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# hw1 - Computer Science 130B Winter 2007 Written...

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Computer Science 130B Winter 2007 Written Assignment #1 Due: 4pm, January 19th, Friday Problem 1 In divide-and-conquer, the way a problem is divided into pieces often affects the effectiveness and applicability of the proposed solution. Consider the Towers of Hanoi problem again. Define the original problem as Hanoi ( n, A, B, C ) , where the first parameter denotes the number of disks, the second parameter the starting peg, the third parameter the ending peg, and the last parameter the temporary storage peg. a. Consider the following divide-and-conquer strategy: Hanoi ( n, A, B, C ) Hanoi (1 , A, C, B ) + Hanoi ( n - 1 , A, B, C ) + Hanoi (1 , C, B, A ) , which divides the original problem into two instances of size 1 and one instance of size n - 1. If you think the strategy will work, give the detailed motion sequence for Hanoi(4,A,B,C) and estimate the complexity of the algorithm. If you think the strategy will not work, provide a counterexample. b. If n = 2 k , consider the following divide-and-conquer strategy: Hanoi ( n, A, B, C ) Hanoi ( n/ 2 , A, C, B ) + Hanoi ( n/ 2
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