How does the complexity of interpolation search compare to binary search?

Interpolation search and binary search are both searching algorithms used to find a target value within a sorted array or list. Binary search has a worst-case time complexity of O(log n), making it highly efficient for large datasets. On the other hand, interpolation search is an improvement over binary search, especially when the data being searched is uniformly distributed. It achieves an average time complexity of O(log log n) under ideal conditions, making it faster in scenarios where the data is evenly spaced. However, interpolation search requires the data to be sorted, and its performance can degrade to O(n) in worst-case scenarios if the data distribution is skewed. Additionally, interpolation search is adaptive, meaning it can adjust its search range based on the target value's estimated position, potentially improving performance further. Understanding these complexities helps in choosing the most appropriate search algorithm based on the nature of the data and distribution characteristics.