Implementation of Prim's Algorithm using STL set in c++

PrimsAlgo.cpp

//
// Created by Harsh Vardhan Kumar on 29-01-2018.
//

#include <iostream>
#include <set>
#include <vector>
#define inf 1000000 ;
#define nil -1000000

using namespace std ;

class node {
public:
    int parent; int key; int node_val ;
    bool operator < (const node & node2) const {
        if(this->key < node2.key) return this->key<node2.key ;
        else if(this->key == node2.key) return this->node_val<node2.node_val ;
        else return this->key < node2.key && this->node_val < node2.node_val ;
        //else return this->key < node2.key && this->node_val > node2.node_val ;
    }
    node(int parentv, int keyv, int node_valv) {
        parent = parentv ;
        key = keyv ;
        node_val = node_valv ;
    }
    node() {}
};

int main() {
    multiset <node> Q ;
    vector<vector<pair<int, int> > >  adList ;
    int no_nodes ; cin>>no_nodes ;
    char nod[no_nodes] ;
    char nodeval = 'a'-1 ;
    for(int i = 0 ; i<no_nodes; i++) {
        nodeval++ ;
        nod[i] = nodeval ;
    }
    node nodes[no_nodes] ;
    for(int i = 0 ; i<no_nodes; i++) {
        vector<pair<int, int> > v ;
        adList.push_back(v) ;
        node s(-1000000,1000000+i, i) ;
        nodes[i] = s ;
    }

    int w ;
    for(int i = 0 ; i<no_nodes; i++) {
        for(int j = 0 ; j<no_nodes; j++) {
            cin>>w ;
            if(w !=  100) {
                adList[i].emplace_back(make_pair(j, w)) ;
            }
        }
    }

    int source; cin>>source ;
    nodes[source].key = 0 ;

    for(int i = 0 ; i<no_nodes; i++) {
        Q.insert(nodes[i]) ;
    }

    while(!Q.empty()) {
        node u  = *Q.begin();
        //cout<<"node popped is "<<nod[u.node_val]<<endl ;
        int u_index = u.node_val ;
        // print the queue
        nodes[u_index] = u ;
        Q.erase(nodes[u_index]) ;

        for(pair<int, int> p : adList[u_index]) {
            node v = nodes[p.first] ;
            if(Q.count(v)>0 && p.second<v.key) {
                //cout<<nod[v.node_val]<<" is found with a keyvalue of "<<v.key<<endl ;
                Q.erase(v) ;

                v.parent = u_index ;
                v.key = p.second ;
                nodes[v.node_val] = v ;
                Q.insert(v) ;

                //cout<<"the new key value is "<<v.key<<" and the parent is "<<v.parent<<endl<<endl ;
            }
        }
    }

    // now print the values in the nodes array
    int weight = 0 ;
    for(node n : nodes) {
        if(n.parent>=0)
            cout<<nod[n.node_val]<<" -- "<<nod[n.parent]<<" "<<endl ;
        else cout<<nod[n.node_val]<<" -- "<<"Nil "<<endl;
        weight+=n.key ;
    }

    cout<<"The total weight is "<<weight<<endl ;
}