Homework #5 Due Date: Monday , November 8th, start of class Please note the Monday due date. 1. We are given a sorted array A [1 ..n ], composed of distinct integers (the values can be neg-ative). We want to determine if there is an index i such that A [ i ] = i . Give an O (log n ) algorithm to solve this problem, and justify its correctness. 2. Suppose we’d like to implement a sorting variant where every element is compared only a small number of times. Note that while Merge Sort has O ( n log n ) comparisons, a particular element may be compared n or more times. (a) Devise a divide-and-conquer algorithm to merge two sorted arrays of length n , which guarantees that every element is included in at most O (log n ) comparisons. Hint: Use binary search to locate the median of one array in the other. (b) Using this modiﬁed Merge, prove that Merge-Sort will include each element in at most O (log 2 n ) comparisons. 3. You are given an array
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This note was uploaded on 12/13/2010 for the course CSCI 570 at USC.