![]() Hence, the next iteration need not include already sorted elements. 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. Procedure bubbleSort( list : array of items ) Pseudocode of BubbleSort algorithm can be written as follows − the array requires no more processing to be sorted, it will come out of the loop. ![]() To ease-out the issue, we use one flag variable swapped which will help us see if any swap has happened or not. This may cause a few complexity issues like what if the array needs no more swapping as all the elements are already ascending. We observe in algorithm that Bubble Sort compares each pair of array element unless the whole array is completely sorted in an ascending order. We further assume that swap function swaps the values of the given array elements. We assume list is an array of n elements. Now we should look into some practical aspects of bubble sort. Notice that after each iteration, at least one value moves at the end.Īnd when there's no swap required, bubble sorts learns that an array is completely sorted. After the second iteration, it should look like this − To be precise, we are now showing how an array should look like after each iteration. After one iteration, the array should look like this − We find that we have reached the end of the array. Then we move to the next two values, 35 and 10. We find that both are in already sorted positions. We find that 27 is smaller than 33 and these two values must be swapped. In this case, value 33 is greater than 14, so it is already in sorted locations. Bubble sort takes Ο(n 2) time so we're keeping it short and precise.īubble sort starts with very first two elements, comparing them to check which one is greater. We take an unsorted array for our example. This algorithm is not suitable for large data sets as its average and worst case complexity are of Ο(n 2) where n is the number of items. 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. Finally, the array gets sorted.Bubble sort is a simple sorting algorithm. This continues until for n iterations where n = number of elements in the array. This is nothing but a recursive argument on the remaining array. By the above recursive argument, this second largest array will then reach the last position in the remaining array (). Here, the largest element in the rest of the array (which is 4) will be nothing but the second largest element in the array. Now that the largest element has reached its correct position (for instance, 5 reached the last position), we can simply ignore it and concentrate on the rest of the array ( in the above case). So, at the end of the first pass, the largest element will always reach its correct position. This is because this largest element will always break the desired order. ![]() In the first “pass” through the array, the largest element will always get swapped until it is placed to the extreme right. This exactly is how bubble sort in C works.Īs an example, check this graphic that pictorially depicts how bubble sort works. Before we get into the details of the sorting algorithm, let us understand the problem statement. This generally means that we want the data to be sorted in ascending order. Given a data that is sorted in ascending order, reverse it and you will get the data in descending order.ĭue to the similar nature of the 2 orders, we often drop the actual order and we say - we want to sort the data. Descending order: descending order is the exact opposite of ascending order.Here, the “smaller than” relation is actually the “<” operator. As a simple example, the numbers 1, 2, 3, 4, 5 are sorted in ascending order. ![]() This “smaller than” relation is an ordered relation over the set from which the data is taken. Ascending order: while sorting the data in ascending order, we try to arrange the data in a way such that each element is in some way “smaller than” its successor.The arrangement of data in a particular order is called as sorting of the data by that order. finding "Joe" in an attendance register of 100 students. These data arrangements give easier access to data for future use for ex. Another example is the attendance register at school/college which contains our names arranged in alphabetical order. For instance, during our school days, we are told to stand in the queue based on our heights. Often in real life, we are supposed to arrange data in a particular order. Sorting forms a great case study for those who want to learn Data Structures and Algorithms. Sorting of data is one of the most fundamental, yet important problem in computer science. Bubble Sort Algorithm in C - Introduction.
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