Searching Algorithms Questions Long
The time complexity of binary interpolation search is O(log(log(n))) on average, where n is the size of the sorted array being searched.
Binary interpolation search is an improvement over binary search, which has a time complexity of O(log(n)). It is used to search for a specific element in a sorted array by estimating its position based on the values of the first and last elements in the array.
The interpolation search algorithm calculates the position of the target element by using interpolation formula:
pos = low + ((target - arr[low]) * (high - low)) / (arr[high] - arr[low])
Here, "low" and "high" represent the indices of the first and last elements in the array, respectively. "target" is the element being searched.
The interpolation formula estimates the position of the target element based on the assumption that the elements in the array are uniformly distributed. However, if the elements are not uniformly distributed, the interpolation search may not perform optimally.
The time complexity of binary interpolation search is derived from the number of iterations required to find the target element. In each iteration, the algorithm calculates the position using the interpolation formula and compares the target element with the element at that position.
In the best-case scenario, the target element is found in the first iteration, resulting in a time complexity of O(1). However, in the worst-case scenario, the target element is located at one of the extremes of the array, and the interpolation formula does not provide an accurate estimate. This can lead to a linear search-like behavior, resulting in a time complexity of O(n).
On average, assuming a uniform distribution of elements, the time complexity of binary interpolation search is O(log(log(n))). This is because the interpolation formula narrows down the search range exponentially, similar to binary search. However, the logarithmic factor is reduced due to the estimation made by the interpolation formula.
It is important to note that the time complexity mentioned above is an average case analysis. The actual time complexity can vary depending on the distribution of elements in the array and the specific values being searched.