Answers for "kruskal algorithm time complexity"

kruskal algorithm time complexity

Time complexity:- O(ElogV)

kruskal's algorithm

#include<bits/stdc++.h>

using namespace std;

int  main()
{
	int n = 9;
	
	int mat[9][9] = {
	{100,4,100,100,100,100,100,8,100},
	{4,100,8,100,100,100,100,100,100},
	{100,8,100,7,100,4,100,100,2},
	{100,100,7,100,9,14,100,100,100},
	{100,100,100,9,100,10,100,100,100},
	{100,100,4,14,10,100,2,100,100},
	{100,100,100,100,100,2,100,1,6},
	{8,100,100,100,100,100,1,100,7},
	{100,100,2,100,100,100,6,7,100}};
	
	int parent[n];
	
	int edges[100][3];
	int count = 0;
	
	for(int i=0;i<n;i++)
		for(int j=i;j<n;j++)
		{
			if(mat[i][j] != 100)
			{
				edges[count][0] = i;
				edges[count][1] = j;
				edges[count++][2] = mat[i][j];	
			}		
		}

	for(int i=0;i<count-1;i++)
		for(int j=0;j<count-i-1;j++)
			if(edges[j][2] > edges[j+1][2])
				{
					int t1=edges[j][0], t2=edges[j][1], t3=edges[j][2];
					
					edges[j][0] = edges[j+1][0];
					edges[j][1] = edges[j+1][1];
					edges[j][2] = edges[j+1][2];
					
					edges[j+1][0] = t1;
					edges[j+1][1] = t2;
					edges[j+1][2] = t3;
				}
				
	int mst[n-1][2];
	int mstVal = 0;
	int l = 0;
	
	cout<<endl;
	
	for(int i=0;i<n;i++)
		parent[i] = -1;
	cout<<endl;
				
	for(int i=0;i<count;i++)
	{
		if((parent[edges[i][0]] == -1 && parent[edges[i][1]] == -1))
		{
			parent[edges[i][0]] = edges[i][0];
			parent[edges[i][1]] = edges[i][0];
			
			mst[l][0] = edges[i][0];
			mst[l++][1] = edges[i][1];
			
			mstVal += edges[i][2];
		}
		
		else if((parent[edges[i][0]] == -1 && parent[edges[i][1]] != -1))
		{
			parent[edges[i][0]] = parent[edges[i][1]];
			
			mst[l][0] = edges[i][1];
			mst[l++][1] = edges[i][0];
			
			mstVal += edges[i][2];
		}
		
		else if((parent[edges[i][0]] != -1 && parent[edges[i][1]] == -1))
		{
			parent[edges[i][1]] = parent[edges[i][0]];
			
			mst[l][0] = edges[i][0];
			mst[l++][1] = edges[i][1];
			
			mstVal += edges[i][2];
		}
		
		else if(parent[edges[i][0]] != -1 && parent[edges[i][1]] != -1 && parent[edges[i][0]] != parent[edges[i][1]])
		{
			int p = parent[edges[i][1]];
			for(int j=0;j<n;j++)
				if(parent[j] == p)
					parent[j] = parent[edges[i][0]];
			
			mst[l][0] = edges[i][0];
			mst[l++][1] = edges[i][1];
			
			mstVal += edges[i][2];
		}
	}
	
	for(int i=0;i<l;i++)
		cout<<mst[i][0]<<" -> "<<mst[i][1]<<endl;
	
	cout<<endl;
	cout<<mstVal<<endl;
		
	return(0);
}

kruskal's algorithm

//MINIMUM SPANNING TREE USING KRUSHKAL ALGORITHM
#include<bits/stdc++.h>
using namespace std;
struct node
{
    int u,v,wt;
    node(int first,int second, int weight)
    {
        u=first;
        v=second;
        wt=weight;
    }
};
bool cmp(node a,node b)
{
    return (a.wt<b.wt);
}
int findpar(int u,vector<int>&parent)
{
    if(u==parent[u])
    {
        return u;
    }
    return findpar(parent[u],parent);
}
void unionoperation(int u,int v,vector<int>&parent,vector<int>&rank)
{
    u=findpar(u,parent);
    v=findpar(v,parent);
    if(rank[u]<rank[v])
    {
        parent[u]=v;
    }
    else if(rank[v]<rank[u])
    {
        parent[v]=u;
    }
    else
    {
        parent[v]=u;
        rank[u]++;
    }
}
int main()
{
    int vertex,ed;
    cout<<"Enter the number of vertex and edges:"<<endl;
    cin>>vertex>>ed;
    vector<node>edges;
     cout<<"enter the links and weight:"<<endl;
    for(int i=0;i<ed;i++)
    {
        int u,v,wt;
        cin>>u>>v>>wt;
        edges.push_back(node(u,v,wt));
    }
    sort(edges.begin(),edges.end(),cmp);
    vector<int>parent(vertex);
    for(int i=0;i<vertex;i++)
    {
        parent[i]=i;
    }
    vector<int>rank(vertex,0);
    int cost=0;
    vector<pair<int,int>>mst;
    for(auto i:edges)
    {
        if(findpar(i.u,parent)!=findpar(i.v,parent))
        {
            cost+=i.wt;
            mst.push_back(make_pair(i.u,i.v));
            unionoperation(i.u,i.v,parent,rank);
        }
    }
    cout<<cost<<endl;
    for(auto i:mst)
    {
        cout<<i.first<<"-"<<i.second<<endl;
    }
    return 0;
}