feat: added Gray Code algorithm #1425

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	/**
	* Generates a Gray code sequence for the given number of bits.
	* @param {number} n - The number of bits in the Gray code sequence.
	* @returns {number[]} - An array of Gray codes in binary format.
	* @description
	* Gray codes are binary sequences in which two successive values differ in only one bit.
	* This function generates a Gray code sequence of length 2^n for the given number of bits.
	*
	* The algorithm follows these steps:
	*
	* 1. Initialize an array `grayCodes` to store the Gray codes. Start with [0, 1] for n = 1.
	* 2. Iterate from 1 to n:
	* a. Calculate `highestBit` as 2^i, where `i` is the current iteration index.
	* b. Iterate in reverse order through the existing Gray codes:
	* - For each Gray code `code`, add `highestBit \| code` to `grayCodes`.
	* - This operation flips a single bit in each existing code, creating new codes.
	* 3. Return the `grayCodes` array containing the Gray codes in decimal representation.
	*
	*resources: [GFG](https://www.geeksforgeeks.org/generate-n-bit-gray-codes/)
	* @example
	* const n = 3;
	* const grayCodes = generateGrayCodes(n);
	* // grayCodes will be [0, 1, 3, 2, 6, 7, 5, 4] for n=3.
	*/
	function generateGrayCodes(n) {
	if (n <= 0) {
	return [0]
	}

	const grayCodes = [0, 1]

	for (let i = 1; i < n; i++) {
	const highestBit = 1 << i
	for (let j = grayCodes.length - 1; j >= 0; j--) {
	grayCodes.push(highestBit \| grayCodes[j])
	}
	}

	return grayCodes
	}

	export { generateGrayCodes }

19 changes: 19 additions & 0 deletions Bit-Manipulation/test/GrayCodes.test.js

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	import { generateGrayCodes } from '../GrayCodes.js'

	describe('Gray codes', () => {
	test.each([
	[0, [0b0]],
	[1, [0b0, 0b1]],
	[2, [0b00, 0b01, 0b11, 0b10]],
	[3, [0b000, 0b001, 0b011, 0b010, 0b110, 0b111, 0b101, 0b100]],
	[
	4,
	[
	0b0000, 0b0001, 0b0011, 0b0010, 0b0110, 0b0111, 0b0101, 0b0100, 0b1100,
	0b1101, 0b1111, 0b1110, 0b1010, 0b1011, 0b1001, 0b1000
	]
	]
	])('n = %i -> %j', (n, expected) => {
	expect(generateGrayCodes(n)).toEqual(expected)
	})
	})

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