Animated Sorting Algorithm Demo: Selection Sort

Algorithm

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

Properties

• Stable
• In place: O(1) extra space
• Ω(n²) comparisons
• Ω(n) swaps
• Completely non-adaptive

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.

Directions

• Click on to restart the animations.
• Click on a size number to change the size of the examples.
• Click on a cell to restart an individual animation.
• Click on a cell title to explore that input order.

Key

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

References

Algorithms in Java, Parts 1-4, 3rd edition by Robert Sedgewick. Addison Wesley, 2003.