Standard disclaimer: use the algorithms from class, such as…

Standard disclaimer: use the algorithms from class, such as DFS, Explore, BFS, Dijkstra’s (using min-heaps), SCC, Kruskal’s, Prim’s etc., as a blackbox subroutine for your algorithm. Make sure to explain your algorithm in words (no pseudocode!), explain the correctness of your design, and state and analyze its running time. Faster – and correct – solutions worth more credit. Design an algorithm to solve the following problem:Input: a connected, undirected, weighted graph G = (V,E), and a subset U of the vertices  .Output: A spanning tree of G of minimal weight with the property that all the vertices in U are leaves. Note that there may be other leaves in the optimal tree and it isn’t necessarily a MST of G.

Insrtuctions for problems 2-5: For each of the following pro…

Insrtuctions for problems 2-5: For each of the following problems, you do not have to prove the correctness of your design or report its runtime. You can use the algorithms from class, such as DFS, Explore, BFS, Dijkstra’s (using min-heaps), SCC, Kruskal’s, Prim’s etc., as a blackbox subroutine for your algorithm. Make sure to explain your algorithm in words (no pseudocode!). Faster – and correct – designs worth more credit.