code and decode with prufer

#include<iostream>
#include<fstream>
#include<vector>
#include<queue>
#include<algorithm>
#include<functional>
using namespace std;

#define INF 999
#define max_size 10000

vector<int> g[max_size];
int n,m;
vector<pair<int,int>> aux; //keeps the rank and parent so it can be accessed
//easier than from the queue
vector<int> prufer_code;
priority_queue < pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> q;
vector<pair<int,int>> edges;
vector<int> code;
void read()
{
    ifstream in("code_file.txt");
    if (in.is_open())
    {
        in >> n >> m;
        int x, y, w;

        aux.assign(n+1,{0,-1});   //second is the parent
        for (int i = 0; i<m; i++)
        {
            in >> x >> y;
            aux[x].first++;
            aux[x].second=y;
            aux[y].first++;
            aux[y].second=x;
        }
        for(int i=1;i<aux.size();i++)
            q.push(aux[i]);
    }
    else
        cout << "Unable to open the file\n";

}

void decrease_rank(int parent)
{
    deque<pair<int, int>> deq;
    pair<int, int> pp;
    while (!q.empty())
    {
        pp = q.top();
        q.pop();
        deq.push_back(pp);
    }
    for (deque<pair<int, int>>::iterator it = deq.begin(); it != deq.end(); ++it)
        if ((*it).second == parent)
        {
            (*it).first--;
            break;
        }
    for (deque<pair<int, int>>::iterator it = deq.begin(); it != deq.end(); ++it)
        q.push(*it);
}
void prufer_code_()
{
    while (!q.empty())
    {
        pair<int, int> p = q.top();
        decrease_rank(p.second);
        q.pop();
        prufer_code.push_back(p.second);
    }
    prufer_code.erase(prufer_code.end()-1);
    prufer_code.erase(prufer_code.end()-1);
}
int find_minimum(vector<int> code)
{
    int minimum=1;
    while(find(code.begin(),code.end(),minimum)!=code.end())
        minimum++;
    return minimum;


}
void prufer_decode_()
{
    int u,v;
    int i=0;
    while(i<code.size()+1)
    {
        u=code[0];
        v=find_minimum(code);
        cout<<"minimum:"<<v<<endl;
        if(i!=code.size())
        {
            code.erase(code.begin());
            code.push_back(v);
            edges.push_back({u,v});
        }
        i++;
    }
    u=find_minimum(code);
    code.push_back(u);
    v=find_minimum(code);
    edges.push_back({u,v});

}
int main()
{
    read();
    prufer_code_();
    cout<<"prufer code:";
    for(int i=0;i<prufer_code.size();i++)
        cout<<prufer_code[i]<<" ";
    cout<<endl;
    code.push_back(1);
    code.push_back(1);
    code.push_back(5);

    prufer_decode_();
    cout<<"the egdes:\n";
    for(int i=0;i<edges.size();i++)
        cout<<edges[i].first<<"-"<<edges[i].second<<endl;


    return 0;
}