Bubble Sort: A Comparison-Based Sorting Technique

Bubble Sort: A Simple But Inefficient Sorting Algorithm

Bubble sort is one of the simplest sorting algorithms that works by repeatedly swapping the adjacent elements if they are in the wrong order. It is easy to understand and implement, but it is very slow and inefficient for large data sets. In this article, we will learn about the bubble sort algorithm, its complexity analysis, its advantages and disadvantages, its applications, its optimization, and its comparison with other sorting algorithms.

What is Bubble Sort?

Bubble sort is a sorting algorithm that compares two adjacent elements and swaps them until they are in the intended order. Just like the movement of air bubbles in the water that rise up to the surface, each element of the array moves to the end in each iteration. Therefore, it is called a bubble sort. It is also referred to as comparison or sinking sort.

bubble sort

How does Bubble Sort work?

Suppose we are trying to sort the elements in ascending order. The algorithm works as follows:

• Starting from the first index, compare the first and the second elements. If the first element is greater than the second element, they are swapped.

• Now, compare the second and the third elements. Swap them if they are not in order.

• The above process goes on until the last element.

• After each iteration, the largest element among the unsorted elements is placed at the end.

• In each iteration, the comparison takes place up to the last unsorted element.

• The array is sorted when all the unsorted elements are placed at their correct positions.

Here is an example of bubble sort visualized:

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The above image shows how bubble sort works on an array of 6 elements. The red bars indicate the elements that are being compared and swapped. The green bars indicate the elements that are already sorted. The number of iterations is equal to the number of elements minus one.

Pseudocode of Bubble Sort

Here is a pseudocode of bubble sort algorithm:

procedure bubbleSort(A : list of sortable items) n := length(A) for i := 0 to n-1 inclusive do for j := 0 to n-i-1 inclusive do //the elements aren't in the right order if A[j] > A[j+1] then //swap the elements swap(A[j], A[j+1]) end if end for end for end procedure

Complexity Analysis of Bubble Sort

In this section, we will analyze the time and space complexity of bubble sort algorithm.

Time Complexity

The time complexity of an algorithm is a measure of how much time it takes to run based on the input size. The time complexity of bubble sort depends on how many comparisons and swaps it performs in each iteration.

• The worst-case time complexity of bubble sort is O(N), where N is the number of elements in the array. This happens when the array is in reverse order and every element needs to be swapped in every iteration.

• The best-case time complexity of bubble sort is O(N), where N is the number of elements in the array. This happens when the array is already sorted and no swaps are needed in any iteration.

• The average-case time complexity of bubble sort is also O(N), where N is the number of elements in the array. This happens when the array is partially sorted and some swaps are needed in some iterations.

Here is a table that summarizes the time complexity of bubble sort:

Case

Time Complexity

Worst

O(N)

Best

O(N)

Average

O(N)

Space Complexity

The space complexity of an algorithm is a measure of how much extra space it requires to run based on the input size. The space complexity of bubble sort is O(1), which means it requires a constant amount of extra space regardless of the input size. This is because bubble sort only uses one temporary variable to swap the elements and does not require any additional data structures.

Advantages and Disadvantages of Bubble Sort

In this section, we will discuss the pros and cons of bubble sort algorithm.

Advantages

• Bubble sort is easy to understand and implement. It does not require any complex logic or data structures.

• Bubble sort is stable, which means it preserves the relative order of equal elements in the array. This is important for some applications that rely on the original order of the data.

• Bubble sort can detect if the array is already sorted in the first iteration and stop the sorting process. This makes it efficient for nearly sorted arrays.

• Bubble sort does not require much extra space. It only uses one temporary variable to swap the elements.

Disadvantages

• Bubble sort is very slow and inefficient for large data sets. It has a quadratic time complexity, which means it takes much longer to sort as the input size increases.

• Bubble sort performs many unnecessary comparisons and swaps even if the array is partially sorted. It does not adapt to the existing order of the data.

• Bubble sort is not suitable for parallel or distributed computing. It cannot take advantage of multiple processors or machines to speed up the sorting process.

• Bubble sort is not widely used in real-world applications. There are many other sorting algorithms that are faster and more efficient than bubble sort.

Applications of Bubble Sort

Despite its drawbacks, bubble sort can be useful for some specific applications. Here are some examples:

• Bubble sort can be used to teach the basic concepts of sorting algorithms to beginners. It helps them understand how comparison and swapping work and how to analyze the complexity of an algorithm.

• Bubble sort can be used to sort small data sets that are already nearly sorted. It can perform well in such cases as it can detect the sorted order in the first iteration and stop the sorting process.

• Bubble sort can be used to sort data that is stored in a linked list or an array with limited memory. It does not require any extra space or data structures to perform the sorting.

• Bubble sort can be used to implement other sorting algorithms such as cocktail shaker sort, comb sort, or gnome sort. These algorithms are variations of bubble sort that improve its performance by modifying some aspects of its logic.

Optimization of Bubble Sort

In this section, we will learn how to optimize bubble sort algorithm to improve its performance.

How to optimize Bubble Sort?

One way to optimize bubble sort is to keep track of the last swapped position in each iteration. This position indicates the boundary of the unsorted elements in the array. Therefore, we do not need to compare or swap any elements beyond this position in the next iteration. This reduces the number of comparisons and swaps and improves the time complexity of bubble sort.

Pseudocode of Optimized Bubble Sort

Here is a pseudocode of optimized bubble sort algorithm:

procedure optimizedBubbleSort(A : list of sortable items) n := length(A) //initialize the boundary as n-1 boundary := n-1 //repeat until no swaps are made repeat //initialize a flag to indicate if any swap is made swapped := false //initialize a new boundary as 0 newBoundary := 0 for i := 0 to boundary-1 inclusive do //the elements aren't in the right order if A[i] > A[i+1] then //swap the elements swap(A[i], A[i+1]) //set the flag to true //update the new boundary as i newBoundary := i end if end for //update the boundary as the new boundary boundary := newBoundary until not swapped end procedure

Comparison with other Sorting Algorithms

In this section, we will compare bubble sort with some other common sorting algorithms such as selection sort, insertion sort, merge sort, and quick sort. We will compare them based on their time complexity, space complexity, stability, and adaptability.

Algorithm

Time Complexity

Space Complexity

Stability

Adaptability

Bubble Sort

O(N)

O(1)

Yes

No

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