Algebraic Preis’ Algorithm Algorithm due to Preis provides a different way to solve the maximal weighted matching problem in a weighted graph. The algorithm consists of the following steps. 1. Input: A weighted graph G = (V, E, w) 2. Output: A maximal weighted matching M of G 3. M ← Ø 4. E ← E 5. V ← V 6. while E = Ø 7. select at random any v ∈ V 8. let e ∈ E be the heaviest edge incident to v 9. M ← M ∪ e 10. V ← V {v} 11. E ← E \ {e and all adjacent edges to e} show two ways of implementing this algorithm in Python

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A: Dear Student, The required algorithm along with explanation is given below -

Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.