Add Prim's algorithm for minimum spanning tree

Author: OmarBazaraa

README.md

@@ -62,7 +62,7 @@ A brief explanation to each of the following topics will be added soon, hopefull
 - [Floyd Warshal's Algorithm](https://github.com/OmarBazaraa/Competitive-Programming/blob/master/graphs/shortest_path/floyd_warshal.cpp)
 - [Minimum Spanning Tree](https://github.com/OmarBazaraa/Competitive-Programming/tree/master/graphs/minimum_spanning_tree)
 - [Kruskal's Algorithm](https://github.com/OmarBazaraa/Competitive-Programming/blob/master/graphs/minimum_spanning_tree/kruskal.cpp)
-- Prim's Algorithm **<i>(comming soon)</i>**
+- [Prim's Algorithm](https://github.com/OmarBazaraa/Competitive-Programming/blob/master/graphs/minimum_spanning_tree/prim.cpp)
 - [Strongly Connected Components (SCC)](https://github.com/OmarBazaraa/Competitive-Programming/tree/master/graphs/strongly_connected_components)
 - [Kosaraju's Algorithm](https://github.com/OmarBazaraa/Competitive-Programming/blob/master/graphs/strongly_connected_components/kosaraju.cpp)
 - [Lowest Common Ancestor (LCA)](https://github.com/OmarBazaraa/Competitive-Programming/tree/master/graphs/lowest_common_ancestor)

graphs/minimum_spanning_tree/prim.cpp

@@ -0,0 +1,67 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+const int N = 100100;
+
+
+// Struct holds all needed information about the edges
+// with comparison operator defined for the priority queue sorting.
+struct edge {
+ int to, weight, weightSum;
+
+ edge() {}
+ edge(int t, int w, int s = 0) : to(t), weight(w), weightSum(s) {}
+
+ // Note that we are actually implementing the greater than operator (not the less than operator)
+ // as the priority queue is implemented as max heap.
+ bool operator<(const edge& rhs) const {
+ return weightSum > rhs.weightSum;
+ }
+};
+
+int n, m;
+bool vis[N];
+vector<edge> edges[N];
+
+// Returns the total weight of the minimum spanning tree of the given weighted graph.
+// O(n.log(n))
+void primMST() {
+ priority_queue<edge> q;
+ q.push(edge(src, 0));
+
+ int MST = 0;
+
+ while (!q.empty()) {
+ int u = q.top().to;
+ int w = q.top().weight;
+ int s = q.top().weightSum;
+ q.pop();
+
+ if (vis[u]++) {
+ continue;
+ }
+
+ MST += w;
+
+ for (edge& e : edges[u]) {
+ if (!vis[e.to]) {
+ q.push(edge(e.to, e.weight, s + e.weight));
+ }
+ }
+ }
+
+ return MST;
+}
+
+// Reads a weighted undirected graph.
+void read() {
+ cin >> n >> m;
+
+ while (m--) {
+ int u, v, w;
+ scanf("%d %d %d", &u, &v, &w);
+ edges[u].push_back(edge(v, w));
+ edges[v].push_back(edge(u, w));
+ }
+}