The growth rate of Interpolation Search time complexity is smaller compared to Binary Search. The number of probes in interpolation search (see [9], [10] or [4]) in the best case is also just 1, in the average case it is in O(loglogn) and in the worst case it is in O(n). Remark: The complexity in the worst case could be improved by running interpolation search The best case for Interpolation Search happens when the middle (our approximation) is the desired key. How many steps would interpolation search require in order to find 68? In such cases interpolation search will be O(n). The third drawback is that the O(log logN) complexity of the interpolation search is for the average case, in worst case itâs O(N) (itâs horrible). Interpolation search Performance. For example, if we are looking for 91 in the original array above, then on our first pass we compute middle as: 91 - 1 middle â (43-1) * ----- + 1 99 - 1 = (42 * 0.918) + 1 = 39.571 = 39 ... (In the worst case, interpolation search performs worse than straight binary search!) If we assume uniform distribution of the values so we'll use simple linear interpolation. Worst case time complexity: O(N) Average case time complexity: O(log log N) Best case time complexity: O(1) Space complexity: O(1) On assuming a uniform distribution of the data on the linear scale used for interpolation, the performance can be shown to be O(log log n). That's all for this topic Interpolation Search Program in Java. Example. Consider the following array of elements: 9, 21, 32, 38, 51, 59, 68, 80, 91, 97, 113, 119, 131, 142, 149; How many steps would binary search require in order to find 68? Solution: In this example, the search process begins from the end of a. In worst case time complexity can be O(n). The successful Searches: - The Best case time complexities: When k number found in the position a(n). This makes the best case time complexity is O(1). See What is the time complexity of interpolation search and why? Average case time complexity of Interpolation search is O(log(log(n))) if the elements are uniformly distributed. The interpolation search is very beneficial when the elements are arranged in more sequencial way (for example, if we have a sorted array of elements whose elements have a common difference of 2 then in such case we can find the position of ⦠This i s unim- References portant, however, for we can get a search technique whose cost is at most twice optimal in both the average [ I ] W. Feller, An Introduction to Probability Theory and its and worst cases: apply conventional interpolation Applications (3rd edition) (John Wiley, New York, 1968). Worst Case: The worst case occurs when ITEM is present at the last location of the list, or it is not there at al. In either situation, we have, C (n) = n. Now, C (n) = n is the worst-case complexity of linear or sequential search algorithm. 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