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For example, the Adleman–Pomerance–Rumely primality test runs for n O(log log n) time on n-bit inputs; this grows faster than any polynomial for large enough n, but the input size must become impractically large before it cannot be dominated by a polynomial with small degree.
Created independently in 1977 by W. Eddy and in 1978 by A. Bykat. Just like the quicksort algorithm, it has the expected time complexity of O(n log n), but may degenerate to O(n 2) in the worst case. Divide and conquer, a.k.a. merge hull — O(n log n) Another O(n log n) algorithm, published in 1977 by Preparata and Hong. This algorithm is also ...
The precise analysis of the performance of a disjoint-set forest is somewhat intricate. However, there is a much simpler analysis that proves that the amortized time for any m Find or Union operations on a disjoint-set forest containing n objects is O(m log * n), where log * denotes the iterated logarithm. [12] [13] [14] [15]
The lesser and greater sublists are then recursively sorted. This yields an average time complexity of O(n log n), with low overhead, and thus this is a popular algorithm. Efficient implementations of quicksort (with in-place partitioning) are typically unstable sorts and somewhat complex but are among the fastest sorting algorithms in practice.
Heapsort has the advantages of simplicity, and a worst case run time of O(n log n), but heapsort's average running time is usually considered slower than in-place quicksort, primarily due to its worse locality of reference. [27] This result is debatable; some publications indicate the opposite.
Binary search Visualization of the binary search algorithm where 7 is the target value Class Search algorithm Data structure Array Worst-case performance O (log n) Best-case performance O (1) Average performance O (log n) Worst-case space complexity O (1) Optimal Yes In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search ...
In computer science, polylogarithmic functions occur as the order of time for some data structure operations. Additionally, the exponential function of a polylogarithmic function produces a function with quasi-polynomial growth, and algorithms with this as their time complexity are said to take quasi-polynomial time. [2]
This running time is better than the () running time of the naive brute force calculation. The baby-step giant-step algorithm could be used by an eavesdropper to derive the private key generated in the Diffie Hellman key exchange , when the modulus is a prime number that is not too large.