Trace selection sort on the list [7, 2, 9, 1]. Order the states the list passes through.

1. [7, 2, 9, 1], initial list
2. [1, 2, 9, 7], smallest (1) swapped to front
3. [1, 2, 9, 7], 2 already in place, no change
4. [1, 2, 7, 9], 7 swapped into third place

Selection sort grows a sorted prefix one guaranteed-correct element per pass, simple to reason about, but each pass rescans the whole tail: $O(n^{2})$ total. Understanding why it is slow is the first step toward appreciating faster sorts.