2005 F

1. (16%) True or False. You need justify your answer.
 * (a) By the master theorem, the solution to the recurrence T(n)=3T(n/3)+logn is T(n)=Θ(nlogn)
 * (b) For hashing an item into a hash table in which collisions are resolved by chaining, the worst-case time is proportional to the load factor of the table.
 * (c) Depth-first search of a graph is asymptotically faster than breadth-first search.
 * (d) For any directed acylclic graph, there is only one topological ordering of the vertices.
 * (e) If some of the edge weights in a graph are negative, the shortest path from s to t can be obtained using Dijkstra's algorithm by first adding a large constant C to each edge weight, where C is chosen laree enough that every resulting edge weight will be nonnegative.
 * (f) If all of edge capacities in a graph are integer multiples of 5 then the maximum flow value is a multiple of 5.
 * (g) If each operation on a data structure runs in O(1) amortized time, then n consecutive operations run in O(n) time in the worst case.
 * (h) A graph algorithm with Θ(ElogV) running time is asymptotically better than an algorithm with a Θ(ElogE) running time for a connected, undirected graph G(V;E).