Add exponential search

src/algorithms/search/exponential-search/README.md

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+# Exponential Search
+
+In computer science, an exponential search is an algorithm.There are numerous ways to implement this with the most common being to determine a range that the search key
+resides in and performing a binary search within that range. This takes O(log i) where i is the position of the search key in the list, if the search key is in the list,
+or the position where the search key should be, if the search key is not in the list.Exponential search can also be used to search in bounded lists. Exponential search 
+can even out-perform more traditional searches for bounded lists, such as binary search, when the element being searched for is near the beginning of the array.
+
+![Exponential Search](https://upload.wikimedia.org/wikipedia/commons/4/45/Exponential_search.svg)
+
+## Complexity
+
+**Time Complexity**: `O(log i)` -  i is the index of the element being searched for in the list
+
+## References
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Exponential_search)

src/algorithms/search/exponential-search/__test__/exponentialSearch.test.js

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+import exponentialSearch from '../exponentialSearch';
+
+describe('exponentialSearch', () => {
+  it('should search number in sorted array', () => {
+    expect(exponentialSearch([], 1)).toBe(-1);
+    expect(exponentialSearch([1], 1)).toBe(0);
+    expect(exponentialSearch([1, 2], 1)).toBe(0);
+    expect(exponentialSearch([1, 2], 2)).toBe(1);
+    expect(exponentialSearch([1, 5, 10, 12], 1)).toBe(0);
+    expect(exponentialSearch([1, 5, 10, 12, 14, 17, 22, 100], 17)).toBe(5);
+    expect(exponentialSearch([1, 5, 10, 12, 14, 17, 22, 100], 1)).toBe(0);
+    expect(exponentialSearch([1, 5, 10, 12, 14, 17, 22, 100], 100)).toBe(7);
+    expect(exponentialSearch([1, 5, 10, 12, 14, 17, 22, 100], 0)).toBe(-1);
+  });
+
+  it('should search object in sorted array', () => {
+    const sortedArrayOfObjects = [
+      { key: 1, value: 'value1' },
+      { key: 2, value: 'value2' },
+      { key: 3, value: 'value3' },
+      { key: 4, value: 'value4' },
+    ];
+
+    const comparator = (a, b) => {
+      if (a.key === b.key) return 0;
+      return a.key < b.key ? -1 : 1;
+    };
+
+    expect(exponentialSearch([], { key: 1 }, comparator)).toBe(-1);
+    expect(exponentialSearch(sortedArrayOfObjects, { key: 4 }, comparator)).toBe(3);
+    expect(exponentialSearch(sortedArrayOfObjects, { key: 1 }, comparator)).toBe(0);
+    expect(exponentialSearch(sortedArrayOfObjects, { key: 2 }, comparator)).toBe(1);
+    expect(exponentialSearch(sortedArrayOfObjects, { key: 3 }, comparator)).toBe(2);
+  });
+});

src/algorithms/search/exponential-search/exponentialSearch.js

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+import Comparator from '../../../utils/comparator/Comparator';
+
+/**
+ * Binary search implementation.
+ *
+ * @param {*[]} sortedArray
+ * @param {*} startIndex
+ * @param {*} endIndex
+ * @param {*} seekElement
+ * @param {function(a, b)} [comparatorCallback]
+ * @return {number}
+ */
+
+function binarySearch(sortedArray, startIndex, endIndex, seekElement, comparatorCallback) {
+  const comparator = new Comparator(comparatorCallback);
+  if (endIndex >= startIndex) {
+    const middleIndex = startIndex + Math.floor((endIndex - startIndex) / 2);
+    // If the element is present at the middle itself
+    if (comparator.equal(sortedArray[middleIndex], seekElement)) {
+      return middleIndex;
+    }
+    // If element is smaller than middleIndex, then it can only be  present n left subarray
+    if (comparator.greaterThan(sortedArray[middleIndex], seekElement)) {
+      return binarySearch(sortedArray, startIndex, middleIndex-1, seekElement, comparatorCallback);
+    }
+    // Else the element can only be present in right subarray
+    return binarySearch(sortedArray, middleIndex + 1, endIndex, seekElement, comparatorCallback);
+  }
+  // We reach here when element is not present in array
+  return -1;
+}
+/**
+ * Exponential search implementation.
+ *
+ * @param {*[]} sortedArray
+ * @param {*} seekElement
+ * @param {function(a, b)} [comparatorCallback]
+ * @return {number}
+ */
+export default function exponentialSearch(sortedArray, seekElement, comparatorCallback) {
+  const comparator = new Comparator(comparatorCallback);
+  const length = sortedArray.length;  
+  // If element is present at first location itself
+  if (sortedArray.length !== 0) {
+    if (comparator.equal(sortedArray[0], seekElement))
+      return 0;
+    }
+    // Find range for binary search by repeated doubling
+    let range = 1;
+    while (range < length && comparator.lessThanOrEqual(sortedArray[range], seekElement)) {
+      range = range * 2;
+    }
+    // Call binary search for the found range.
+    return binarySearch(sortedArray, range/2, Math.min(range, length - 1), seekElement, comparatorCallback);
+}