Bubble Sort is a simple sorting algorithm that repeatedly compares adjacent elements and swaps them if they are in the wrong order.
Large elements “bubble up” to the end of the list, like bubbles in water — hence the name.
Bubble Sort is a comparison-based sorting algorithm in which adjacent elements are repeatedly swapped if they are in the wrong order until the array becomes sorted.
Steps:
A = [5, 1, 4, 2, 8]
| Comparison | Action |
|---|---|
| 5 > 1 | Swap → [1, 5, 4, 2, 8] |
| 5 > 4 | Swap → [1, 4, 5, 2, 8] |
| 5 > 2 | Swap → [1, 4, 2, 5, 8] |
| 5 < 8 | No swap |
👉 Largest (8) is in correct position
| Comparison | Action |
|---|---|
| 1 < 4 | No swap |
| 4 > 2 | Swap → [1, 2, 4, 5, 8] |
| 4 < 5 | No swap |
No swaps needed → array already sorted
[1, 2, 4, 5, 8]
BubbleSort(A, n)
1. for i = 0 to n-1
2. for j = 0 to n-i-2
3. if A[j] > A[j+1]
4. swap(A[j], A[j+1])
def bubble_sort(arr):
n = len(arr)
for i in range(n):
for j in range(0, n - i - 1):
if arr[j] > arr[j + 1]:
arr[j], arr[j + 1] = arr[j + 1], arr[j]
return arr
# Example
arr = [5, 1, 4, 2, 8]
result = bubble_sort(arr)
print("Sorted Array:", result)
Sorted Array: [1, 2, 4, 5, 8]
| Case | Complexity |
|---|---|
| Best Case | O(n) (already sorted) |
| Worst Case | O(n²) |
| Average Case | O(n²) |
| Feature | Bubble Sort | Selection Sort | Insertion Sort |
|---|---|---|---|
| Speed | Slow | Slow | Medium |
| Complexity | O(n²) | O(n²) | O(n²) |
| Stability | Yes | No | Yes |
| Best Use | Small data | Small data | Nearly sorted data |