Add counting sort.

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Oleksii Trekhleb 2018-05-29 07:29:28 +03:00
parent b1a613e03e
commit 0c1f6851d5
5 changed files with 202 additions and 0 deletions

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@ -80,6 +80,7 @@ a set of rules that precisely defines a sequence of operations.
* [Merge Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/merge-sort) * [Merge Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/merge-sort)
* [Quicksort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/quick-sort) - in-place and non-in-place implementations * [Quicksort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/quick-sort) - in-place and non-in-place implementations
* [Shellsort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/shell-sort) * [Shellsort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/shell-sort)
* [Counting Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/counting-sort)
* **Tree** * **Tree**
* [Depth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/depth-first-search) (DFS) * [Depth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/depth-first-search) (DFS)
* [Breadth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/breadth-first-search) (BFS) * [Breadth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/breadth-first-search) (BFS)
@ -225,3 +226,4 @@ Below is the list of some of the most used Big O notations and their performance
| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Yes | | **Merge sort** | n log(n) | n log(n) | n log(n) | n | Yes |
| **Quick sort** | n log(n) | n log(n) | n^2 | log(n) | No | | **Quick sort** | n log(n) | n log(n) | n^2 | log(n) | No |
| **Shell sort** | n log(n) | depends on gap sequence | n (log(n))^2 | 1 | No | | **Shell sort** | n log(n) | depends on gap sequence | n (log(n))^2 | 1 | No |
| **Counting sort** | n + r | n + r | n + r | n + r | Yes |

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@ -11,6 +11,7 @@ export class SortTester {
expect(sorter.sort([1])).toEqual([1]); expect(sorter.sort([1])).toEqual([1]);
expect(sorter.sort([1, 2])).toEqual([1, 2]); expect(sorter.sort([1, 2])).toEqual([1, 2]);
expect(sorter.sort([2, 1])).toEqual([1, 2]); expect(sorter.sort([2, 1])).toEqual([1, 2]);
expect(sorter.sort([3, 4, 2, 1, 0, 0, 4, 3, 4, 2])).toEqual([0, 0, 1, 2, 2, 3, 3, 4, 4, 4]);
expect(sorter.sort(sortedArr)).toEqual(sortedArr); expect(sorter.sort(sortedArr)).toEqual(sortedArr);
expect(sorter.sort(reverseArr)).toEqual(sortedArr); expect(sorter.sort(reverseArr)).toEqual(sortedArr);
expect(sorter.sort(notSortedArr)).toEqual(sortedArr); expect(sorter.sort(notSortedArr)).toEqual(sortedArr);

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@ -0,0 +1,69 @@
import Sort from '../Sort';
export default class CountingSort extends Sort {
/**
* @param {number[]} originalArray
* @param {number} [biggestElement]
*/
sort(originalArray, biggestElement = 0) {
// Detect biggest element in array in order to build in order to build
// number bucket array later.
let detectedBiggestElement = biggestElement;
if (!detectedBiggestElement) {
originalArray.forEach((element) => {
// Visit element.
this.callbacks.visitingCallback(element);
if (this.comparator.greaterThan(element, detectedBiggestElement)) {
detectedBiggestElement = element;
}
});
}
// Init buckets array.
// This array will hold frequency of each number from originalArray.
const buckets = Array(detectedBiggestElement + 1).fill(0);
originalArray.forEach((element) => {
// Visit element.
this.callbacks.visitingCallback(element);
buckets[element] += 1;
});
// Add previous frequencies to the current one for each number in bucket
// to detect how many numbers less then current one should be standing to
// the left of current one.
for (let bucketIndex = 1; bucketIndex < buckets.length; bucketIndex += 1) {
buckets[bucketIndex] += buckets[bucketIndex - 1];
}
// Now let's shift frequencies to the right so that they show correct numbers.
// I.e. if we won't shift right than the value of buckets[5] will display how many
// elements less than 5 should be placed to the left of 5 in sorted array
// INCLUDING 5th. After shifting though this number will not include 5th anymore.
buckets.pop();
buckets.unshift(0);
// Now let's assemble sorted array.
const sortedArray = Array(originalArray.length).fill(null);
for (let elementIndex = 0; elementIndex < originalArray.length; elementIndex += 1) {
// Get the element that we want to put into correct sorted position.
const element = originalArray[elementIndex];
// Visit element.
this.callbacks.visitingCallback(element);
// Get correct position of this element in sorted array.
const elementSortedPosition = buckets[element];
// Put element into correct position in sorted array.
sortedArray[elementSortedPosition] = element;
// Increase position of current element in the bucket for future correct placements.
buckets[element] += 1;
}
// Return sorted array.
return sortedArray;
}
}

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@ -0,0 +1,61 @@
# Counting Sort
In computer science, **counting sort** is an algorithm for sorting
a collection of objects according to keys that are small integers;
that is, it is an integer sorting algorithm. It operates by
counting the number of objects that have each distinct key value,
and using arithmetic on those counts to determine the positions
of each key value in the output sequence. Its running time is
linear in the number of items and the difference between the
maximum and minimum key values, so it is only suitable for direct
use in situations where the variation in keys is not significantly
greater than the number of items. However, it is often used as a
subroutine in another sorting algorithm, radix sort, that can
handle larger keys more efficiently.
Because counting sort uses key values as indexes into an array,
it is not a comparison sort, and the `Ω(n log n)` lower bound for
comparison sorting does not apply to it. Bucket sort may be used
for many of the same tasks as counting sort, with a similar time
analysis; however, compared to counting sort, bucket sort requires
linked lists, dynamic arrays or a large amount of preallocated
memory to hold the sets of items within each bucket, whereas
counting sort instead stores a single number (the count of items)
per bucket.
Counting sorting works best when the range of numbers for each array
element is very small.
## Algorithm
**Step I**
In first step we calculate the count of all the elements of the
input array `A`. Then Store the result in the count array `C`.
The way we count is depected below.
![Counting Sort](https://3.bp.blogspot.com/-jJchly1BkTc/WLGqCFDdvCI/AAAAAAAAAHA/luljAlz2ptMndIZNH0KLTTuQMNsfzDeFQCLcB/s1600/CSortUpdatedStepI.gif)
**Step II**
In second step we calculate how many elements exist in the input
array `A` which are less than or equals for the given index.
`Ci` = numbers of elements less than or equals to `i` in input array.
![Counting Sort](https://1.bp.blogspot.com/-1vFu-VIRa9Y/WLHGuZkdF3I/AAAAAAAAAHs/8jKu2dbQee4ap9xlVcNsILrclqw0UxAVACLcB/s1600/Step-II.png)
**Step III**
In this step we place the input array `A` element at sorted
position by taking help of constructed count array `C` ,i.e what
we constructed in step two. We used the result array `B` to store
the sorted elements. Here we handled the index of `B` start from
zero.
![Counting Sort](https://1.bp.blogspot.com/-xPqylngqASY/WLGq3p9n9vI/AAAAAAAAAHM/JHdtXAkJY8wYzDMBXxqarjmhpPhM0u8MACLcB/s1600/ResultArrayCS.gif)
## References
- [Wikipedia](https://en.wikipedia.org/wiki/Counting_sort)
- [YouTube](https://www.youtube.com/watch?v=OKd534EWcdk&index=61&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
- [EfficientAlgorithms](https://efficientalgorithms.blogspot.com/2016/09/lenear-sorting-counting-sort.html)

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@ -0,0 +1,69 @@
import CountingSort from '../CountingSort';
import {
equalArr,
notSortedArr,
reverseArr,
sortedArr,
SortTester,
} from '../../SortTester';
// Complexity constants.
const SORTED_ARRAY_VISITING_COUNT = 60;
const NOT_SORTED_ARRAY_VISITING_COUNT = 60;
const REVERSE_SORTED_ARRAY_VISITING_COUNT = 60;
const EQUAL_ARRAY_VISITING_COUNT = 60;
describe('CountingSort', () => {
it('should sort array', () => {
SortTester.testSort(CountingSort);
});
it('should allow to use specify maximum integer value in array to make sorting faster', () => {
const visitingCallback = jest.fn();
const sorter = new CountingSort({ visitingCallback });
// Detect biggest number in array in prior.
const biggestElement = notSortedArr.reduce((accumulator, element) => {
return element > accumulator ? element : accumulator;
}, 0);
const sortedArray = sorter.sort(notSortedArr, biggestElement);
expect(sortedArray).toEqual(sortedArr);
// Normally visitingCallback is being called 60 times but in this case
// it should be called only 40 times.
expect(visitingCallback).toHaveBeenCalledTimes(40);
});
it('should visit EQUAL array element specified number of times', () => {
SortTester.testAlgorithmTimeComplexity(
CountingSort,
equalArr,
EQUAL_ARRAY_VISITING_COUNT,
);
});
it('should visit SORTED array element specified number of times', () => {
SortTester.testAlgorithmTimeComplexity(
CountingSort,
sortedArr,
SORTED_ARRAY_VISITING_COUNT,
);
});
it('should visit NOT SORTED array element specified number of times', () => {
SortTester.testAlgorithmTimeComplexity(
CountingSort,
notSortedArr,
NOT_SORTED_ARRAY_VISITING_COUNT,
);
});
it('should visit REVERSE SORTED array element specified number of times', () => {
SortTester.testAlgorithmTimeComplexity(
CountingSort,
reverseArr,
REVERSE_SORTED_ARRAY_VISITING_COUNT,
);
});
});