A packet in C++ which helps finding minimum spanning tree. It is subset of connected edge-weighted graph that connects all vertices together without cycles and minimum total edge weight

The packet helps in finding a **minimum spanning tree out of an input graph**. A **graph may contain cycles and loops in it but a tree never contains a cycle in it**. **The tree formed consists of all the vertices mentioned in the graph but it's not the same case with edges given in the graph**. The packet can be used to find out the minimum path connecting all the points having the least cost of all possible paths in the graph.

**The packet uses the standard library in C++, bits/stdc++.h**. **Kruskal's Algorithm is a greedy approach that finds a connection between all the points which is of the least total weight. The algorithm subsequently selects the next minimum edge in the graph and checks whether using it will create a loop in the tree or not if it does not then the edge is selected.**

The packet has three functions:

1. **Function Sorter**. It is used to sort the edge sequences in increasing order of their weights. It is custom sorting function.

2.** Function get_parent**. When an edge is selected, one of the points is made the parent of another point of the edge. The function helps to prevent the creation of a cycle in the tree. If an edge is selected with both the points having the same parent the corresponding edge is not selected.

3. **Function get_MS**T. It is the parent function that uses the get_parent function in its definition. Selects one edge at a time uses get_parent function on each edge and decides whether to add it to the Minimum Spanning Tree.

**The packet asks for 3 types of inputs**.

1. Number of vertices in the graph

2. Number of edges in the graph

3. List of edges of the form **{G1, G2, X}, where G1, G2 are two vertices having an edge between them of weight 'X'**.

**The packet outputs the list of edges and corresponding edge weights which will be included to form an MST**.

**Sample Input / Ouput **

**Sample Graph**

**Inputs on the basis of above graph**

**The resultant tree structure without any loops with least cost**

Submitted by Dhruv Prakash Raipure (DhruvRaipure)

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