Question

Divide and Conquer & Algorithm Design 5. (20 points) Consider the following algorithm Precondition: S is a sorted list index mystery (index low, index high, const Array S[], number x) if low S high then mid = (low + high) / 2 if x = Smid] then return mid elsif x < s[mid] then return mystery (low, mid-1, s, x) else return mystery (mid+1, high, s, x) else return 0 end What does the recursive algorithm above compute? Explain why?

Answer 1

Explanation of the Above code:

In the above algorithm, we are searching a number.

Actually it is a Binary search algorithm

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let's we have the following array:

array = [4, 5,7, 17 , 20] --Sorted Array

Here is the following parameter passed :

index low --> index 0 of the array

index high --> last index of the array i.e. index 4

S[] --> this is the array

number x --> number we are searching let's suppose 17

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Now , we check if index low is less than high, we calculate mid point

mid = (low + high ) / 2

mid = (0 + 4 ) / 2 = 2

mid = 2

S[mid] = 7

Now , we check if S[mid] == x, we get the result

Otherwise, if x is less than S[mid], then we pass the array from start the one less to the mid

else, if x is greater than S[mid[, then we pass the array from mid+1 to the end.

Just we do it recursively, untill we get the number x in array or the index low becomes greater than high