Cycle_of_Edges.cpp

#include <bits/stdc++.h>
using namespace std;

const int N = 1e5 + 5;
int parent[N];
int group_size[N];

void dsu_initialize(int n)
{
    for (int i = 0; i < n; i++)
    {
        parent[i] = -1;
        group_size[i] = 1;
    }
}

int dsu_find(int node)
{
    if (parent[node] == -1)
        return node;
    int leader = dsu_find(parent[node]);
    parent[node] = leader;
    return leader;
}

void dsu_union_by_size(int node1, int node2)
{
    int leaderA = dsu_find(node1);
    int leaderB = dsu_find(node2);
    if (leaderA != leaderB)
    {
        if (group_size[leaderA] > group_size[leaderB])
        {
            parent[leaderB] = leaderA;
            group_size[leaderA] += group_size[leaderB];
        }
        else
        {
            parent[leaderA] = leaderB;
            group_size[leaderB] += group_size[leaderA];
        }
    }
}

int main()
{
    int n, e;
    cin >> n >> e;
    dsu_initialize(n + 1);

    int cycleEdgeCount = 0;

    while (e--)
    {
        int a, b;
        cin >> a >> b;

        int leaderA = dsu_find(a);
        int leaderB = dsu_find(b);

        if (leaderA == leaderB)
        {
            cycleEdgeCount++;
        }
        else
        {
            dsu_union_by_size(a, b);
        }
    }

    cout << cycleEdgeCount << endl;

    return 0;
}