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The HyperLogLog has three main operations: add to add a new element to the set, count to obtain the cardinality of the set and merge to obtain the union of two sets. Some derived operations can be computed using the inclusion–exclusion principle like the cardinality of the intersection or the cardinality of the difference between two HyperLogLogs combining the merge and count operations.
In computer science, merge sort (also commonly spelled as mergesort and as merge-sort [2]) is an efficient, general-purpose, and comparison-based sorting algorithm.Most implementations produce a stable sort, which means that the relative order of equal elements is the same in the input and output.
O(n)[1] In computer science, a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of disjoint (non-overlapping) sets. Equivalently, it stores a partition of a set into disjoint subsets. It provides operations for adding new sets, merging sets (replacing them ...
Timsort is a stable sorting algorithm (order of elements with same key is kept) and strives to perform balanced merges (a merge thus merges runs of similar sizes). In order to achieve sorting stability, only consecutive runs are merged. Between two non-consecutive runs, there can be an element with the same key inside the runs.
Perhaps confusingly, some of the same terms are used for both data structures and composites. For example, " binary tree " can refer to either: as a data structure it is a means of accessing a linear sequence of items, and the actual positions of items in the tree are irrelevant (the tree can be internally rearranged however one likes, without ...
k. -way merge algorithm. In computer science, k-way merge algorithms or multiway merges are a specific type of sequence merge algorithms that specialize in taking in k sorted lists and merging them into a single sorted list. These merge algorithms generally refer to merge algorithms that take in a number of sorted lists greater than two.
A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem. The divide-and-conquer technique is the basis of efficient algorithms ...
In the merge sort algorithm, this subroutine is typically used to merge two sub-arrays A[lo..mid], A[mid+1..hi] of a single array A. This can be done by copying the sub-arrays into a temporary array, then applying the merge algorithm above. [1] The allocation of a temporary array can be avoided, but at the expense of speed and programming ease.