This question is about the procedure linearSearch, which was discussed in the lectures. 1  procedure linearSearch(x, a1, a2 ⋯, an)  2      for k := 1 to n  3          if x = ak  4          then return k  5      return 0 The procedure searches a sequence of objects a1, a2 ⋯, an in order. If it finds an object that is equal to x at line 3, then it returns the object’s index k at line 4. If it does not find such an object, then it returns 0 at line 5 instead. Suppose that linearSearch searches five objects, and always finds one of them. The probability that an object ai will be found is p(ai), where 1 ≤ i ≤ 5. The probabilities for all objects are shown below. p(a1)   =   0.5 p(a2)   =   0.3 p(a3)   =   0.1 p(a4)   =   0.05 p(a5)   =   0.05 What is the expected number of comparisions (=) executed by linearSearch at line 3? Your answer must be a number. Show how you got the answer.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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This question is about the procedure linearSearch, which was discussed in the lectures.

1  procedure linearSearch(xa1a2 ⋯, an
2      for k := 1 to n 
3          if x = ak 
4          then return k 
5      return 0

The procedure searches a sequence of objects a1a2 ⋯, an in order. If it finds an object that is equal to x at line 3, then it returns the object’s index k at line 4. If it does not find such an object, then it returns 0 at line 5 instead. Suppose that linearSearch searches five objects, and always finds one of them. The probability that an object ai will be found is p(ai), where 1 ≤ i ≤ 5. The probabilities for all objects are shown below.

p(a1)

  =  

0.5

p(a2)

  =  

0.3

p(a3)

  =  

0.1

p(a4)

  =  

0.05

p(a5)

  =  

0.05

What is the expected number of comparisions (=) executed by linearSearch at line 3? Your answer must be a number. Show how you got the answer.

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