It is quite clear from the figure that the rate by which the complexity increases for Linear search is much faster than that for binary search. Assuming that comparing each element with the desired key takes constant time, the worst-case complexity is [math]O(n)[/math], where [math]n[/math] is the number of elements in the input. Target element is compared sequentially with each element of a collection until it is found. share | improve this … That is because the worst Well, a linear search has linear time complexity, O(n), but with a fixed sized array like yours one could say that it has constant time complexity, O(1). So time complexity in the best case would be Θ(1) Most of the When we analyse an algorithm, we use a notation to represent its time complexity and that notation is Big O notation. A linear search runs in at worst linear time and makes at most n comparisons, where n is the length of the list. The time does not always increase by exactly the same value, but it does so sufficiently precisely to demonstrate that logarithmic time is significantly cheaper than linear time (for which the time required would also increase by . (linear search is O(n), linear search has linear time complexity) The number of steps in binary search is: c log 2 n + d ⇒ Binary search has time complexity O(log n) Because O(log n) ⊊ O(n), binary search is faster (from last Linear search (known as sequential search) is an algorithm for finding a target value within a list. Linear search is used to find a particular element in a list or collection of items. Otherwise it will traverse through that list until it reaches to the end of the list. The number of operations in the best case is constant (not dependent on n). It sequentially checks each element of the list for the target value until a match is found or until all the elements have been If each element is equally likely to be searched, then linear search has an average case of n+1 / 2 comparisons, but the average case can be affected if the search probabilities for each element vary. In the linear search problem, the best case occurs when x is present at the first location.