Added Prims Algorithm

Implemented Prims Algorithm in cpp using priority Queue For Implicit Graphs.

Author: amarks444

Prims.cpp

@@ -0,0 +1,64 @@
+#include <bits/stdc++.h>
+using namespace std;
+#define ll long long int
+#define pb push_back
+#define mp make_pair
+#define f first
+#define s second
+#define mod 1000000007
+#define iAmInevitable ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
+//map<ll,ll> freq;
+//map<ll,ll> :: iterator itr;
+//for(itr=freq.begin();itr!=freq.end();itr++)
+//itr->f itr->s
+
+const int MAX = 1e6+ 5;
+typedef pair<ll, ll> PII;
+bool marked[MAX];
+vector <PII> adj[MAX];
+
+ll prim(int x)
+{
+ priority_queue<PII, vector<PII>, greater<PII> > Q; // For creating minHeap
+ ll y;
+ ll minimumCost = 0;
+ PII p;
+ Q.push(make_pair(0, x));
+ while(!Q.empty())
+ {
+ // Select the edge with minimum weight
+ p = Q.top();
+ Q.pop();
+ x = p.second;
+ // Checking for cycle
+ if(marked[x] == true)
+ continue;
+ minimumCost += p.first; //adding Edge Weight
+ marked[x] = true;
+ for(ll i = 0;i < adj[x].size();++i)
+ {
+ y = adj[x][i].second;
+ if(marked[y] == false)
+ Q.push(adj[x][i]);
+ }
+ }
+ return minimumCost;
+}
+
+int main()
+{
+ int nodes, edges, x, y;
+ long long weight, minimumCost;
+ cin >> nodes >> edges;
+ for(int i = 0;i < edges;++i)
+ {
+ cin >> x >> y >> weight;
+ adj[x].push_back(make_pair(weight, y));
+ adj[y].push_back(make_pair(weight, x));
+ }
+ // Selecting 1 as the starting node
+ minimumCost = prim(1);
+ cout << minimumCost << endl;
+ return 0;
+}
+//This Code is Contributed by Amar Shankar