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In worst case time complexity can be O(n). The average time complexity of Interpolation search is O(log(log(n))) if all elements are uniformly distributed. If we assume uniform distribution of the values so we'll use simple linear interpolation. So if the values are: 1,2,3,4,5,6,7,8,9,10000000 And we search for number 9, searching using linear interpolation will go through all (excluding the first and last) the indices before finding the correct one. The space complexity of the Interpolation search is O(1) as Single auxiliary space is required to hold a position variable. The third drawback is that the O(log logN) complexity of the interpolation search is for the average case, in worst case it’s O(N) (it’s horrible). The 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). 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). How many steps would interpolation search require in order to find 68? 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 … In such cases interpolation search will be O(n). 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 ← (43-1) * ----- + 1 99 - 1 = (42 * 0.918) + 1 = 39.571 = 39 ... (In the worst case, interpolation search performs worse than straight binary search!) In either situation, we have, C (n) = n. Now, C (n) = n is the worst-case complexity of linear or sequential search algorithm. Therefore, the time complexities in the best case will be: T BSeqSearch (n)=4=Θ(1) - The Worst case time complexities: when k … Example. Space complexity of Interpolation search is O(1) as no auxiliary space is required. Interpolation search Performance. 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 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). The best case for Interpolation Search happens when the middle (our approximation) is the desired key. 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