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Selection Sort

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

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

Play All
Play animation
Random
Play animation
Nearly Sorted
Play animation
Reversed
Play animation
Few Unique

Algorithm:

for i = 1:n,
    k = i
    for j = i+1:n, if a[j] < a[k], k = j
    → invariant: a[k] smallest of a[i..n]
    swap a[i,k]
    → invariant: a[1..i] in final position
end

Discussion:

From the comparions presented here, one might conclude that selection sort should never be used. It does not adapt to the data in any way (notice that the four animations above run in lock step), so its runtime is always quadratic.

However, selection sort has the property of minimizing the number of swaps. In applications where the cost of swapping items is high, selection sort very well may be the algorithm of choice.

Key:

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

Properties:

  • Not stable
  • O(1) extra space
  • Θ(n2) comparisons
  • Θ(n) swaps
  • Not adaptive

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