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Add quick sort.
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‎README.md

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* [Insertion Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/insertion-sort)
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* [Heap Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/heap-sort)
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* [Merge Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/merge-sort)
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* [Quick Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/quick-sort)
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* [Quicksort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/quick-sort)
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* [Shellsort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/shell-sort)
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## Running Tests
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### Array Sorting Algorithms Complexity
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| Name | Best | Average | Worst | Memory | Stable |
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| --------------------- | :-------: | :-------: | :-------: | :-------: | :-------: |
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| **Bubble sort** | n | n^2 | n^2 | 1 | Yes |
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| **Insertion sort** | n | n^2 | n^2 | 1 | Yes |
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| **Selection sort** | n^2 | n^2 | n^2 | 1 | No |
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| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | No |
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| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Yes |
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| **Quick sort** | n log(n) | n log(n) | n^2 | log(n) | No |
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| Name | Best | Average | Worst | Memory | Stable |
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| --------------------- | :-------: | :-------: | :-----------: | :-------: | :-------: |
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| **Bubble sort** | n | n^2 | n^2 | 1 | Yes |
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| **Insertion sort** | n | n^2 | n^2 | 1 | Yes |
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| **Selection sort** | n^2 | n^2 | n^2 | 1 | No |
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| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | No |
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| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Yes |
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| **Quick sort** | n log(n) | n log(n) | n^2 | log(n) | No |
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| **Shell sort** | n log(n) | depends on gap sequence | n (log(n))^2 | 1 | No |

‎src/algorithms/sorting/SortTester.js

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expect(sorter.sort([''])).toEqual(['']);
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expect(sorter.sort(['a'])).toEqual(['a']);
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expect(sorter.sort(['aa', 'a'])).toEqual(['a', 'aa']);
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expect(sorter.sort(['aa', 'q', 'a', 'bbbb', 'ccc'])).toEqual(['q', 'a', 'aa', 'ccc', 'bbbb']);
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expect(sorter.sort(['aa', 'q', 'bbbb', 'ccc'])).toEqual(['q', 'aa', 'ccc', 'bbbb']);
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expect(sorter.sort(['aa', 'aa'])).toEqual(['aa', 'aa']);
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}
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const sorter = new SortingClass(callbacks);
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expect(sorter.sort(['bb', 'aa', 'c'])).toEqual(['c', 'bb', 'aa']);
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expect(sorter.sort(['aa', 'q', 'a', 'bbbb', 'ccc'])).toEqual(['q', 'a', 'aa', 'ccc', 'bbbb']);
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}
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static testAlgorithmTimeComplexity(SortingClass, arrayToBeSorted, numberOfVisits) {

‎src/algorithms/sorting/shell-sort/README.md

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# Shellsort
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Shellsort, also known as Shell sort or Shell's method,
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is an in-place comparison sort. It can be seen as either a
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generalization of sorting by exchange (bubble sort) or sorting
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by insertion (insertion sort). The method starts by sorting
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pairs of elements far apart from each other, then progressively
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reducing the gap between elements to be compared. Starting
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with far apart elements, it can move some out-of-place
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elements into position faster than a simple nearest neighbor
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exchange
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![Shellsort](https://upload.wikimedia.org/wikipedia/commons/d/d8/Sorting_shellsort_anim.gif)
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## How Shell Sort Works
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For our example and ease of understanding, we take the interval
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of `4`. Make a virtual sub-list of all values located at the
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interval of 4 positions. Here these values are
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`{35, 14}`, `{33, 19}`, `{42, 27}` and `{10, 44}`
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![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort_gap_4.jpg)
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We compare values in each sub-list and swap them (if necessary)
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in the original array. After this step, the new array should
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look like this
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![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort_step_1.jpg)
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Then, we take interval of 2 and this gap generates two sub-lists
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- `{14, 27, 35, 42}`, `{19, 10, 33, 44}`
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![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort_gap_2.jpg)
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We compare and swap the values, if required, in the original array.
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After this step, the array should look like this
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![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort_step_2.jpg)
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Finally, we sort the rest of the array using interval of value 1.
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Shell sort uses insertion sort to sort the array.
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![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort.jpg)
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## References
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* [Tutorials Point](https://www.tutorialspoint.com/data_structures_algorithms/shell_sort_algorithm.htm)
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* [Wikipedia](https://en.wikipedia.org/wiki/Shellsort)

‎src/algorithms/sorting/shell-sort/ShellSort.js

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import Sort from '../Sort';
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export default class ShellSort extends Sort {
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sort(originalArray) {
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// Prevent original array from mutations.
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const array = originalArray.slice(0);
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// Define a gap distance.
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let gap = Math.floor(array.length / 2);
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// Until gap is bigger then zero do elements comparisons and swaps.
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while (gap > 0) {
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// Go and compare all distant element pairs.
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for (let i = 0; i < (array.length - gap); i += 1) {
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let currentIndex = i;
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let gapShiftedIndex = i + gap;
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while (currentIndex >= 0) {
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// Call visiting callback.
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this.callbacks.visitingCallback(array[currentIndex]);
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// Compare and swap array elements if needed.
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if (this.comparator.lessThen(array[gapShiftedIndex], array[currentIndex])) {
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const tmp = array[currentIndex];
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array[currentIndex] = array[gapShiftedIndex];
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array[gapShiftedIndex] = tmp;
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}
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gapShiftedIndex = currentIndex;
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currentIndex -= gap;
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}
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}
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// Shrink the gap.
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gap = Math.floor(gap / 2);
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}
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// Return sorted copy of an original array.
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return array;
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}
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}

‎src/algorithms/sorting/shell-sort/__test__/ShellSort.test.js

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import ShellSort from '../ShellSort';
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import {
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equalArr,
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notSortedArr,
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reverseArr,
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sortedArr,
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SortTester,
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} from '../../SortTester';
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// Complexity constants.
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const SORTED_ARRAY_VISITING_COUNT = 320;
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const NOT_SORTED_ARRAY_VISITING_COUNT = 320;
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const REVERSE_SORTED_ARRAY_VISITING_COUNT = 320;
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const EQUAL_ARRAY_VISITING_COUNT = 320;
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describe('ShellSort', () => {
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it('should sort array', () => {
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SortTester.testSort(ShellSort);
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});
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it('should sort array with custom comparator', () => {
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SortTester.testSortWithCustomComparator(ShellSort);
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});
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it('should visit EQUAL array element specified number of times', () => {
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SortTester.testAlgorithmTimeComplexity(
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ShellSort,
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equalArr,
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EQUAL_ARRAY_VISITING_COUNT,
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);
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});
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it('should visit SORTED array element specified number of times', () => {
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SortTester.testAlgorithmTimeComplexity(
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ShellSort,
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sortedArr,
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SORTED_ARRAY_VISITING_COUNT,
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);
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});
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it('should visit NOT SORTED array element specified number of times', () => {
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SortTester.testAlgorithmTimeComplexity(
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ShellSort,
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notSortedArr,
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NOT_SORTED_ARRAY_VISITING_COUNT,
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);
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});
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it('should visit REVERSE SORTED array element specified number of times', () => {
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SortTester.testAlgorithmTimeComplexity(
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ShellSort,
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reverseArr,
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REVERSE_SORTED_ARRAY_VISITING_COUNT,
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);
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});
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});

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