Linear search

In computer science, a linear search or sequential search is a method for finding an element within a list. It sequentially checks each element of the list until a match is found or the whole list has been searched. In computer science, a linear search or sequential search is a method for finding an element within a list. It sequentially checks each element of the list until a match is found or the whole list has been searched. A linear search runs in at worst linear time and makes at most n comparisons, where n is the length of the list. If each element is equally likely to be searched, then linear search has an average case of n/2 comparisons, but the average case can be affected if the search probabilities for each element vary. Linear search is rarely practical because other search algorithms and schemes, such as the binary search algorithm and hash tables, allow significantly faster searching for all but short lists. A linear search sequentially checks each element of the list until it finds an element that matches the target value. If the algorithm reaches the end of the list, the search terminates unsuccessfully. Given a list L of n elements with values or records L0 .... Ln−1, and target value T, the following subroutine uses linear search to find the index of the target T in L. The basic algorithm above makes two comparisons per iteration: one to check if Li equals t, and the other to check if i still points to a valid index of the list. By adding an extra record Ln to the list (a sentinel value) that equals the target, the second comparison can be eliminated until the end of the search, making the algorithm faster. The search will reach the sentinel if the target is not contained within the list. If the list is ordered such that L0 ≤ L1 ... ≤ Ln−1, the search can establish the absence of the target more quickly by concluding the search once Li exceeds the target. This variation requires a sentinel that is greater than the target. For a list with n items, the best case is when the value is equal to the first element of the list, in which case only one comparison is needed. The worst case is when the value is not in the list (or occurs only once at the end of the list), in which case n comparisons are needed. If the value being sought occurs k times in the list, and all orderings of the list are equally likely, the expected number of comparisons is