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Java offers the Set interface to support sets (with the HashSet class implementing it using a hash table), and the SortedSet sub-interface to support sorted sets (with the TreeSet class implementing it using a binary search tree).
Representations might also be more complicated, for example using indexes or ancestor lists for performance. Trees as used in computing are similar to but can be different from mathematical constructs of trees in graph theory , trees in set theory , and trees in descriptive set theory .
Collection implementations in pre-JDK 1.2 versions of the Java platform included few data structure classes, but did not contain a collections framework. [4] The standard methods for grouping Java objects were via the array, the Vector, and the Hashtable classes, which unfortunately were not easy to extend, and did not implement a standard member interface.
Small finite examples: The three partially ordered sets on the left are trees (in blue); one branch of one of the trees is highlighted (in green). The partially ordered set on the right (in red) is not a tree because x 1 < x 3 and x 2 < x 3, but x 1 is not comparable to x 2 (dashed orange line).
Depending on the problem at hand, pre-order, post-order, and especially one of the number of subtrees − 1 in-order operations may be optional. Also, in practice more than one of pre-order, post-order, and in-order operations may be required. For example, when inserting into a ternary tree, a pre-order operation is performed by comparing items.
Graphic example of the structure of the segment tree. This instance is built for the segments shown at the bottom. In computer science, the segment tree is a data structure used for storing information about intervals or segments. It allows querying which of the stored segments contain a given point. A similar data structure is the interval tree.
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The nested set model is a technique for representing nested set collections (also known as trees or hierarchies) in relational databases.. It is based on Nested Intervals, that "are immune to hierarchy reorganization problem, and allow answering ancestor path hierarchical queries algorithmically — without accessing the stored hierarchy relation".