Searching Algorithms Questions Long
Exponential interpolation search is a variation of interpolation search, which is a searching algorithm used to find a specific element in a sorted array. The time complexity of exponential interpolation search can be explained as follows:
In exponential interpolation search, the algorithm uses exponential increments to probe the array for the target element. It starts by comparing the target element with the element at the first position of the array. If the target element is found at this position, the search is successful. Otherwise, the algorithm increases the position exponentially until it either finds the target element or overshoots it.
The time complexity of exponential interpolation search can be analyzed in terms of the number of comparisons made during the search process. Let's assume the size of the array is 'n' and the target element is located at position 'pos'.
In the best-case scenario, where the target element is located at the first position of the array, the algorithm will find it in just one comparison. Therefore, the time complexity in the best case is O(1).
In the worst-case scenario, where the target element is located at the last position of the array or beyond, the algorithm will keep doubling the position until it overshoots the target element. This doubling process can be represented as a geometric series, where the initial position is 1 and the common ratio is 2. The number of comparisons made in the worst case can be approximated by log2(pos), as the algorithm doubles the position until it overshoots the target element.
Hence, the time complexity of exponential interpolation search in the worst case is O(log2(pos)).
However, it is important to note that exponential interpolation search assumes a uniform distribution of elements in the array. If the distribution is not uniform, the performance of the algorithm may degrade, and the time complexity may not hold true.
In summary, the time complexity of exponential interpolation search is O(log2(pos)), where 'pos' represents the position of the target element in the sorted array.