insertions(+)
 create mode 100644 Coding/C++/Cycle_detection_using_D.cpp

diff --git a/Coding/C++/Cycle_detection_using_D.cpp b/Coding/C++/Cycle_detection_using_D.cpp
new file mode 100644
index 00000000..0eed7c7a
--- /dev/null
+++ b/Coding/C++/Cycle_detection_using_D.cpp
@@ -0,0 +1,83 @@
+#include <bits/stdc++.h>
+using namespace std;
+ 
+using ll = long long ;
+
+// DSU -> cycle detection in unidirected graphs (krukshal algorithm)
+// implementing a data structure that will operate over disjoint sets
+// main focus will be on union and find functions 
+// intial complexity = O(n) ;
+// final after some optimisations =O(1);
+
+// path compression optimisation -->find function 
+// union by rank optimisation  ---->union function
+
+class graph{
+     ll V;
+     list <pair<ll,ll>> l;
+     public : 
+     graph(ll V){
+        this->V=V;
+     } 
+
+     void merge(ll u,ll v){
+        l.push_back(make_pair(u,v));
+     }
+
+     ll leader(ll i,vector<ll>& parent){
+        if(parent[i]==-1){
+            return i;
+        }
+        return parent[i]=leader(parent[i],parent);
+     }
+     
+     void union_set(ll x,ll y,vector<ll>& parent){
+         ll s1 = leader(x,parent);
+         ll s2 = leader(y,parent);
+         if(s1!=s2){
+            parent[s2]=s1;
+         }
+     }
+     
+     bool cycle_detection(){
+          vector<ll> parent(V);
+          for(int i=0;i<V;i++){
+             parent[i]=-1;
+          } 
+          for(auto i: l){
+             ll x = leader(i.first,parent);
+             ll y = leader(i.second,parent);
+             if(x!=y){
+                union_set(i.first,i.second,parent);
+             }else{
+                return true;
+             }
+          }
+          parent.clear();
+          return false;
+     }
+       
+};
+
+
+
+int main(){
+
+   int t; cin>>t;
+   while(t--){
+      ll n;cin>>n; 
+      graph p(n);ll flag=1;
+      vector<int> cnt(n);
+      for(int i=0;i<n;i++ ){
+         int a,b;cin>>a>>b;
+         a--; b--;
+         p.merge(a,b);
+         cnt[a]++; cnt[b]++; 
+         if(cnt[a]>=3|| cnt[b]>=3){
+            flag=0;
+            
+         }
+      }
+   }
+}
+