From 632a5fa32b5b8c2c983ed84c97da9c7f61518cfb Mon Sep 17 00:00:00 2001
From: Ilim Ugur <ilimugur@gmail.com>
Date: Wed, 2 Oct 2019 15:13:58 +0300
Subject: [PATCH] Add Prim's MST algorithm.

---
 graph/c++/primMST.cpp | 92 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 92 insertions(+)
 create mode 100644 graph/c++/primMST.cpp

diff --git a/graph/c++/primMST.cpp b/graph/c++/primMST.cpp
new file mode 100644
index 0000000..1014b64
--- /dev/null
+++ b/graph/c++/primMST.cpp
@@ -0,0 +1,92 @@
+#include<bits/stdc++.h>
+
+using namespace std;
+
+
+class UndirectedGraph
+{
+    typedef vector< vector < pair<int, long long> > > AdjList;
+
+    int V;    // Number of vertices
+  
+    AdjList adjList;
+public:
+    UndirectedGraph(int V);
+
+    void addEdge(int u, int v, long long w);
+
+    // Finds the shortest path from source to destination
+    UndirectedGraph primMinimumSpanningTree();
+};
+
+UndirectedGraph::UndirectedGraph(int n) : adjList(n), V(n)
+{
+}
+ 
+void UndirectedGraph::addEdge(int u, int v, long long w)
+{
+    adjList[u].emplace_back(v, w);
+    adjList[v].emplace_back(u, w);
+}
+  
+UndirectedGraph UndirectedGraph::primMinimumSpanningTree()
+{
+    set<int> included;
+    set< pair<long long, pair<int, int> > > pq;
+
+    int startIndex = 0; // Can be any valid vertex index
+    included.insert(startIndex);
+    for(int i=0; i < adjList[startIndex].size(); ++i)
+    {
+        int v = adjList[startIndex][i].first;
+        long long vWeight = adjList[startIndex][i].second;
+        pq.insert( make_pair(vWeight, make_pair(startIndex, v)) );
+    }
+
+    UndirectedGraph result(V);
+
+    int leftToConnect = V - 1;
+    while(!pq.empty() && leftToConnect > 0)
+    {
+        set< pair<long long, pair<int, int> > >::iterator it = pq.begin();
+        long long vWeight = it->first;
+        int u = it->second.first;
+        int v = it->second.second;
+        pq.erase(it);
+
+        if(included.find(v) == included.end())
+        {
+            result.addEdge(u, v, vWeight);
+            cout << "Added edge (" << u << ", " << v << ") with weight: " << vWeight << endl;
+
+            for(int i=0; i < adjList[v].size(); ++i)
+            {
+                int w = adjList[v][i].first;
+                long long wWeight = adjList[v][i].second;
+
+                pq.insert( make_pair(wWeight, make_pair(v, w)) );
+            }
+
+            --leftToConnect;
+            included.insert(v);
+        }
+    }
+
+    return result;
+}
+
+// Driver program to test methods of graph class
+int main()
+{
+    // Create a graph given in the above diagram
+    UndirectedGraph g(5);
+    g.addEdge(0, 1, 3LL);
+    g.addEdge(1, 3, 6LL);
+    g.addEdge(3, 4, 2LL);
+    g.addEdge(1, 2, 4LL);
+    g.addEdge(2, 3, 1LL);
+
+    UndirectedGraph mst = g.primMinimumSpanningTree();
+
+    return 0;
+}