96 lines
2.2 KiB
C++
96 lines
2.2 KiB
C++
|
/*
|
||
|
|
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;
|
||
|
|
}
|