Please give a proof of correctness as well. Thank you!

1. (a) Describe and analyze an algorithm to compute the maximum-weight spanning tree of a given edge-weighted graph. (b) A feedback edge set of an undirected graph G is a subset F of the edges such that every cycle in G contains at least one edge in F. In other words, removing every edge in F makes the graph G acyclic. Describe and analyze a fast algorithm to compute the minimum weight feedback edge set of a given edge-weighted graph. The running time for both parts should be in terms of V and E, the number of vertices and edges in the input graph. 1. (a) Describe and analyze an algorithm to compute the maximum-weight spanning tree of a given edge-weighted graph. (b) A feedback edge set of an undirected graph G is a subset F of the edges such that every cycle in G contains at least one edge in F. In other words, removing every edge in F makes the graph G acyclic. Describe and analyze a fast algorithm to compute the minimum weight feedback edge set of a given edge-weighted graph. The running time for both parts should be in terms of V and E, the number of vertices and edges in the input graph