bubble sort algorithm

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bubble sort algorithm tutorial

*overview:*
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. the algorithm gets its name from the way smaller elements "bubble" to the top of the list.

*characteristics:*
*time complexity:*
best case: \(o(n)\) (when the array is already sorted)
average case: \(o(n^2)\)
worst case: \(o(n^2)\)

*space complexity:* \(o(1)\) (in-place sorting)

*stable:* yes (does not change the relative order of elements with equal keys)

*adaptive:* can be optimized to stop early if the list is already sorted.

how bubble sort works

1. start at the beginning of the array.
2. compare the first two adjacent elements.
3. if the first element is greater than the second, swap them.
4. move to the next pair of adjacent elements and repeat the comparison and possible swap.
5. continue this process for the entire array until no swaps are needed, indicating that the array is sorted.

code example

here’s a simple implementation of the bubble sort algorithm in python:

```python
def bubble_sort(arr):
n = len(arr)
traverse through all array elements
for i in range(n):
swapped = false
last i elements are already in place, no need to check them
for j in range(0, n-i-1):
compare the adjacent elements
if arr[j] arr[j+1]:
swap if they are in the wrong order
arr[j], arr[j+1] = arr[j+1], arr[j]
swapped = true
if no elements were swapped, the array is sorted
if not swapped:
break

example usage
if _name_ == "__main__":
sample_array = [64, 34, 25, 12, 22, 11, 90]
print("original array:", sample_array)
bubble_sort(sample_array)
print("sorted array:", sample_array)
```

explanation of the code

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#BubbleSort #SortingAlgorithm #numpy
Bubble sort
sorting algorithm
comparison sort
stable sort
time complexity
space complexity
algorithm efficiency
data structure
iterative sorting
in-place sorting
best case scenario
worst case scenario
average case scenario
educational algorithm
programming fundamentals