Exponential search and binary search are two algorithms used to find a target element in a sorted array. While both algorithms have their advantages and disadvantages, exponential search is generally not considered to be faster than binary search.

Time Complexity of Exponential Search:

The time complexity of exponential search is O(log n), where n is the size of the array. This means that the search time doubles with each iteration. Binary search, on the other hand, has a time complexity of O(log n), which means that the search time increases logarithmically with the size of the array.

In practice, binary search is much faster than exponential search for large arrays. For example, if the array contains 1 million elements, exponential search will take approximately 20 iterations to find the target element, while binary search will take only 10 iterations.

Auxiliary Space of Exponential Search:

Both exponential search and binary search require O(1) auxiliary space, which means that they do not require any additional memory beyond the array itself.

Advantages of Exponential Search:

• Exponential search is useful for unbounded search
• Exponential search works faster when the element to be searched is closer to the beginning of the array.

Advantages of Binary Search:

• Binary search is much faster than exponential search in general.

Conclusion:

In general, binary search is a more efficient algorithm than exponential search for finding a target element in a sorted array. Binary search has a lower time complexity and is easier to implement. However, exponential search may be a better choice for certain applications like unbounded arrays or when the element to be searched is closer to the first element.