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# Bubble Sort

Animation, code, analysis, and discussion of bubble sort on 4 initial conditions.

How to use: Press **"Play all"**, or choose the button.

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## Algorithm:

```
for i = 1:n,
swapped = false
for j = n:i+1,
if a[j] < a[j-1],
swap a[j,j-1]
swapped = true
→ invariant: a[1..i] in final position
break if not swapped
end
```

## Discussion:

Bubble sort has many of the same properties as insertion sort, but has slightly higher overhead. In the case of nearly sorted data, bubble sort takes O(n) time, but requires at least 2 passes through the data (whereas insertion sort requires something more like 1 pass).

## Key:

- Black values are sorted.
- Gray values are unsorted.
- A red triangle marks the algorithm position.

## Properties:

- Stable
- O(1) extra space
- O(n
^{2}) comparisons and swaps - Adaptive: O(n) when nearly sorted