(Homework Solution): You have a list of 1024 sorted numbers and are looking for a particular value.

You have a list of 1024 sorted numbers and are looking for a particular value. It takes one time unit to compare each number to see if it’s the one you want.

a)  If we searching exhaustively across the list and the number we are looking for isn’t there , how long will it take to work out that the number isn’t there? You may assume that any operations other than comparison take up negligible time.

b)  If we used binary search, how long would it take us, a tmost, to determine that the number wasn’t there. You may assume that any operations other than comparison take up negligible time

Expert Answer

answers

A linear search scans one item at a time, without jumping to any item .

The worst case complexity is O(n).

Time taken to search elements keep increasing as the number of elements are increased.

so if we have a list of 1024 numbers and if the number we are searching is not present , then worst time complexity will be O(1024) i.e 1024 comparisons by using linear search

A binary search  reduces your search to half as soon as you find middle of a sorted list.

  1. The middle element is looked to check if it is greater than or less than the value to be searched.
  2. Accordingly, search is done to either half of the given list

n / (2k) = 1

2k = n

k = log2n

so,  worst case, time complexity of binary search algorithm is log(n).

so if we have a list of 1024 numbers and if the number we are searching is not present , then worst time complexity will be log2(1024) i.e 10 comparisons by using binary search

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