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The naive implementation for generating a suffix tree going forward requires O(n 2) or even O(n 3) time complexity in big O notation, where n is the length of the string. By exploiting a number of algorithmic techniques, Ukkonen reduced this to O ( n ) (linear) time, for constant-size alphabets, and O ( n log n ) in general, matching the ...
For typical serial sorting algorithms, good behavior is O(n log n), with parallel sort in O(log 2 n), and bad behavior is O(n 2). Ideal behavior for a serial sort is O(n), but this is not possible in the average case. Optimal parallel sorting is O(log n). Swaps for "in-place" algorithms. Memory usage (and use of other computer resources).
It has a O(n 2) time complexity, which makes it inefficient on large lists, and generally performs worse than the similar insertion sort. Selection sort is noted for its simplicity and has performance advantages over more complicated algorithms in certain situations, particularly where auxiliary memory is limited.
The heapsort algorithm can be divided into two phases: heap construction, and heap extraction. The heap is an implicit data structure which takes no space beyond the array of objects to be sorted; the array is interpreted as a complete binary tree where each array element is a node and each node's parent and child links are defined by simple arithmetic on the array indexes.
Thus, the overall algorithm may be performed by operating on only (n/t) 2 blocks instead of on n 2 matrix cells, where n is the side length of the matrix. In order to keep the size of the lookup tables (and the time needed to initialize them) sufficiently small, t is typically chosen to be O(log n).
Karatsuba multiplication is an O(n log 2 3) ≈ O(n 1.585) divide and conquer algorithm, that uses recursion to merge together sub calculations. By rewriting the formula, one makes it possible to do sub calculations / recursion. By doing recursion, one can solve this in a fast manner.
It requires O(n + N) time. It is similar to counting sort, but differs in that it "moves items twice: once to the bucket array and again to the final destination [whereas] counting sort builds an auxiliary array then uses the array to compute each item's final destination and move the item there." [2] The pigeonhole algorithm works as follows:
In this algorithm, one recursively draws a line to split the vertices into two sets. The Delaunay triangulation is computed for each set, and then the two sets are merged along the splitting line. Using some clever tricks, the merge operation can be done in time O(n), so the total running time is O(n log n). [17]