Bubble sort is a simple sorting algorithm. This sorting algorithm is comparison-based algorithm in which each pair of adjacent elements is compared and the elements are swapped if they are not in order. This algorithm is not suitable for large data sets as its average and worst case complexity are of Ο(n2) where n is the number of items.
We observe in algorithm that Bubble Sort compares each pair of array element unless the whole array is completely sorted in an ascending order. This may cause a few complexity issues like what if the array needs no more swapping as all the elements are already ascending.
Bubble Sort Algorithm Data Structures
One more issue we did not address in our original algorithm and its improvised pseudocode, is that, after every iteration the highest values settles down at the end of the array. Hence, the next iteration need not include already sorted elements. For this purpose, in our implementation, we restrict the inner loop to avoid already sorted values.
In this article, we will discuss the Bubble sort Algorithm. The working procedure of bubble sort is simplest. This article will be very helpful and interesting to students as they might face bubble sort as a question in their examinations. So, it is important to discuss the topic.
Bubble sort works on the repeatedly swapping of adjacent elements until they are not in the intended order. It is called bubble sort because the movement of array elements is just like the movement of air bubbles in the water. Bubbles in water rise up to the surface; similarly, the array elements in bubble sort move to the end in each iteration.
Although it is simple to use, it is primarily used as an educational tool because the performance of bubble sort is poor in the real world. It is not suitable for large data sets. The average and worst-case complexity of Bubble sort is O(n2), where n is a number of items.
Bubble sort is a simple and well-known sorting algorithm. It is used in practice once in a blue moon and its main application is to make an introduction to the sorting algorithms. Bubble sort belongs to O(n2) sorting algorithms, which makes it quite inefficient for sorting large data volumes. Bubble sort is stable and adaptive.
You can imagine that on every step big bubbles float to the surface and stay there. At the step, when no bubble moves, sorting stops. Let us see an example of sorting an array to make the idea of bubble sort clearer.
Average and worst case complexity of bubble sort is O(n2). Also, it makes O(n2) swaps in the worst case. Bubble sort is adaptive. It means that for almost sorted array it gives O(n) estimation. Avoid implementations, which don't check if the array is already sorted on every step (any swaps made). This check is necessary, in order to preserve adaptive property.
One more problem of bubble sort is that its running time badly depends on the initial order of the elements. Big elements (rabbits) go up fast, while small ones (turtles) go down very slow. This problem is solved in the Cocktail sort.
Rabbit example. Array 6, 1, 2, 3, 4, 5 is almost sorted too, but it takes O(n) iterations to sort it. Element 6 is a rabbit. This example demonstrates adaptive property of the bubble sort.
Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed. These passes through the list are repeated until no swaps had to be performed during a pass, meaning that the list has become fully sorted. The algorithm, which is a comparison sort, is named for the way the larger elements "bubble" up to the top of the list.
This simple algorithm performs poorly in real world use and is used primarily as an educational tool. More efficient algorithms such as quicksort, timsort, or merge sort are used by the sorting libraries built into popular programming languages such as Python and Java.[2][3]
While any sorting algorithm can be made O ( n ) \displaystyle O(n) on a presorted list simply by checking the list before the algorithm runs, improved performance on almost-sorted lists is harder to replicate.
Various efforts have been made to eliminate turtles to improve upon the speed of bubble sort. Cocktail sort is a bi-directional bubble sort that goes from beginning to end, and then reverses itself, going end to beginning. It can move turtles fairly well, but it retains O ( n 2 ) \displaystyle O(n^2) worst-case complexity. Comb sort compares elements separated by large gaps, and can move turtles extremely quickly before proceeding to smaller and smaller gaps to smooth out the list. Its average speed is comparable to faster algorithms like quicksort.
Take an array of numbers "5 1 4 2 8", and sort the array from lowest number to greatest number using bubble sort. In each step, elements written in bold are being compared. Three passes will be required;
Although bubble sort is one of the simplest sorting algorithms to understand and implement, its O(n2) complexity means that its efficiency decreases dramatically on lists of more than a small number of elements. Even among simple O(n2) sorting algorithms, algorithms like insertion sort are usually considerably more efficient.
Due to its simplicity, bubble sort is often used to introduce the concept of an algorithm, or a sorting algorithm, to introductory computer science students. However, some researchers such as Owen Astrachan have gone to great lengths to disparage bubble sort and its continued popularity in computer science education, recommending that it no longer even be taught.[4]
The Jargon File, which famously calls bogosort "the archetypical [sic] perversely awful algorithm", also calls bubble sort "the generic bad algorithm".[5] Donald Knuth, in The Art of Computer Programming, concluded that "the bubble sort seems to have nothing to recommend it, except a catchy name and the fact that it leads to some interesting theoretical problems", some of which he then discusses.[6]
Bubble sort is asymptotically equivalent in running time to insertion sort in the worst case, but the two algorithms differ greatly in the number of swaps necessary. Experimental results such as those of Astrachan have also shown that insertion sort performs considerably better even on random lists. For these reasons many modern algorithm textbooks avoid using the bubble sort algorithm in favor of insertion sort.
Bubble sort also interacts poorly with modern CPU hardware. It produces at least twice as many writes as insertion sort, twice as many cache misses, and asymptotically more branch mispredictions.[citation needed] Experiments by Astrachan sorting strings in Java show bubble sort to be roughly one-fifth as fast as an insertion sort and 70% as fast as a selection sort.[4]
In computer graphics bubble sort is popular for its capability to detect a very small error (like swap of just two elements) in almost-sorted arrays and fix it with just linear complexity (2n). For example, it is used in a polygon filling algorithm, where bounding lines are sorted by their x coordinate at a specific scan line (a line parallel to the x axis) and with incrementing y their order changes (two elements are swapped) only at intersections of two lines. Bubble sort is a stable sort algorithm, like insertion sort.
In 2007, former Google CEO Eric Schmidt asked then-presidential candidate Barack Obama during an interview about the best way to sort one million integers; Obama paused for a moment and replied: "I think the bubble sort would be the wrong way to go."[10][11]
Bubble sort, also known as sinking sort, is the easiest sorting algorithm. It works on the idea of repeatedly comparing the adjacent elements, from left to right, and swapping them if they are out-of-order.
Since it compares all the elements one by one, bubble sort is a slow algorithm and performs inefficiently in real-world scenarios. It is generally used for educational purposes or to determine if the sorted given list is already sorted or not.
In the first pass, the highest element (5 in this case) was bubbled out on the right side of the list. Similarly, after each iteration, the largest among the unsorted elements was placed at its position. This is the reason why this sorting algorithm is known as bubble sort.
Element 2 took a significant number of passes to arrange itself at its position in the sorted list. Thus, if any element of the list takes more passes, it is known as the turtle. Whereas element 5 took only one pass to reach its position, which is rare for bubble sort. Such elements are known as rabbits due to a low number of passes.
Notice how we used bubble sort to sort cars according to their speed. Here, with every overtake we were comparing the speeds of the cars, and if the car at the back was faster than the car at the front, they exchanged their positions, just like it is done in bubble sort.
The bubble sort algorithm is a reliable sorting algorithm. This algorithm has a worst-case time complexity of O(n2). The bubble sort has a space complexity of O(1). The number of swaps in bubble sort equals the number of inversion pairs in the given array. When the array elements are few and the array is nearly sorted, bubble sort is effective and efficient.
The process of traversing the list is repeated until the list is sorted. The comparison sort algorithm is named after smaller or larger elements "bubble" at the top of the list. The following image depicts the real-time implementation of Bubble Sort.
Bubble Sort in Data Structure is one of the easiest sorting algorithm being used. The idea behind this algorithm is to repeatedly compare the elements one by one and swap the adjacent elements to bring them in the correct sorted order. Thus if there are n number of elements in the array, then each element will undergo n-1 comparisons. This way, after comparing one element with other elements in the array, an element is placed at its place in the sorted list just like a bubble rises up and move. Thus this algorithm is known as Bubble Sort. Several comparisons are more; thus, its complexity is more. 2ff7e9595c
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