Prove an Algorithm

  1. I have to come up with an algorithm to search a sorted array. Here it is:

    Code (Text):
    def binarySearch(inputArray, match):
       x = -1
       start = 0
       end = len(inputArray) - 1
       while not start == end:
           midPt = (start + end) / 2
           if match < inputArray[midPt]:
               end = midPt - 1
           elif match > inputArray[midPt]:
               start = midPt + 1
           else:
               return midPt
       if inputArray[start] == match:
           x = start
       return x
    The code is Python, but I figure anyone can read it without much explination. I have to prove that this algorithm works. I don't know how to do this!! Any help would be appreciated!!

    Thanks
     
  2. jcsd
  3. AKG

    AKG 2,585
    Science Advisor
    Homework Helper

    Maybe you can use strong induction. Show that it works when len(inputArray) = 1, then show that if it works for all arrays of length k or less, then it works for an array of length k+1. Note that if you go through the while loop once, you come back to the top essentially dealing with an array of 1/2 the length, so it would fit in the category of "arrays of length k or less".
     
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