Exponential search

search/exponential_search.ts

@@ -0,0 +1,49 @@
+/**
+ * @description Exponential search algorithm for a sorted array.
+ *
+ * The algorithm searches for a specific value in a sorted array by first finding a range
+ * where the value may be present and then performing a binary search within that range.
+ *
+ * @param {number[]} array - sorted list of numbers
+ * @param {number} x - target number to search for
+ * @return {number | null} - index of the target number in the list, or null if not found
+ * @see [ExponentialSearch](https://www.geeksforgeeks.org/exponential-search/)
+ * @example exponentialSearch([1, 2, 3, 4, 5], 3) => 2
+ * @example exponentialSearch([10, 20, 30, 40, 50], 35) => null
+ */
+
+export const exponentialSearch = (
+  array: number[],
+  x: number
+): number | null => {
+  const arrayLength = array.length
+  if (arrayLength === 0) return null
+
+  if (array[0] === x) return 0
+
+  let i = 1
+  while (i < arrayLength && array[i] <= x) {
+    i = i * 2
+  }
+
+  return binarySearch(array, x, i / 2, Math.min(i, arrayLength - 1))
+}
+
+const binarySearch = (
+  array: number[],
+  x: number,
+  start: number,
+  end: number
+): number | null => {
+  while (start <= end) {
+    const mid = Math.floor((start + end) / 2)
+    if (array[mid] === x) {
+      return mid
+    } else if (array[mid] < x) {
+      start = mid + 1
+    } else {
+      end = mid - 1
+    }
+  }
+  return null
+}

search/test/exponential_search.test.ts

@@ -0,0 +1,19 @@
+import { exponentialSearch } from '../exponential_search'
+
+describe('Exponential search', () => {
+  test.each([
+    [[1, 2, 3, 4, 5], 3, 2],
+    [[10, 20, 30, 40, 50], 35, null],
+    [[10, 20, 30, 40, 50], 10, 0],
+    [[10, 20, 30, 40, 50], 50, 4],
+    [[10, 20, 30, 40, 50], 60, null],
+    [[], 10, null],
+    [[1, 2, 3, 4, 5], 1, 0],
+    [[1, 2, 3, 4, 5], 5, 4]
+  ])(
+    'of %o, searching for %o, expected %i',
+    (array: number[], target: number, expected: number | null) => {
+      expect(exponentialSearch(array, target)).toBe(expected)
+    }
+  )
+})