Searching Algorithms Questions Long
The time complexity of interpolation search is determined by the distribution of the elements in the sorted array and the value being searched for. In the best-case scenario, when the elements are uniformly distributed, the time complexity of interpolation search is O(log log n), where n is the number of elements in the array.
Interpolation search is an improvement over binary search, as it uses the value being searched for to estimate its position within the array. It calculates the probable position by using a formula that takes into account the range of values and their distribution. This estimation allows interpolation search to make a more informed decision about where to continue the search, potentially reducing the number of comparisons required.
However, in the worst-case scenario, when the elements are not uniformly distributed, the time complexity of interpolation search can degrade to O(n), making it less efficient than binary search. This occurs when the value being searched for is located at one of the extremes of the array, causing the interpolation formula to repeatedly estimate positions that are far from the actual target.
In practice, the time complexity of interpolation search tends to be closer to O(log log n) for most cases, making it a favorable choice when the elements are uniformly distributed. However, it is important to note that the actual time complexity can vary depending on the specific distribution of the elements and the value being searched for.