feat(Search): add Jump Search optimized version (works for descending... #1844

Original file line number	Diff line number	Diff line change
Expand Up		@@ -28,6 +28,6 @@ export const mobiusFunction = (number) => {
		return primeFactorsArray.length !== new Set(primeFactorsArray).size
		? 0
		: primeFactorsArray.length % 2 === 0
	? 1
	: -1
	? 1
	: -1
		}

59 changes: 59 additions & 0 deletions Search/JumpSearchOptimized.js

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Original file line number	Diff line number	Diff line change
		@@ -0,0 +1,59 @@
	/**
	* This version of Jump Search works for both ascending and descending sorted arrays.
	*
	* Time Complexity: O(√n)
	* Space Complexity: O(1)
	*
	* Example:
	* jumpSearchOptimized([1, 3, 5, 7, 9, 11], 7) -> 3
	* jumpSearchOptimized([20, 15, 10, 5, 0], 10) -> 2
	*/

	function jumpSearchOptimized(arr, target) {
	if (!Array.isArray(arr) \|\| arr.length === 0) return -1

	const n = arr.length
	const step = Math.floor(Math.sqrt(n))
	let prev = 0

	// Detect array order
	const isAscending = arr[0] < arr[n - 1]

	// Jump in blocks based on order
	while (prev < n) {
	const next = Math.min(prev + step, n)
	const value = arr[next - 1]

	if ((isAscending && value >= target) \|\| (!isAscending && value <= target)) {
	// Linear search in the found block
	for (let i = prev; i < next; i++) {
	if (arr[i] === target) return i
	}
	return -1
	}

	prev = next
	}

	return -1
	}

	module.exports = { jumpSearchOptimized }

	/* -----------------------------------------
	Quick local test: run `node Search/JumpSearchOptimized.js`
	----------------------------------------- */
	if (require.main === module) {
	const tests = [
	{ arr: [1, 3, 5, 7, 9, 11], target: 7 },
	{ arr: [20, 15, 10, 5, 0], target: 10 },
	{ arr: [2, 4, 6, 8, 10, 12], target: 11 },
	{ arr: [], target: 3 }
	]

	tests.forEach(({ arr, target }) => {
	console.log(
	`Array: [${arr}] \| Target: ${target} \| Index: ${jumpSearchOptimized(arr, target)}`
	)
	})
	}

37 changes: 37 additions & 0 deletions Search/test/JumpSearchOptimized.test.js

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Original file line number	Diff line number	Diff line change
		@@ -0,0 +1,37 @@
	import { jumpSearchOptimized } from '../JumpSearchOptimized'

	test('jumpSearchOptimized([0, 0, 4, 7, 10, 23, 34, 40, 55, 68, 77, 90], 77) => 10', () => {
	const arr = [0, 0, 4, 7, 10, 23, 34, 40, 55, 68, 77, 90]
	const res = jumpSearchOptimized(arr, 77)
	expect(res).toEqual(10)
	})

	test('jumpSearchOptimized([11, 12, 15, 65, 78, 90], 4) => -1', () => {
	const arr = [11, 12, 15, 65, 78, 90]
	const res = jumpSearchOptimized(arr, 4)
	expect(res).toEqual(-1)
	})

	test('jumpSearchOptimized([11, 12, 15, 65, 78, 90], 11) => 0', () => {
	const arr = [11, 12, 15, 65, 78, 90]
	const res = jumpSearchOptimized(arr, 11)
	expect(res).toEqual(0)
	})

	test('jumpSearchOptimized([], 50) => -1', () => {
	const arr = []
	const res = jumpSearchOptimized(arr, 50)
	expect(res).toEqual(-1)
	})

	test('jumpSearchOptimized([5, 10, 15, 20, 25], 25) => 4', () => {
	const arr = [5, 10, 15, 20, 25]
	const res = jumpSearchOptimized(arr, 25)
	expect(res).toEqual(4)
	})

	test('jumpSearchOptimized([1, 3, 5, 7, 9], 2) => -1', () => {
	const arr = [1, 3, 5, 7, 9]
	const res = jumpSearchOptimized(arr, 2)
	expect(res).toEqual(-1)
	})

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