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How it works

Selection Sort is the algorithm you'd use if you were sorting a row of books on a shelf by hand: find the shortest one, put it on the far left, then find the next shortest, and so on. 📚

The Real-World Analogy

Imagine a row of 10 numbered cards face-up on a table. You want them sorted, smallest to largest. You scan all the cards, find the smallest, and swap it with whatever card is in position 1. Now position 1 is locked in. You scan positions 2–10, find the smallest of those, and swap it into position 2. Repeat until you reach the end.

At every moment, the array has two regions:

[ sorted | unsorted ]

The sorted region grows by one element each pass.

How It Works (Step by Step)

1. Start at index 0.

2. Look through the rest of the array and find the index of the smallest value.

3. Swap that smallest value into the current index.

4. Move to the next index and repeat — but only scan what's still unsorted.

5. Stop when you've placed every element.

Tiny Trace — `[5, 2, 8, 1, 9]`

Pass 1: smallest in [5,2,8,1,9] is 1 → swap → [1, 2, 8, 5, 9]
Pass 2: smallest in   [2,8,5,9] is 2 → already there → [1, 2, 8, 5, 9]
Pass 3: smallest in     [8,5,9] is 5 → swap → [1, 2, 5, 8, 9]
Pass 4: smallest in       [8,9] is 8 → already there → [1, 2, 5, 8, 9]
Pass 5: only one element left → done!

Why Use It?

Minimum number of swaps: At most n - 1 swaps total. If writing to memory is expensive (e.g., flash storage), this matters.

Predictable behavior: It always does the same amount of work regardless of input order.

Easy to teach and code: Two nested loops, one swap. That's the whole thing.

Time & Space Complexity

Best case: O(n^2) — Even on an already-sorted array, it still scans the entire unsorted portion every pass.

Average case: O(n^2)

Worst case: O(n^2)

Space Complexity: O(1) — Sorts in-place, no extra arrays.

Swaps: O(n) — At most one swap per outer loop iteration.

Selection Sort vs Bubble Sort vs Insertion Sort

All three are O(n^2), but they trade off differently:

Algorithm	Best case	Swaps	Adaptive?	Stable?
Bubble Sort	O(n)	O(n^2)	Yes (early exit)	Yes
Insertion Sort	O(n)	O(n^2)	Yes (loves sorted)	Yes
Selection Sort	O(n^2)	O(n)	No	No

Pick selection sort when: writes are expensive and you only care about minimizing swaps. Skip it when: the data might already be partially sorted — insertion sort will crush it in that scenario.

A Note on Stability

Selection sort is not stable — equal elements can have their order flipped by the long-distance swap. If you need stable sorting (e.g., sorting records by a secondary key), reach for insertion sort or merge sort instead.

Related examples

Algorithms

Selection Sort in Python