Prim (OWN)

//note : do not use INT_MAX for comparison,use a big number (i.e. : 999999) instead
//note : non-directed graph
#include<iostream>
using namespace std;

int vertex,edge,source;
int adjacency_matrix[100][100],weight_matrix[100][100];
int parent[100],cost[100],visited[100];

void inputGraph();
void Initialize_Single_Source();
int Extract_Min();
void Prim();
void printCostAndPath();

int main(void)
{
    inputGraph();
    Initialize_Single_Source();
    Prim();
    printCostAndPath();
    return 0;
}
void inputGraph()
{
    cout<<"Total vertex : ";
    cin>>vertex;
    cout<<"Total edge   : ";
    cin>>edge;
    int i,j;
    //make all weight infinity
    for(i=1; i<=vertex; i++)
    {
        for(j=1; j<=vertex; j++)
        {
            weight_matrix[i][j]=999999;
        }

    }
    // scan adjacency matrix and weight
    for(i=1; i<=edge; i++)
    {
        int start,finish;
        cout<<"Enter start and end node for edge "<<i<<" : ";
        cin>>start;
        cin>>finish;
        //non directed
        adjacency_matrix[start][finish]=1;
        adjacency_matrix[finish][start]=1;
        cout<<"Enter weight for edge "<<i<<" : ";
        int wt;
        cin>>wt;
        //non directed
        weight_matrix[start][finish]=wt;
        weight_matrix[finish][start]=wt;
    }
    cout<<endl<<"The adjacency matrix is : "<<endl<<endl;
    for(i=1; i<=vertex; i++)
    {
        for(j=1; j<=vertex; j++)
        {
            cout<<adjacency_matrix[i][j]<<" ";
        }
        cout<<endl;
    }
    cout<<endl<<"The weight matrix is : "<<endl<<endl;
    for(i=1; i<=vertex; i++)
    {
        for(j=1; j<=vertex; j++)
        {
            cout<<weight_matrix[i][j]<<" ";
        }
        cout<<endl;
    }
}
void Initialize_Single_Source()
{
    cout<<endl<<"Enter source : ";
    cin>>source;
    int i;
    for(i=1; i<=vertex; i++)
    {
        cost[i]=999999;
        parent[i]=0;
        //extra line
        visited[i]=0;
    }
    cost[source]=0;
    cout<<endl;
}
int Extract_Min()
{
    int minimumCost = 999999;
    int i=0,saveNode=0;
    for(i=1; i<=vertex; i++)
    {
        if(visited[i]==0)
        {
            if(cost[i]<minimumCost)
            {
                minimumCost=cost[i];
                saveNode=i;
            }
        }
    }
    visited[saveNode]=1;
    return saveNode;
}
void relax(int u,int v)
{
    if( cost[v]> (cost[u]+weight_matrix[u][v]))
    {
        cost[v]=(cost[u]+weight_matrix[u][v]);
        parent[v]=u;
    }
}
void Prim()
{
    int i,j,totalVertex=1;
    while(totalVertex<=vertex)
    {
        int minCost = Extract_Min();
        for(j=1; j<=vertex; j++)
        {
            if(adjacency_matrix[minCost][j]==1)
            {
                if(visited[j]==0)
                {
                    if(weight_matrix[minCost][j]<cost[j])
                    {
                        parent[j]=minCost;
                        cost[j]=weight_matrix[minCost][j];
                    }
                }
            }
        }
        totalVertex++;
    }
}

void printCostAndPath()
{
    cout<<endl<<"Safe Edges and Weights : "<<endl<<endl;
    int i,totalMincost=0;
    for(i=1; i<=vertex; i++)
    {
        //cout<<"For node "<<i<<" : "<<endl;
        //cout<<"Cost : "<<cost[i]<<endl;


        //cout<<"Path : End <- "<<i<<" <- ";
        int l = parent[i];
        while(true)
        {
            if(l==source||l==0)
            {
                if(l==source)
                {
                    //cout<<l<<" <- ";
                }
                break;
            }
            else
            {
                //cout<<l<<" <- ";
                l=parent[l];
            }
        }
        //cout<<" Start"<<endl;
        if(i!=source)
        {
            cout<<"Edge : ("<<i<<","<<parent[i]<<") \t Weight : "<<cost[i]<<endl<<endl;
        }
        totalMincost=totalMincost+cost[i];
    }
    /*
    //for minimum cost
    int minCost = 999999;
    int nodeSaver;
    for(i=1; i<=vertex; i++)
    {
        // do not count if it is source node
        if(i!=source)
        {
            if(cost[i]<minCost)
            {
                minCost=cost[i];
                nodeSaver=i;
            }
        }
    }
    cout<<"From source node the minimum cost (without source node) is : "<<endl;
    cout<<"Node number : "<<nodeSaver<<endl;
    cout<<"Cost : "<<minCost<<endl;
    cout<<"Path : End <- "<<nodeSaver<<" <- ";
    int l = parent[nodeSaver];
    while(true)
    {
        if(l==source||l==0)
        {
            if(l==source)
            {
                cout<<l<<" <- ";
                break;
            }
        }
        else
        {
            cout<<l<<" <- ";
            l=parent[l];
        }
    }
    cout<<" Start"<<endl;
    */
    cout<<endl<<"Total minimum weight : "<<totalMincost<<endl;
}