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If the data structure is instead viewed as a partition of a set, then the MakeSet operation enlarges the set by adding the new element, and it extends the existing partition by putting the new element into a new subset containing only the new element. In a disjoint-set forest, MakeSet initializes the node's parent pointer and the node's size or ...
In computer science, a set is an abstract data type that can store unique values, without any particular order. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set.
The primitive graph operations that the algorithm uses are to enumerate the vertices of the graph, to store data per vertex (if not in the graph data structure itself, then in some table that can use vertices as indices), to enumerate the out-neighbours of a vertex (traverse edges in the forward direction), and to enumerate the in-neighbours of a vertex (traverse edges in the backward ...
similar to a set, multiset, map, or multimap, respectively, but implemented using a hash table; keys are not ordered, but a hash function must exist for the key type. These types were left out of the C++ standard; similar containers were standardized in C++11, but with different names (unordered_set and unordered_map). Other types of containers ...
If x = m, add it to the set of c copies of m (and increment c). If x ≠ m and c > 0, then remove one of the c copies of m from the left-over set and pair it with the final value (and decrement c). If c = 0, then set m ← x and add x to the (previously empty) set of copies of m (and set c to 1). In all cases, the loop invariant is maintained. [1]
Set-builder notation can be used to describe a set that is defined by a predicate, that is, a logical formula that evaluates to true for an element of the set, and false otherwise. [2] In this form, set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate. Thus there is a variable on the left of the ...
The subset sum problem (SSP) is a decision problem in computer science.In its most general formulation, there is a multiset of integers and a target-sum , and the question is to decide whether any subset of the integers sum to precisely . [1]
So the intersection of the empty family should be the universal set (the identity element for the operation of intersection), [4] but in standard set theory, the universal set does not exist. However, when restricted to the context of subsets of a given fixed set X {\displaystyle X} , the notion of the intersection of an empty collection of ...