- Prepare
- Algorithms
- Graph Theory
- Kruskal (MST): Really Special Subtree

# Kruskal (MST): Really Special Subtree

# Kruskal (MST): Really Special Subtree

Given an undirected weighted connected graph, find the Really Special SubTree in it. The Really Special SubTree is defined as a subgraph consisting of all the nodes in the graph and:

- There is only one exclusive path from a node to every other node.
- The subgraph is of minimum overall weight (sum of all edges) among all such subgraphs.
- No cycles are formed

To create the Really Special SubTree, always pick the edge with smallest weight. Determine if including it will create a cycle. If so, ignore the edge. If there are edges of equal weight available:

- Choose the edge that minimizes the sum where and are vertices and is the edge weight.
- If there is still a collision, choose any of them.

Print the overall weight of the tree formed using the rules.

For example, given the following edges:

```
u v wt
1 2 2
2 3 3
3 1 5
```

First choose at weight . Next choose at weight . All nodes are connected without cycles for a total weight of .

**Function Description**

Complete the function in the editor below. It should return an integer that represents the total weight of the subtree formed.

kruskals has the following parameters:

*g_nodes*: an integer that represents the number of nodes in the tree*g_from*: an array of integers that represent beginning edge node numbers*g_to*: an array of integers that represent ending edge node numbers*g_weight*: an array of integers that represent the weights of each edge

**Input Format**

The first line has two space-separated integers and , the number of nodes and edges in the graph.

The next lines each consist of three space-separated integers , and , where and denote the two nodes between which the **undirected** edge exists and denotes the weight of that edge.

**Constraints**

**Note: ** If there are edges between the same pair of nodes with different weights, they are to be considered as is, like multiple edges.

**Output Format**

Print a single integer denoting the total weight of the Really Special SubTree.

4 6

1 2 5

1 3 3

4 1 6

2 4 7

3 2 4

3 4 5

**Sample Output 1**

`12`

**Explanation 1**

The graph given in the test case is shown above.

Applying Kruskal's algorithm, all of the edges are sorted in ascending order of weight.

After sorting, the edge choices are available as :

and

Select 2 \rightarrow 3 (w=4)$ because it has the lowest weight without creating a cycle

The edge would form a cycle, so it is ignored

Select to finish the MST yielding a total weight of