Search Algorithms

Search Algorithms

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Sequential (linear) search – Compares an item in a list to a target and moves on to the next item, sequentially.

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Depending on the arrangement of data in a list, an algorithm can take much longer or shorter to run. Best Case – The target value is the first item stored in a list during a sequential search, making it O(1) complexity. (NOTE: It is often best to worry more about average and worst-case performances rather than best.) Worst Case – Target is not in the list or is the last item, meaning n iterations are made and it is O(n). Average Case – Add the number of iterations to find the target at each possible position and divide the sum by n. This ends up being O(n) in a sequential search, and the worst and average case are often the same.

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Best, Worst, and Average Case Performance

Binary Search Algorithm A binary search algorithm can be used only on a sorted list. Upper and lower bounds are established (first index and last of the list) and then the midpoint is checked for the target value. Depending on whether the midpoint is lower or higher than the target, the upper and lower bounds are redefined and a new midpoint is checked until the target is found or determined to not be in the list.

Selection Sort Algorithm Goes through the list searching for the smallest number, compares it to the number in list[0], and if list[0] is bigger their places are swapped. This is repeated again except with the position list[1] up until list[n-1]. O(n2) in all cases.

Bubble Sort Goes through list comparing first and second values, then second and third, and so on until it compare n and n-1. Each comparison it will see if the larger number occupies the larger index, and if it doesn’t the values will be swapped. This process is then repeated except it only swaps up to the n-2 and n-1 comparison, and so on. O(n2).

Insertion Sort Starts from the second item and compares it to the first, swapping if the first is large. Then it compares the third item to the two before it, and so on. Meaning after i iterations the first I numbers are sorted. O(n2)

Quicksort Begin by selecting the midpoint in the list, called the pivot point. Everything less of the pivot is moved to the left of the pivot, and anything else is moved to the right. This guarantees the pivot is in the correct place for the fully sorted list. Repeat this process with the partitions left and right of the pivot, and then repeat it with their partitions, and so on. The process terminates each time it encounters a sublist with fewer than two items. O(n log n) best case/average case

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O(n2) worst case

Mergesort The middle position of list divides the list in two sublists, which are then each divided into two more sublists, and so on in that manner until there are individual elements left. Two individual elements will be merged into one sublist of two elements which will then merge with another sublist of two elements to form an ordered list of four elements and so on. Eventually the two main partitions will be sorted and merge together to create a sorted list. O(n log n)