Searching Algorithms Questions Long
The time complexity of binary interpolation search is O(log(log(n))) on average and O(n) in the worst case scenario.
Binary interpolation search is an improvement over binary search, which is a divide and conquer algorithm used to search for a specific element in a sorted array. The main difference between binary search and binary interpolation search is the way the middle element is calculated.
In binary search, the middle element is calculated as the average of the low and high indices, which is (low + high) / 2. However, in binary interpolation search, the middle element is calculated using interpolation formula:
mid = low + ((high - low) / (arr[high] - arr[low])) * (x - arr[low])
Here, "x" is the element being searched, "arr" is the sorted array, "low" is the starting index, and "high" is the ending index.
The interpolation formula allows the algorithm to estimate the position of the desired element based on the values of the first and last elements in the array. This estimation helps in reducing the number of iterations required to find the element, especially when the elements are uniformly distributed.
The time complexity of binary interpolation search is determined by the number of iterations required to find the element. On average, it has a time complexity of O(log(log(n))), where "n" is the number of elements in the array. This is because the interpolation formula helps in narrowing down the search range faster than binary search.
However, in the worst case scenario, when the elements are not uniformly distributed, binary interpolation search can degrade to O(n) time complexity. This occurs when the interpolation formula consistently overestimates or underestimates the position of the desired element, leading to a linear search.
In conclusion, binary interpolation search has an average time complexity of O(log(log(n))) and a worst-case time complexity of O(n). It is a more efficient searching algorithm compared to binary search when the elements are uniformly distributed, but it can perform poorly when the distribution is uneven.