feat: add exponential search

Author: Fechuli

search/exponential_search.ts

@@ -0,0 +1,50 @@
+/**
+ * @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;
+  };
+