Selection Sort Visualization & Simulator

Q: What is the time complexity of selection sort?

O(n²) for best, average and worst cases because it always scans the whole unsorted part. Space complexity is O(1).

About this visualization

Selection sort divides the list into a sorted part and an unsorted part. Each round it scans the unsorted part for the smallest item and swaps it to the front. It always makes the same number of comparisons but at most n − 1 swaps, which matters when writing data is expensive.

How it works

Scan the unsorted part to find the smallest item.
Swap it with the first item of the unsorted part.
Grow the sorted part by one and repeat.

Worked example

Sort [64, 25, 12, 22, 11]. Round 1 finds 11 and swaps it with 64 → [11, 25, 12, 22, 64]. Round 2 finds 12 → [11, 12, 25, 22, 64]. Round 3 finds 22 → [11, 12, 22, 25, 64]. Round 4 finds 25 already in place. That is 10 comparisons and 3 swaps.

Enter these numbers in the simulator above to see every step.

Complexity and properties

Best case	$O(n^{2})$
Average case	$O(n^{2})$
Worst case	$O(n^{2})$
Space	$O(1)$
Stable	No
In-place	Yes

Always makes at most n − 1 swaps, which helps when writes are expensive.

When to use it

Understanding the 'find the minimum' idea behind sorting.
Situations where the number of writes must be minimised.
Comparing with insertion sort on nearly sorted data.

Frequently asked questions

What is the time complexity of selection sort?

$O(n^{2})$ for best, average and worst cases because it always scans the whole unsorted part. Space complexity is $O(1)$ .

Is selection sort stable?

The usual swap-based version is not stable, because swapping can move an equal item past another.

How many swaps does selection sort make?

At most n − 1 swaps, one per round, which is fewer than bubble sort or insertion sort.