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![The Binary Search Algorithm (BSA) is described by this pseudocode:
ALGORITHM 3 The Binary Search Algorithm.
procedure binary search (x: integer, a₁, a2, ..., an: increasing integers)
i = 1 {i is left endpoint of search interval}
j:= n {j is right endpoint of search interval}
while i < j
m := [(i+j)/2]
if x > am then i:=m+1
else j := m
if x = a; then location := i
else location : 0
return location{location is the subscript i of the term a; equal to x, or 0 if x is not found}
a. Derive f(n), a function giving the number of comparisons performed by the BSA in
terms of the size of the list n. For simplicity, assume n equals an integer power of 2;
that is, n = 2k, k E N, the natural numbers (positive integers).](https://content.bartleby.com/qna-images/question/fa06b614-497d-40f0-b077-f4b4fca47baf/9d4dc3ed-836e-4bc6-b9c4-0511abd24a0f/5i8r6du_processed.png)
Transcribed Image Text:The Binary Search Algorithm (BSA) is described by this pseudocode:
ALGORITHM 3 The Binary Search Algorithm.
procedure binary search (x: integer, a₁, a2, ..., an: increasing integers)
i = 1 {i is left endpoint of search interval}
j:= n {j is right endpoint of search interval}
while i < j
m := [(i+j)/2]
if x > am then i:=m+1
else j := m
if x = a; then location := i
else location : 0
return location{location is the subscript i of the term a; equal to x, or 0 if x is not found}
a. Derive f(n), a function giving the number of comparisons performed by the BSA in
terms of the size of the list n. For simplicity, assume n equals an integer power of 2;
that is, n = 2k, k E N, the natural numbers (positive integers).
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