“tree”的概念、定义、翻译、参考文献-科学参考

tree

Mathematics

A connected graph with no cycles. A disconnected graph with no cycles is called a forest. It can be shown that a connected simple graph with n vertices is a tree if and only if it has n − 1 edges. The figure shows all the trees with up to five vertices (see Cayley’s Theorem).

Trees with five vertices or fewer
Particularly in applications, one of the vertices of a tree may be designated as the root, and the tree may be drawn with the vertices at different levels indicating their distance from the root. A rooted tree in which every vertex (except the root, of degree 2) has degree either 1 or 3, as shown below, is called a binary tree.

A rooted, binary tree

Computer

1. Most commonly, short for rooted tree, i.e. a finite set of one or more nodes such that firstly there is a single designated node called the root and secondly the remaining nodes are partitioned into n≥0 disjoint sets, T₁, T₂,…, T_n, where each of these sets is itself a tree. The sets T₁, T₂,…, T_n are called subtrees of the root. If the order of these subtrees is significant, the tree is called an ordered tree, otherwise it is sometimes called an unordered tree.
A tree corresponds to a graph with the root node matching a vertex connected by (directed) arcs to the vertices, which match the root nodes of each of its subtrees. An alternative definition of a (directed) tree can thus be given in terms from graph theory: a tree is a directed acyclic graph such that firstly there is a unique vertex, which no arcs enter, called the root, secondly every other vertex has exactly one arc entering it, and thirdly there is a unique path from the root to any vertex. The diagram shows different representations of a tree.
2. Any connected acyclic graph.
3. Any data structure representing a tree (def. 1 or 2). For example, a rooted tree can be represented as a pointer to the representation of the root node. A representation of a node would contain pointers to the subtrees of the node as well as the data associated with the node itself. Because the number of subtrees of a node may vary, it is common practice to use a binary-tree representation.
Tree. Sample tree represented as a Venn diagram (top) and as a directed graph
The terminology associated with trees is either of a botanic nature, as with forest, leaf, root, or is genealogical, as with ancestor, descendant, child, parent, sibling. See also binary tree.

单词	tree
释义	tree Mathematics A connected graph with no cycles. A disconnected graph with no cycles is called a forest. It can be shown that a connected simple graph with n vertices is a tree if and only if it has n − 1 edges. The figure shows all the trees with up to five vertices (see Cayley’s Theorem). Trees with five vertices or fewer Particularly in applications, one of the vertices of a tree may be designated as the root, and the tree may be drawn with the vertices at different levels indicating their distance from the root. A rooted tree in which every vertex (except the root, of degree 2) has degree either 1 or 3, as shown below, is called a binary tree. A rooted, binary tree Computer 1. Most commonly, short for rooted tree, i.e. a finite set of one or more nodes such that firstly there is a single designated node called the root and secondly the remaining nodes are partitioned into n≥0 disjoint sets, T₁, T₂,…, T_n, where each of these sets is itself a tree. The sets T₁, T₂,…, T_n are called subtrees of the root. If the order of these subtrees is significant, the tree is called an ordered tree, otherwise it is sometimes called an unordered tree. A tree corresponds to a graph with the root node matching a vertex connected by (directed) arcs to the vertices, which match the root nodes of each of its subtrees. An alternative definition of a (directed) tree can thus be given in terms from graph theory: a tree is a directed acyclic graph such that firstly there is a unique vertex, which no arcs enter, called the root, secondly every other vertex has exactly one arc entering it, and thirdly there is a unique path from the root to any vertex. The diagram shows different representations of a tree. 2. Any connected acyclic graph. 3. Any data structure representing a tree (def. 1 or 2). For example, a rooted tree can be represented as a pointer to the representation of the root node. A representation of a node would contain pointers to the subtrees of the node as well as the data associated with the node itself. Because the number of subtrees of a node may vary, it is common practice to use a binary-tree representation. Tree. Sample tree represented as a Venn diagram (top) and as a directed graph The terminology associated with trees is either of a botanic nature, as with forest, leaf, root, or is genealogical, as with ancestor, descendant, child, parent, sibling. See also binary tree.
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