Linear Search Time Complexity Analysis: Part 1

Linear search is one of the simplest algorithms. Consider an unsorted array A of size n. Given an element x, we would like to determine whether x exits in A or not. Linear search goes like this: search A for x in order by considering A[1], A[2], …, A[n] until either it finds A[i] = x or it reaches the end of the array which means that the element does not exist. Because the algorithm always starts at 1 and continue sequentially up to n, we call it deterministic. We don’t make any assumptions about whether A contains one or more equal copies of the same element. However, we assume that the elements of the array, whatever they are, are equally likely to appear in any order. Also we will consider only the number of comparisons that involves elements from A when computing the running time. Continue reading