find the graph is minimal spanig tree or not

1#include <iostream>
2#include <vector>
3#include <utility>
4#include <algorithm>
5
6using namespace std;
7const int MAX = 1e4 + 5;
8int id[MAX], nodes, edges;
9pair <long long, pair<int, int> > p[MAX];
10
11void initialize()
12{
13    for(int i = 0;i < MAX;++i)
14        id[i] = i;
15}
16
17int root(int x)
18{
19    while(id[x] != x)
20    {
21        id[x] = id[id[x]];
22        x = id[x];
23    }
24    return x;
25}
26
27void union1(int x, int y)
28{
29    int p = root(x);
30    int q = root(y);
31    id[p] = id[q];
32}
33
34long long kruskal(pair<long long, pair<int, int> > p[])
35{
36    int x, y;
37    long long cost, minimumCost = 0;
38    for(int i = 0;i < edges;++i)
39    {
40        // Selecting edges one by one in increasing order from the beginning
41        x = p[i].second.first;
42        y = p[i].second.second;
43        cost = p[i].first;
44        // Check if the selected edge is creating a cycle or not
45        if(root(x) != root(y))
46        {
47            minimumCost += cost;
48            union1(x, y);
49        }    
50    }
51    return minimumCost;
52}
53
54int main()
55{
56    int x, y;
57    long long weight, cost, minimumCost;
58    initialize();
59    cin >> nodes >> edges;
60    for(int i = 0;i < edges;++i)
61    {
62        cin >> x >> y >> weight;
63        p[i] = make_pair(weight, make_pair(x, y));
64    }
65    // Sort the edges in the ascending order
66    sort(p, p + edges);
67    minimumCost = kruskal(p);
68    cout << minimumCost << endl;
69    return 0;
70}