chore(CPlusPlus): add prim's graph algorithm (#816)

Co-authored-by: angshudas <offangshudas123@gmail.com>
Co-authored-by: Ming Tsai <37890026+ming-tsai@users.noreply.github.com>

algorithms/CPlusPlus/Graphs/prim's_algorithm.cpp

@@ -0,0 +1,96 @@
+/*
+  PREREQUISITE --> 
+    1. GRAPH
+    2. PRIORITY QUEUE
+*/
+
+#include<bits/stdc++.h>
+using namespace std;
+
+vector<vector<pair<int,int>>> graph;
+vector<bool> vis;
+
+int primAlgorithm(){
+  int totalCost = 0;
+  // totalCost will store the minimum spanning tree 
+  set<pair<int,int>> pq; 
+  /*
+    here pq -> priority queue ( it sorts all elements )
+    it takes two value 
+      1. weight 
+      2. vertex
+
+    Here, priority queue will be sorted according to weight     
+  */
+
+
+  pq.insert({0,1});
+  /*
+    initialising the priority queue with {0,1}
+    Since, vertex 1 is the first vertex so we don't have to travel through a
+    edge to reach vertex 1
+  */
+
+  while( !pq.empty() ){
+    // taking the values of first elements from priority queue
+    int wt = (*pq.begin()).first; // weight of first vertex in priority queue
+    int v = (*pq.begin()).second; // first vertex
+    pq.erase(pq.begin());
+
+    if( vis[v] ) continue;
+    // if the vertex 'v' is visited then continue and don't proceed
+    vis[v] = true;
+    totalCost += wt;
+    // if the vertex is not visited then mark it visited
+    // and add the weight to total cost
+
+
+    // traverse all the child of vertex 'v'
+    for( auto elem : graph[v] ){
+      
+      if( vis[elem.first] ) continue;
+
+      // if child is visited then don't insert in priority queue
+      // else insert in priority queue
+      pq.insert({elem.second,elem.first});
+    }
+  }
+
+  graph.clear(); // clearing all values in graph
+  return totalCost;
+}
+
+int main()
+{
+  int n,e; cin>>n>>e;
+  // n -> number of vertex in graph
+  // e -> number of edges in graph
+
+  // initialising the graph
+  graph = vector<vector<pair<int,int>>> (n+1);
+
+  // initialising the visited vector to false 
+  // it represent if the vertex is visited or not
+  vis = vector<bool>(n+1,false);
+
+
+  // taking the input of 'e' edges
+  for(int i=0; i<e; i++)
+  {
+    int a,b,wt; cin>>a>>b>>wt;
+    /*
+      a,b -> vertexs of graph
+      wt -> weight of edge between vertex 'a' and 'b'
+    */
+
+    graph[a].push_back({b,wt});
+    graph[b].push_back({a,wt});
+    // it creates adjcency list by pushing all
+    // the vertexs(with weight) which are directly connected by edges.
+    
+  }
+
+  cout<<primAlgorithm();
+    
+  return 0;
+}

algorithms/CPlusPlus/README.md

@@ -53,6 +53,7 @@
 - [Connected Components](Graphs/total-connected-components.cpp)
 - [Dijkstra's Algorithm](Graphs/dijkstra.cpp)
 - [Cycle Detection](Graphs/cycle-detection.cpp)
+- [Prim's Algorithm](Graphs/prim's_algorithm.cpp)
 - [Floyd Warshall](Graphs/floyd-warshall.cpp)
 
 ## Multiplication