Searching Algorithms Questions Long
Sublinear interpolation search is an improved version of interpolation search, which is a searching algorithm used to find a specific element in a sorted array. The time complexity of sublinear interpolation search can be explained as follows:
In interpolation search, the algorithm estimates the position of the target element by using a linear interpolation formula. It calculates the probable position of the target element based on the values of the first and last elements of the array, and the target value itself. This estimation helps in reducing the search space and narrowing down the range where the target element might be located.
The time complexity of interpolation search is typically considered to be O(log log n), where n is the size of the array. This is because the algorithm reduces the search space exponentially with each iteration, resulting in a sublinear time complexity.
However, sublinear interpolation search further improves the time complexity by using a modified interpolation formula. Instead of using a linear interpolation, it uses a sublinear interpolation formula that takes into account the distribution of the elements in the array. This modified formula provides a more accurate estimation of the target element's position, leading to faster search times.
The time complexity of sublinear interpolation search can be considered as O(log log log n), which is an improvement over the original interpolation search. This means that the algorithm reduces the search space even more rapidly, resulting in faster search times for larger arrays.
It is important to note that the time complexity mentioned above is an average case analysis. In the worst case scenario, where the target element is located at one of the extremes of the array, the time complexity can degrade to O(n), making it similar to a linear search. However, in practice, sublinear interpolation search performs well for most cases and provides efficient search times for sorted arrays.