The Selection sort algorithm

About the #sorting-algorithms series

The #sorting-algorithms series is a collection of posts about reimplemented sorting algorithms in JavaScript.

If you are not familiar with sorting algorithms, a quick introduction and the full list of reimplemented sorting algorithms can be found in the introduction post of the series on sorting algorithms in JavaScript.

If you feel comfortable with the concept of each sorting algorithm and only want to see the code, have a look at the summary post of the series. It removes all explanations and contains only the JavaScript code for all sorting algorithms discussed in the series.

Get the code on Github

Of course, all the code can also be found on Github in the repository sorting-algorithms-in-javascript.

A good way to compare all of them

Unlike the data structures, all sorting algorithms have the same goal and they can all take the same input data. So, for every sorting algorithms of the series, we are going sort an array of 10 numbers from 1 to 10.

By doing so we will be able to compare the different sorting algorithms more easily. Sorting algorithms are very sensitive to the input data so we will also try different input data to see how they affect the performances.

Definition

The Selection sort algorithm divides the input list into two parts: the sublist of items already sorted and the sublist of items remaining to be sorted that occupy the rest of the list. Initially, the sorted sublist is empty and the unsorted sublist is the entire input list. The algorithm proceeds by finding the smallest element in the unsorted sublist, exchanging it with the leftmost unsorted element, and moving the sublist boundaries one element to the right. From Wikipedia

Visualization

If you want to have a nice visualization of the algorithm, the visualgo.net website is a nice resource. You can play with many parameters and see which part of the algorithm is doing what.

Complexity

Time complexity

Best => O(n^2), Average => O(n^2), Worst => O(n^2)

To get a full overview of the time and space complexity of the Selection sort algorithm, have a look to this excellent Big O cheat sheet.

The code

For each sorting algorithm, we are going to look at 2 versions of the code. The first one is the final/clean version, the one that you should remember. The second one implements some counters in order to demonstrate the different time complexities depending of the inputs.

Clean version

// array to sort
var array = [9, 2, 5, 6, 4, 3, 7, 10, 1, 8];

// swap function helper
function swap(array, i, j) {
var temp = array[i];
array[i] = array[j];
array[j] = temp;
}

function selectionSort(array) {
for(var i = 0; i < array.length; i++) {
var min = i;
for(var j = i + 1; j < array.length; j++) {
if(array[j] < array[min]) {
min = j;
}
}
if(i !== min) {
swap(array, i, min);
}
}
return array;
}

console.log(selectionSort(array)); // => [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]

Version with counters

// sample of arrays to sort
var arrayRandom = [9, 2, 5, 6, 4, 3, 7, 10, 1, 8];
var arrayOrdered = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
var arrayReversed = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1];

// swap function helper
function swap(array, i, j) {
var temp = array[i];
array[i] = array[j];
array[j] = temp;
}

function selectionSort(array) {
var countOuter = 0;
var countInner = 0;
var countSwap = 0;

for(var i = 0; i < array.length; i++) {
countOuter++;
var min = i;
for(var j = i + 1; j < array.length; j++) {
countInner++;
if(array[j] < array[min]) {
min = j;
}
}
if(i !== min) {
countSwap++;
swap(array, i, min);
}
}

console.log('outer:', countOuter, 'inner:', countInner, 'swap:', countSwap);
return array;
}

selectionSort(arrayRandom.slice()); // => outer: 10 inner: 45 swap: 5
selectionSort(arrayOrdered.slice()); // => outer: 10 inner: 45 swap: 0
selectionSort(arrayReversed.slice()); // => outer: 10 inner: 45 swap: 5

Originally published at blog.benoitvallon.com.