programming-for-dummies

394 Using Bubble Sort

394 Using Bubble Sort Speed measures how fast the algorithm can sort data of different sizes. Some sorting algorithms work quickly with small lists but slow down dramatically when dealing with larger lists. Other sorting algorithms work quickly when a list is mostly sorted but slow to a crawl when working with completely unsorted lists. Memory requirements define how much memory the sorting algorithm needs to run. Some sorting algorithms can accept and sort data while they receive the data, which is an online algorithm. (An offline algorithm has to wait to receive the complete set of data before it can even start the sorting process.) Sorting algorithms that use recursion (see Book II, Chapter 6) may be easy to implement and fast but can require lots of memory to sort large amounts of data. Another factor that determines a sorting algorithm’s memory requirements is whether the algorithm is an in-place algorithm. An in-place algorithm can sort data by using the existing data structure that holds the data. For example, if you have an array of numbers, an in-place algorithm can sort the data in that array without needing a separate data structure to hold the data temporarily. Stability refers to whether a sorting algorithm preserves the order of identical data. Suppose you had a list of first and last names, such as John Smith and Mary Smith, and the name John Smith appears at the beginning of a list and Mary Smith appears at the end. A stable sorting algorithm sorts both names and keeps John Smith ahead of Mary Smith, but an unstable algorithm moves Mary Smith ahead of John Smith. (Out of all the sorting algorithms presented in this chapter, heap sort is the only unstable algorithm.) Ultimately, there’s no perfect sorting algorithm; however, a trade-off in size, speed, and ease of implementation finds the best sorting algorithm. Using Bubble Sort The simplest way to sort any amount of data is to start at the beginning and compare the first two adjacent items. So if you need to sort a list of numbers, you compare the first number with the second number. If the first number is bigger, you swap its place with the second number. If the second number is bigger, you don’t do anything at all. After comparing the first two items, you move down to comparing the second and third items, and so on. Repetitively comparing two adjacent items is the basic idea behind the bubble sort algorithm, as shown in Figure 1-1. The bubble sort algorithm gets its name because small values tend to bubble up to the top.

Using Bubble Sort 395 32 9 74 21 Original list 9 32 74 21 Bubble sort compares the first two items and sorts them. 9 32 74 21 Bubble sort compares the next two adjacent items. If they are already sorted, then nothing happens. 9 32 21 74 After reaching the end of the list, bubble sort must go back through the list again. Figure 1-1: A bubble sort repetitively compares two adjacent items. 9 32 21 74 9 21 32 74 9 21 32 74 List is finally sorted. Basically the bubble sort algorithm works like this: 1. Compare two adjacent items. 2. Swap the two items if necessary. 3. Repeat Steps 1 and 2 with each pair of adjacent items. 4. Repeat Steps 1–3 to examine the entire list again until no swapping occurs and then the list is sorted. Although the bubble sort algorithm is easy to implement, it’s also the slowest and most inefficient algorithm because it must examine an entire list multiple times. For sorting a small list of pre-sorted data, the bubble sort algorithm works efficiently. For sorting large lists of unsorted data, any other sorting algorithm is much faster than the bubble sort algorithm, as shown in Figure 1-2. Book IV Chapter 1 Sorting Algorithms