A bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the list, compares adjacent elements and swaps them if they are in the wrong order.

The pass through the list is repeated until the list is sorted. The algorithm, which is a comparison sort, is named for the way smaller or larger elements “bubble” 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

Bubble sort has a worst-case and average complexity of *О*(*n*^{2}), where *n* is the number of items being sorted. Most practical sorting algorithms have substantially better worst-case or average complexity, often *O*(*n* log *n*).

Even other *О*(*n*^{2}) sorting algorithms, such as insertion sort, generally run faster than bubble sort, and are no more complex. Therefore, bubble sort is not a practical sorting algorithm.

### Step-by-step example

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;

- First Pass
- (
**5****1**4 2 8 ) → (**1****5**4 2 8 ), Here, algorithm compares the first two elements, and swaps since 5 > 1. - ( 1
**5****4**2 8 ) → ( 1**4****5**2 8 ), Swap since 5 > 4 - ( 1 4
**5****2**8 ) → ( 1 4**2****5**8 ), Swap since 5 > 2 - ( 1 4 2
**5****8**) → ( 1 4 2**5****8**), Now, since these elements are already in order (8 > 5), algorithm does not swap them. - Second Pass
- (
**1****4**2 5 8 ) → (**1****4**2 5 8 ) - ( 1
**4****2**5 8 ) → ( 1**2****4**5 8 ), Swap since 4 > 2 - ( 1 2
**4****5**8 ) → ( 1 2**4****5**8 ) - ( 1 2 4
**5****8**) → ( 1 2 4**5****8**)

Now, the array is already sorted, but the algorithm does not know if it is completed. The algorithm needs one additional **whole** pass without **any** swap to know it is sorted.

- Third Pass
- (
**1****2**4 5 8 ) → (**1****2**4 5 8 ) - ( 1
**2****4**5 8 ) → ( 1**2****4**5 8 ) - ( 1 2
**4****5**8 ) → ( 1 2**4****5**8 ) - ( 1 2 4
**5****8**) → ( 1 2 4**5****8**)

### Code

# Bubble Sort def bubbleSort(arr): n = len(arr) # Traverse through all array elements for i in range(n): # Last i elements are already in place for j in range(0, n-i-1): # traverse the array from 0 to n-i-1 # Swap if the element found is greater than the next element if arr[j] > arr[j+1] : arr[j], arr[j+1] = arr[j+1], arr[j] # test array of numbers arr = [95, 56, 25, 75, 43, 11, 80, 32, 64] bubbleSort(arr) print ("Sorted array is:") for i in range(len(arr)): print ("%d" %arr[i]),