# Topic 02b Divide & Conquer SOLUTIONS.pdf - Topic 2b...

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Topic 2b, Divide & Conquer: Solutions Copyright (c) 2017 Daniel D. Suthers. All rights reserved. These solution notes may only be used by students in sections of ICS 311 Fall 2017 at the University of Hawaii. 1. Correctness of Binary Search Consider the Binary Search algorithm shown below (a Divide & Conquer algorithm). The inputs are a sorted array A of integers. You will use a loop invariant to show that the algorithm finds x correctly if it is in the range of A to be searched. Binary-Search ( x , A , min , max ) 1 low = min 2 high = max 3 while low <= high 4 mid = ( low + high ) / 2 5 if x < A [ mid ] 6 high = mid - 1 7 else if x > A [ mid ] 8 low = mid + 1 9 else return mid // since x == A [ mid ] 10 return “NOT FOUND” (1 pt) a. State the loop invariant for the while loop. Hint: Think about what the algorithm does and why you think it is correct. Second Hint: "If x is in A[min,max] then ..." what must remain true each pass? If x is in the range of the array A[min,max] to be searched it is in the subarray A[low,high]. b. ( Initialization ) Referencing the code, show the invariant is true at loop initialization: Trivially true because low=min and high=max in lines 1 and 2.

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• Fall '08
• Barjaktarovic,M

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