Bubble Sort Program in C with Explanation

Bubble Sort Program in C with Explanation

Bubble Sort algorithm is an easy comparison sorting method which reiterates through a list, contrasts neighbors, and swaps them should they be out of sequence order. One goes on with this until the list is sorted, and bigger elements figuratively bubble up to their appropriate places.

The Way Bubble Sort Works

The bubble sort algorithm works by making several passes over the array to put the objects into their desired position which is usually ascending or descending. In the case of sorting in ascending order, the algorithm will scan elements and compare those that are next to each other and swap those two elements provided the element first is greater than the second.

Step-by-Step Process

As an example, let there be an array to be sorted in the ascending order:

° First Iteration: Then the comparison of the first and the second elements of the array starts. The two elements are exchanged in case one of them is greater than the other one. This comparison and possible swapping then happens with the second and third elements and so on and so forth until the end of the array is reached.

° Subsequent Iterations: The same procedure of comparison and swapping is again done again in further iterations. At the end of every complete iteration the largest unsorted element is shifted to the proper position at the last of the unsorted segment of the array. The comparisons at every next stage are made only until the last unsorted element. An array is said to be overflowed when the unordered elements are put in place of their correct places.

This is illustrated by an example:

• The algorithm compares the first two elements (5 and 1), and swaps them since 5 > 1 hence, the algorithm then leads to.
• then compared 5 and 4, doing a swap to obtain.
• Comparison of 5 with 2 results in a swap giving a yield of.
• Last, 5 and 8 are compared, and there is no exchange since these two numbers are sorted.

This pass relocates the biggest element (8) at the last position in the unsorted area. This is repeated in the next pass until the end when the array would be fully sorted.

Time and Space Complexity of Bubble Sort

Knowledge of the performance properties of the sorting algorithms i.e. time and space complexities of the sorting algorithms plays a very important role in choosing the most suitable algorithm to be used to perform a certain task.

Time Complexity

Bubble Sort has time complexity that is different when used on an array in different initial states:

• Worst-Case Complexity: The worst-case scenario of Bubble Sort:𝑂(𝑛2)O(n2). This is when the array is made of the biggest to smallest value and is to be made into smallest to the biggest one such that it takes the maximum number of comparisons and swaps. Here the algorithm traverses the array about n 1 times, and each in turn, and each makes a smaller and smaller number of comparisons, which added up to 𝑛(𝑛−1)/2 Approximately, a number of n(n-1)/2 comparisons. 𝑛2n2.
• Average-Case Complexity: The average-case time complexity is also 𝑂(𝑛2)O(n2) . This is true in the cases where array elements are in some random (not ascending or descending) order.
• Best-Case Complexity: Bubble Sort has best-case time complexity: O(n). This is when the array is almost sorted, and the algorithm has to make only one pass to be sure that it does not need to make any swaps. Improved versions of Bubble Sort may terminate early when they find during a pass that no swaps have taken place, so they are more efficient on already sorted or nearly sorted arrays.

Space Complexity

The space complexity of Bubble Sort is O(1). This is to say that it is an in-place algorithm, in the sense that it has no more than a constant extra memory needed (to store a temporary variable used during swaps) no matter what size of input is to be processed.

Sorting with Advantages and Disadvantages Bubble Sort

Despite its simplicity, Bubble Sort has certain advantages and disadvantages that determine its practice.

Advantages

Simplicity: Based on simplicity, bubble sort is simple to comprehend as well as easy to implement; hence, a good algorithm to teach a basic sorting algorithm.

Minimal Memory: It needs no more memory than a single temporary variable to act as a stack to perform swapping, that is, it is an in-place sorting algorithm.

Stability: The Bubble Sort is a stable sorting algorithm i.e. input elements with same values are ending in their relative order in the result of the sort.

Adaptive: It is able to work effectively on nearly-sorted lists and can beat other algorithms such as quicksort on these special cases.

Disadvantages

Inefficiency on Large Datasets: Lack of Proper Result in an average and worst-case setting of time complexity. 𝑂(𝑛2)O(n2) so Bubble sort is extremely slow with large amounts of data and as such is not practical to most real world uses involving large amounts of data.

Little Real Life Uses: Bubble Sort has limited practical use in real life because it has high time complexity and is almost exclusively utilized as a demonstration method to illustrate how sorting functions. More effective algorithms such as quick sort, time sort or merge sort are usually used.

Performs many writes and cache misses: Because a wide variety of CPU hardware may be affected, this may translate into generally worse performance than other sorting algorithms such as insertion sort.

C Program of Bubble Sort

Bubble Sort in C is done through the use of inner loops to traverse the array taking its elements two by two, and comparing.

C Code explanation:

° #include <stdio.h>: This is a line that includes the standard input/output library in C language and gives functions such as the printf to print out the output.

° void bubbleSort(int array, int size): The function accepts an array as (integer) parameter and size. It has loops within loops, to apply the sorting logic.

• Outer Loop (for (int step = 0; step < size -1; ++step)): It is executed size - 1 times. At every iteration, the biggest unsorted element rises to the top, to its correct location at the end of the unused portion of the array.
• Inner Loop (for (int i = 0; i <  - step - 1; +i)): Inner loop loops through the part of the array that is not sorted. The step - 1 part guarantees that the element that has been sorted before in the previous passes will not be compared again.
• Comparison and Swap (if (array > array)): Within the inner loop adjacent elements array and array are compared. In case array is larger than array (in case of ascending order) then array and array are swapped through variable temp. In order to sort in descending order the > sign must be replaced with <.

° void printArray(int array, int size): It is a helper function and traverses the array and prints its elements.

° int main(): It is the main part in which the program execution starts.

•  int data [{ - 2, 45, 0, 11, - 9 }]: The data is an array of type integer, which is not sorted.
• int size = sizeof(data)/sizeof(data);: This will give the amount of data within the array of data.
• bubbleSort(data, size);: This is to invoke bubbleSort.
• printf("Sorted Array in Ascending Order:"");: A line is printed to give out the resulting message of the sorted array.
• printArray(data, size);: The sorting is printed using the printArray command.

C Optimized Bubble Sort Program

Bubble Sort may terminate early when a pass completes without any two-way exchanges, thus the array is already in order. With such an optimization, a boolean variable (or int flag in C) is added to indicate whether or not there were swaps.

Description of Optimised C Code:

• bool swapped = false;: A swapped boolean is set to false as every iteration of the outer loop starts.
• swapped = true;: In the inner loop swapped is true in case there is any element swapping.
• if (swapped == false) { break; }: At the end of every entire run within the inner loop, this condition ascertains the status of swapped, whether it is false or not. When no swaps are made the array should already be sorted and the program breaks the outer loop using break and this will make a huge difference in the running time of the partially or fully sorted arrays.

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