Searching Algorithms Questions Long
Binary interpolation search is a variant of the binary search algorithm that aims to improve the efficiency of searching for a specific element in a sorted array. It is based on the concept of interpolation, which involves estimating the position of the target element within the array.
The binary interpolation search algorithm starts by assuming that the elements in the array are uniformly distributed. It then uses this assumption to estimate the probable position of the target element by using interpolation formula:
position = low + ((target - arr[low]) * (high - low)) / (arr[high] - arr[low])
In this formula, "low" represents the lower bound of the array, "high" represents the upper bound, "target" is the element being searched, and "arr" is the sorted array.
Once the estimated position is calculated, the algorithm compares the target element with the element at the estimated position. If they match, the search is successful. If the target element is smaller, the algorithm updates the upper bound to be one less than the estimated position and repeats the process. Similarly, if the target element is larger, the algorithm updates the lower bound to be one more than the estimated position and repeats the process.
This process continues until the target element is found or the lower bound becomes greater than the upper bound, indicating that the element is not present in the array.
Binary interpolation search has a time complexity of O(log(log(n))) on average, making it more efficient than traditional binary search in certain scenarios. However, it requires a uniformly distributed array for accurate estimations, and its performance can degrade to O(n) in worst-case scenarios where the array is not uniformly distributed.