feat(Search): add Jump Search optimized version (works for descending…

Maths/MobiusFunction.js

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

Search/JumpSearchOptimized.js

@@ -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)}`
+    )
+  })
+}

Search/test/JumpSearchOptimized.test.js

@@ -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)
+})