a) (T/F). Prims algorithm cannot be applied to directed weighted graphs. b) (T/F). For a dynamic programming algorithm, computing all values in a bottom-up fashion is asymptotically faster than using recursion and memoization. c) (T/F). In an undirected weighted graph, the shortest path between two nodes always lies on some minimum spanning tree. d) (T/F). For a graph with nonnegative edge weights, when a node u is removed from the priority queue in Dijkstras algorithm its distance label is correct (i.e., equal to the length of the shortest su path.) e) (T/F). We have n operations, each of which takes amortized O(1). Then, the worst-case running time for any single operation can be (n 2 ). f) (T/F). The spanning tree of maximum weight in G is the minimum spanning tree in a copy of G with all edge weights negated. g) (T/F). Suppose G is a weighted undirected graph with positive edge weights, where each edge e E has weight we, and let G be a graph that is identical to G except that every edge e has weight w 2 e . Any MST of G is an MST of G. h) (T/F). Let T(n) = 3T( n 3 ) + O(log n) be a recurrence equation. Then we can conclude that T(n) = (n log n) by the Master theorem. i) (T/F). Any function which is (log(log n))) is also (log n). j) (T/F). p log2 n = (n 1 log2 n ).