added Backtracking/AllCombinationsOfSizeK #748

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	/*
	Problem: Given two numbers, n and k, make all unique combinations of k numbers from 1 to n and in sorted order

	What is combinations?
	- Combinations is selecting items froms a collections without considering order of selection

	Example:
	- We have an apple, a banana, and a jackfruit
	- We have three objects, and need to choose two items, then combinations will be

	1. Apple & Banana
	2. Apple & Jackfruit
	3. Banana & Jackfruit

	To read more about combinations, you can visit the following link:
	- https://betterexplained.com/articles/easy-permutations-and-combinations/

	Solution:
	- We will be using backtracking to solve this questions
	- Take one element, and make all them combinations for k-1 elements
	- Once we get all combinations of that element, pop it and do same for next element
	*/

	class Combinations {
	constructor (n, k) {
	this.n = n
	this.k = k
	this.combinationArray = [] // will be used for storing current combination
	}

	findCombinations (high = this.n, total = this.k, low = 1) {
	if (total === 0) {
	console.log(this.combinationArray)
	return
	}
	for (let i = low; i <= high; i++) {
	this.combinationArray.push(i)
	this.findCombinations(high, total - 1, i + 1)
	this.combinationArray.pop()
	}
	}
	}

	export { Combinations }

13 changes: 13 additions & 0 deletions Backtracking/tests/AllCombinationsOfSizeK.test.mjs

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	import { Combinations } from '../AllCombinationsOfSizeK'

	describe('AllCombinationsOfSizeK', () => {
	it('should return 3x2 matrix solution for n = 3 and k = 2', () => {
	const test1 = new Combinations(3, 2)
	expect(test1.findCombinations).toEqual([[1, 2], [1, 3], [2, 3]])
	})

	it('should return 6x2 matrix solution for n = 3 and k = 2', () => {
	const test2 = new Combinations(4, 2)
	expect(test2.findCombinations).toEqual([[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]])
	})
	})

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