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hw2 - Computer Science 130B Spring 2012 Homework#2 Due 4pm...

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Computer Science 130B Spring 2012 Homework #2 Due: 4pm, Feb. 3, Friday Problem 1 Consider the coin change problem. You are at a check out register, and have an unlimited supply of quarters, dimes, nickels, and pennies. You have to make change for a customer. Design a greedy algorithm to make out an amount of x cents that uses the smallest number of coins. Prove the optimality of your algorithm. Problem 2 We know that a minimum-cost spanning tree links all the vertices in a connected undirected graph together in such a way that the total cost of the tree arcs is minimized. Does this fact imply that given two vertices i and j in a graph and a minimum-cost spanning tree of that graph, the shortest path from i to j must contain only the tree arcs in the minimum-cost spanning tree? If you think so, prove it, otherwise, give a counterexample. Problem 3 Consider the graph shown in figure 1. a. Find the shortest path from vertex a to vertex e using Dijkstra’s algorithm. Show intermediate steps in executing the algorithm.
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