Write an MST and EdgeWeightedGraph client check() that uses the following cut optimality conditions implied by Proposition J to verify that a proposed set of edges is in fact an MST: A set of edges is an MST if it is a spanning tree and every edge is a minimum-weight edge in the cut defined by removing that edge from the tree. What is the order of growth of the running time of your method?

Create an algorithm for the monotonic evaluation function, algorithm A*.Graph G = (V, E); start vertex s; target vertex r; A-Star(G, s, r) in; out: maps as: V VLocal: Heuristic lower bound estimate h(u v), open list S, cost function g(u v),

What is the worst-case running-time of the isGraphConnected function below which tests whether a graph G with n vertices and m edges is connected. Algorithm isGraphConnected(G) Input: graph G Output: true if G is connected and false otherwise v <- a vertex in G DFS(G) starting at v foreach u in G.vertices) do if u was not visited by DFS then return false return true a. O(mn) O b. O(n 2+mn) O c. O(n 2) O d. O(n 3) e. O(n+m)

What is the distinction between cohesion and coupling in the context of software architecture?