Minimum Spanning Tree
Medium Accuracy: 49.39% Submissions: 34686 Points: 4

Given a weighted, undirected and connected graph of V vertices and E edges. The task is to find the sum of weights of the edges of the Minimum Spanning Tree.

 

Example 1:

Input:

Output:
4
Explanation:

The Spanning Tree resulting in a weight
of 4 is shown above.

Example 2:

Input:

Output:
5
Explanation:
Only one Spanning Tree is possible
which has a weight of 5.

 

Your task:
Since this is a functional problem you don't have to worry about input, you just have to complete the function  spanningTree() which takes number of vertices V and an adjacency matrix adj as input parameters and returns an integer denoting the sum of weights of the edges of the Minimum Spanning Tree. Here adj[i] contains a list of lists containing two integers where the first integer a[i][0] denotes that there is an edge between i and a[i][0] and second integer a[i][1] denotes that the distance between edge i and a[i][0] is a[i][1].

Expected Time Complexity: O(ElogV).
Expected Auxiliary Space: O(V2).

 

Constraints:
2
V 1000
V-1
E (V*(V-1))/2
1
w 1000
Graph is connected and doesn't contain self loops & multiple edges.

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Minimum Spanning Tree

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