Kruskal's algorithm for spanning tree

Another popular algorithm for finding a minimum spanning tree is Kruskal's algorithm. It is similar to Prim's algorithm and uses a greedy approach to find the solution. Here are the steps we need to implement Kruskal's algorithm:

1. Create a forest T (a set of trees), where each vertex in the graph is a separate tree.
2. Create a set S containing all the edges in the graph.
3. While S is non-empty and T is not yet spanning:

1. Remove an edge with the minimum weight from S.

2. If that edge connects two different trees, then add it to the forest, combining two trees into a single tree; otherwise, discard that edge.

We will use the same graph that we used for Prim's algorithm. Here is the implementation of Kruskal's algorithm:

function Kruskal(array $graph): array { 
    $len = count($graph); 
    $tree = []; 

    $set = []; 
    foreach ($graph as $k => $adj) { 
    $set[$k] = [$k]; 
    } 

    $edges = []; 
    for ($i = 0; $i < $len; $i++) { 
      for ($j ...