From 3f5e08a48b6c62072e2a8bc00e7f33151e9f894d Mon Sep 17 00:00:00 2001
From: Shrey Gupta <75122294+Shreygupta2002@users.noreply.github.com>
Date: Sat, 7 Oct 2023 13:43:06 +0530
Subject: [PATCH] Added Prims Algorithm

---
 c++/prims.cpp | 64 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 64 insertions(+)
 create mode 100644 c++/prims.cpp

diff --git a/c++/prims.cpp b/c++/prims.cpp
new file mode 100644
index 0000000..9a0e5e4
--- /dev/null
+++ b/c++/prims.cpp
@@ -0,0 +1,64 @@
+#include<bits/stdc++.h>
+using namespace std;
+typedef long long int ll;
+int INF = 1e9;
+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;
+    vector<pair<int,int>> graph[vertices+1];
+    for(int i=0;i<edges;i++)
+    {
+    	int u, v, w;
+    	cin>>u>>v>>w;
+    	graph[u].push_back({v,w});
+    	graph[v].push_back({u,w});
+    }
+    int parent[vertices+1];
+    int key[vertices+1];
+    bool mst[vertices+1];
+    for(int i=1;i<=vertices;i++)
+    {
+    	key[i]=INF;
+    	mst[i]=false;
+    	parent[i]=-1;
+    }
+
+    priority_queue<pair<int,int>,vector<pair<int,int>>, greater<pair<int,int>> > pq;
+    key[1]=0;
+    pq.push({0,1});
+    for(int i=0;i<vertices-1;i++)
+    {
+    	int u=pq.top().second;
+    	pq.pop();
+    	mst[u]=true;
+    	for(auto it:graph[u])
+    	{
+    		int v=it.first;
+    		int w=it.second;
+    		if(mst[v]==false && w<key[v])
+    		{
+    			key[v]=w;
+    			parent[v]=u;
+    			pq.push({key[v],v});
+    		}
+    	}
+    }
+    
+   	cout<<"MST is as follows :--"<<endl;
+   	for(int i=2;i<=vertices;i++)
+   	{
+   		cout<<parent[i]<<"---"<<i<<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