Find Connected Component in Disjoint Set

#include <bits/stdc++.h>
using namespace std;
#define N_VERTICES 1000

class DisjointSet {
    int p[N_VERTICES];

  public:
    void make_set(int x) {
        p[x] = x;
    }

    int find_set(int x) {
        while (x != p[x]) {
            x = p[x];
        }
        return x;
    }

    void union_set(int x, int y) {
        int a = find_set(x);
        int b = find_set(y);
        p[a] = b;
    }

    bool same_set(int x, int y) {
        if (find_set(x) == find_set(y)) {
            return true;
        }
        return false;
    }
};


class Graph {
  public:
    int mat[N_VERTICES][N_VERTICES];

    void init_graph() {
        for (int i = 0; i < N_VERTICES; i++) {
            for (int j = 0; j < N_VERTICES; j++) {
                mat[i][j] = 0;
            }
        }
    }

    void add_edge(int u, int v) {
        mat[u][v] = 1;
        mat[v][u] = 1;
    }

    DisjointSet connected_component(int n) {
        DisjointSet S;
        for (int i = 0; i < n; i++) {
            S.make_set(i);
        }

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (mat[i][j]) {
                    if (S.find_set(i) != S.find_set(j)) {
                        S.union_set(i, j);
                    }
                }
            }
        }
        return S;
    }
};


int main() {
    Graph G;
    G.init_graph();

    int v, e;
    cin >> v >> e;

    for (int i = 0; i < e; i++) {
        int u, v;
        cin >> u >> v;
        G.add_edge(u, v);
    }

    DisjointSet ds = G.connected_component(v);

    set<int> st;
    for (int i = 0; i < v; i++) {
        st.insert(ds.find_set(i));
    }
    cout << st.size() << endl;
}


/*
Input:

4
3
0 1
2 3
3 2

3
3
0 1
1 2
2 0

*/