Searching Algorithms Questions Long
Binary interpolation search is a variant of binary search that aims to improve the efficiency of searching in sorted arrays. It uses interpolation formula to estimate the position of the target element within the array.
The time complexity of binary interpolation search can be analyzed as follows:
1. Best Case: In the best case scenario, the target element is found at the first comparison itself. This occurs when the target element is located at the middle of the array. In this case, the time complexity is O(1), as only one comparison is required.
2. Worst Case: The worst case scenario in binary interpolation search occurs when the target element is either the first or the last element of the array, or when the array is uniformly distributed. In this case, the time complexity is O(log(log(n))), where n is the number of elements in the array. This is because the interpolation formula estimates the position of the target element by assuming a uniform distribution, and the binary search algorithm further reduces the search space by half in each iteration.
3. Average Case: The average case time complexity of binary interpolation search is also O(log(log(n))). This is because, on average, the interpolation formula provides a good estimate of the target element's position, reducing the search space significantly in each iteration.
It is important to note that the time complexity of binary interpolation search assumes that the array is sorted. If the array is not sorted, an additional step of sorting the array would be required, which would have a time complexity of O(n log(n)).
In conclusion, the time complexity of binary interpolation search is O(log(log(n))) in both the worst and average cases, making it a relatively efficient searching algorithm for sorted arrays.