Do the order of edges matter in union find?

I am learning union-find and to understand it better, I have written a small program:

#include <iostream>
#include <vector>
#include <numeric>
using namespace std;
 
vector<int> parent, sz;
 
int find(int i) {
    if(parent[i]==i) return i;
    return parent[i]=find(parent[i]);
}
 
void merge(int i, int j) {
    int p1=find(i);
    int p2=find(j);
 
    if(p1==p2) return;
    if(sz[p1]<sz[p2]) {
        parent[p1]=p2;
        sz[p2]+=sz[p1];
    } else {
        parent[p2]=p1;
        sz[p1]+=sz[p2];
    }
}
 
int main() {
    vector<vector<int>> allowedSwaps={{0,4},{4,2},{1,3},{1,4}};
 
    int n=5;    //hard-code for now
    sz.resize(n,1);
    parent.resize(n);
    iota(begin(parent),end(parent),0);
 
    cout<<"Parents before: \n";
    for(auto& e: parent)
        cout<<e<<" ";
    cout<<"\n";
 
    for(vector<int>& currswap: allowedSwaps) {
        merge(currswap[0],currswap[1]);
    }
 
    cout<<"Parents after: \n";
    for(auto& e: parent)
        cout<<e<<" ";
    cout<<"\n";
 
    return 0;
}

allowedSwaps essentially denotes all the components that are connected to each other. For the code above, all of them are connected.

However, if you notice the output:

Parents before: 
0 1 2 3 4 
Parents after: 
0 0 0 1 0 

It shows that one of them (3, 0-indexed) is not connected. I think that is because when we process the edge {1,3}, both the vertices 1 and 3 have not been connected to the larger component yet (they are later, by {1,4}) and so Union Find determines that it is a different component.

Does this mean that the order of edges matter for Union find? Or, am I missing something?

>Solution :

The output you got does not signify that one node is disconnected.

The parent data structure represents links from one node to another (or itself, when it is a root).

At the start you have this:

And at the end we have this:

The important thing here is that there is one tree. It is not required that all nodes are linked directly to the root, just that they have a path to the root, which is also true for the node with index 3.

NB: if you would call find(3), then also index 3 would receive value 0. It is just something that gets optimised by calling find, but it doesn’t change the meaning of result.