Summary of concepts related to the basic definition of tree in data structure

definition

The recursive definition of the tree is as follows (personal preferred definition, from Baidu Encyclopedia): a single node is a tree, the root is the node itself.

T1,t2,.., tk is a tree with root nodes of N1,n2,.., NK respectively. With a new node n as N1,n2,.., NK's father, he gets a new tree, and the node n is the root of the new tree. We call N1,n2,.., NK as a group of sibling nodes, all of which are node N's sub-nodes. We also call T1,t2,.., tk as a subtree of node n.

An empty collection is also a tree, called an empty tree. There are no nodes in the empty tree. related terms (from Wikipedia, with changes)

1, the degree of the node: a node contains the number of sub-tree is called the degree of the node;
2, the degree of the tree: the maximum value of all nodes in a tree is called the degree of the tree;
3, leaf node or end node: zero degree node;
4, non-terminal node or branch node: The node is not zero degrees;

5, Father node or parent node: If a node contains child nodes, then this node is called the parent node of its child nodes;
6, child node or child node: A node contains a subtree of the root node is called the node's child nodes;
7, sibling nodes: nodes with the same parent node are called sibling nodes;

8, the level of the node: Define a tree root node level is 1, the other node hierarchy is its parent node level plus 1;
9. Height or depth of tree: the maximum value of all nodes in a tree is called the depth of this tree;

10, Cousin node: The parent node in the same layer of the nodes are each other cousins;
11, the ancestor of the node: from the root to the node on the branch of all nodes;
12. Descendants: Any node in a subtree that is rooted in a node is called the descendant of that node.
13. Forest: The collection of trees that are not intersected by M (m>=0) is called the forest;

need to be explained below: node = nodes, all originated from the English word node. leaf node = leaf node type

Unordered tree: There is no sequential relationship between the sub-nodes of any node in the tree, which is called the unordered tree, also known as the free tree;
Ordered tree: There is a sequential relationship between the sub-nodes of any node in the tree, which is called ordered tree;

Binary tree: A tree with a maximum of two subtrees per node is called a binary tree;
Binary search tree (binary sort tree)
Complete binary Tree
Full two fork Tree
Balanced two-pronged tree
Hoffman: The shortest two-fork tree with the right path is called Huffman tree or optimal binary tree;

Red and black Trees
B-Tree representation method

The most intuitive is the tree representation
There is another common method: first put the root node in a pair of parentheses, the root node immediately after a pair of parentheses, and then put its subtree in left-to-right order into the parentheses, the same layer of the subtree separated by commas. As in the preceding tree notation can be expressed as: (1 (2 (4), 3 (5,6)))