Algorithm 1 int linearSearch(int A[0...n1], int val) i = 0; while i < n do if va
ID: 3751848 • Letter: A
Question
Algorithm 1 int linearSearch(int A[0...n1], int val)
i = 0;
while i < n do
if val == A[i] then
return i;
end if
i + +;
end while
return 1;
Suppose before we call linearSearch we randomly permute (i.e., reorder) the elements in A. In the following problem, we will nd the expected asymptotic runtime of linearSearch.
a) (1 point) What is the best case asymptotic runtime of linearSearch on an array of n elements? What index must val be located at to elicit this runtime?
b) (1 point) What is the worst case asymptotic runtime of linearSearch on an array of n elements? What index must val be located at to elicit this runtime?
c) (1 point) For the sake of simplicity, assume val is in A. Let Xj be the random variable which, given an permutation of the elements in our array, is 1 if index A[j] will be checked in our linearSearch for that permutation and 0 otherwise. What is the expected value of Xj?
d) (1 point) Let X be the random variable which, given an permutation of the elements in our array, is the number of elements of A which will be checked in our linearSearch for that permutation. Dene X using n copies of the random variable dened in the previous step.
I need help please.
Explanation / Answer
Answer a:
The bese case of linear search is the O(1) when the we have the val in in the index 0
Answer b:
The worst case of linear search is the O(n) when the we have the val in in the index size-1
Answer c:it will search from the 0 th location to till it finds expected value is 1
Answer d: for given any value in linear search it will check all the elements untill it finds the exact match, if A has 20 elements than to find the X it will matches with the 20 elements
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