Bubble sort algorithm tutorial

bubble 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.

here is a step-by-step explanation of the bubble sort algorithm:
1. start at the beginning of the list.
2. compare the first two elements. if the first element is greater than the second element, swap them.
3. move to the next pair of elements and repeat step 2.
4. continue this process until you reach the end of the list.
5. repeat steps 1-4 until no more swaps are needed, indicating that the list is sorted.

bubble sort is not the most efficient sorting algorithm, especially for large datasets, as it has a time complexity of o(n^2) in the worst case. however, it is easy to understand and implement.

here is an example of bubble sort algorithm implemented in python:

in this code snippet, the `bubble_sort` function takes an array `arr` as input and sorts it using the bubble sort algorithm. the function iterates over the array multiple times, comparing adjacent elements and swapping them if necessary. the process continues until no more swaps are needed, at which point the sorted array is returned.

you can run this code in a python environment to see how bubble sort works on a sample list of numbers.

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