# Answered Essay: Crabbe and Goyle are arguing about binary search. Goyle writes the following pseudocode on the board, which he c

algorithms

Crabbe and Goyle are arguing about binary search. Goyle writes the following pseudocode on the board, which he claims implements a binary search for a target value v within input array A containing n elements. bSearch(A, v) { return binarySearch(A, 0, n, v) } binarySearch (A, 1, r, v) { if 1 > = r then return -1 p = floor ((1 + r)/2) if A[p] == v then return m if A[m]

(a)

the goyle algorithm has bugs :

the value used to store (l+r)/2 and a[m]==v should be m not p as in futher steps we used m to check the values and returned m

———————————–

the not found condition must be l>r then return -1 beacuse if we consider the example

no of elements 5

elements are 1 2 5 7 8

and key is 2

then the fisrt mid value is 2 then a[2] is 5 as 5 is greater than 2 binarySearch(A,0,2-1,v) is called

then mid is 0 as a[0] is 1 as 1 is less than 2 binarySearch(A,0+1,1,v) is called

now l is equal to r so it returns -1 but the element is present so the condition should be l>r

then mid is i=1 a[1]=2 as 2 is equal to 2 it returns the index of 2.

——————————————

(b)

Goyle is correct .

If we consider the worst -case binary search makes (log n to base 2)*2+1 searches where as trinary search makes

(log n to base 3)*4+1 searches which can be written as (2/(log 3 to base 2) )*(log n to base 2) whose value is greater than 1. so tinary search makes more comparisions hence binary search is the best of two

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