What is the average complexity of sequential search

Easy Normal Medium Hard Expert. Writing code in comment? Please use ide. Load Comments. What's New. Most popular in Analysis. Most visited in Articles. The diagram below shows how this search works.

Starting at the first item in the list, we simply move from item to item, following the underlying sequential ordering until we either find what we are looking for or run out of items. If we run out of items, we have discovered that the item we were searching for was not present. Sequential search of a list of integers. The Python implementation for this algorithm is shown below. The function needs the list and the item we are looking for and returns a boolean value as to whether it is present.

Remember in practice we would use the Python in operator for this purpose, so you can think of the below algorithm as what we would do if in were not provided for us. To analyze searching algorithms, we need to decide on a basic unit of computation. Recall that this is typically the common step that must be repeated in order to solve the problem. For searching, it makes sense to count the number of comparisons performed.

Each comparison may or may not discover the item we are looking for. In addition, we make another assumption here. We can define a stronger version of "typical": suppose for any list, any permutation of the list is equally likely.

Then we can average over all possible permutations:. A second point to be made about average case analysis: sometimes it makes sense to analyse different cases separately. The analysis above assumes x is always in the list; if x is not in the list, you always get n comparisons. For instance if you're programming the computer controlling a car, and you want to tell if you're in a crash and should activate the air bags, you don't want to be running some algorithm that usually takes half a second but maybe sometimes takes as much as five minutes.

Random numbers are very useful in this respect. The idea is to "scramble" the input so that it looks typical. We say that an algorithm is randomized if it uses random numbers. An algorithm that is not randomized is called deterministic.

The "expected time" analysis of a random algorithm is measured in terms of time input,sequence of random numbers. For some particular input I, the expected time of the algorithm is just the average over different sequences of random numbers:.

Sc in Data Science — University of Arizona. Software Engineering All Courses M. Table of Contents. Compare linear search and binary search using their complexities. Is there any other method to search an element in an array? What are the different time complexities of interpolation search? Leave a comment. Cancel reply Your email address will not be published. Comment Name Email Website. Related Articles. How to Reverse a Number in Python?

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