From 4d12b9886e884c69b7d30b30fcedeaf818246302 Mon Sep 17 00:00:00 2001
From: Shrey Gupta <75122294+Shreygupta2002@users.noreply.github.com>
Date: Sat, 7 Oct 2023 13:35:34 +0530
Subject: [PATCH] Added Kruskal Algorithm

Please add Hacktober Fest Tag
---
 c++/kruskal.cpp | 107 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 107 insertions(+)
 create mode 100644 c++/kruskal.cpp

diff --git a/c++/kruskal.cpp b/c++/kruskal.cpp
new file mode 100644
index 0000000..0e6a0c0
--- /dev/null
+++ b/c++/kruskal.cpp
@@ -0,0 +1,107 @@
+#include<bits/stdc++.h>
+using namespace std;
+typedef long long int ll;
+const int N=1e5;
+class DSU
+{
+public:
+	int parent[N+1];
+	int Rank[N+1];
+	DSU(int n)
+	{
+		for(int i=1;i<=n;i++)
+		{
+			parent[i]=i;
+			Rank[i]=0;
+		}
+	}
+	int findPar(int node)
+	{
+		if(node==parent[node])
+			return node;
+		else return parent[node] = findPar(parent[node]);
+	}
+	void Union(int u, int v)
+	{
+		u=findPar(u);
+		v=findPar(v);
+		if(u!=v)
+		{
+			if(Rank[u]<Rank[v])
+			{
+				parent[u]=v;
+			}	
+			else if(Rank[u]>Rank[v])
+			{
+				parent[v]=u;
+			}
+			else
+			{
+				parent[v]=u;
+				Rank[u]++;
+			}
+		}
+	}	
+};
+bool cmp(pair<pair<int,int>,int> p1, pair<pair<int,int>,int> p2)
+{
+	return p1.second<p2.second;
+}
+int main()
+{
+    ios::sync_with_stdio(0);cin.tie(0);
+    mt19937 rng((unsigned int) chrono::steady_clock::now().time_since_epoch().count());
+    auto start=chrono::high_resolution_clock::now();
+    
+    //code here
+   	int vertices, edges;
+   	cin>>vertices>>edges;
+   	pair<pair<int,int>,int> graph[edges];
+   	for(int i=0;i<edges;i++)
+   	{
+   		int u, v, w;
+   		cin>>u>>v>>w;
+   		graph[i]={{u,v},w};
+   	}
+   	sort(graph,graph+edges,cmp);
+   	DSU d(vertices);
+   	int cnt=0;
+   	int cost=0;
+   	vector<pair<pair<int,int>,int>> ans;
+   	for(int i=0;i<edges;i++)
+   	{
+   		if(cnt==vertices-1)
+   		{
+   			break;
+   		}
+   		int u, v, w;
+   		u=graph[i].first.first;
+   		v=graph[i].first.second;
+   		w=graph[i].second;
+   		if(d.findPar(u)==d.findPar(v))
+   		{
+   			continue;
+   		}	
+   		ans.push_back({{u,v},w});
+   		cnt++;
+   		cost+=w;
+   		d.Union(u,v);
+   	}
+   	cout<<"Minimum Cost of the MST is  = "<<cost<<endl;
+   	cout<<"MST is as follows :--"<<endl;
+   	for(int i=0;i<ans.size();i++)
+   	{
+   		int u, v, w;
+   		u=ans[i].first.first;
+   		v=ans[i].first.second;
+   		w=ans[i].second;
+   		cout<<u<<"----"<<v<<" == "<<w<<endl;
+   	}
+
+
+
+
+    auto stop=chrono::high_resolution_clock::now();
+    auto duration=chrono::duration_cast<chrono::microseconds>(stop-start);
+    cerr<<duration.count()/1000.0<<" ms\n";
+}
\ No newline at end of file