Searching Algorithms Questions Long
Exponential interpolation search is a searching algorithm that is used to find the position of a target value within a sorted array. It is an improved version of interpolation search, which estimates the position of the target value based on the values at the ends of the array.
The time complexity of exponential interpolation search can be analyzed as follows:
1. Best Case: In the best case scenario, the target value is found at the first comparison itself. This occurs when the target value is equal to the value at the start of the array. In this case, the time complexity is O(1), as only one comparison is required.
2. Average Case: In the average case scenario, the target value is found after a few comparisons. The algorithm estimates the position of the target value using interpolation and then performs a binary search within a range to find the exact position. The time complexity of the interpolation step is O(log(log(n))), where n is the size of the array. This is because the interpolation step reduces the search range exponentially. After the interpolation step, a binary search is performed, which has a time complexity of O(log(n)). Therefore, the overall time complexity in the average case is O(log(log(n))) + O(log(n)), which can be simplified to O(log(log(n))).
3. Worst Case: In the worst case scenario, the target value is either at the beginning or the end of the array, or it is not present in the array at all. In this case, the algorithm performs a binary search on the entire array. The time complexity of the binary search step is O(log(n)). Therefore, the overall time complexity in the worst case is O(log(n)).
In summary, the time complexity of exponential interpolation search can be considered as O(log(log(n))) in the average case and O(log(n)) in the worst case. It is important to note that this algorithm is most effective when the array is uniformly distributed, as it relies on the assumption of a uniform distribution for accurate interpolation estimates.