Basic knowledge of tree and binary tree (detailed illustration)

One 、 Trees

（1） Trees （ Tree ） yes n ( n >0） A finite set of nodes . n =0 Time is called empty tree . In any non-empty tree ： There is and only one specific one called a root （ Root ） The node of ;

（2） When n >1 when , The rest of the nodes can be divided into m ( m >0） A finite set that doesn't intersect each other T 、T2、…………、 Tm , Each set itself is a tree , And called the root of the subtree （ SubTree ), As shown in the figure below .

Two 、 The node of the tree

（1） The number of subtrees a node has is called the degree of the node (Degree).

（2） Degree is 0 The nodes of are called leaf nodes (Leaf) Or terminal node ;

（3） The degree is not for 0 The nodes of are called non terminal nodes or branch nodes .

（4） Except for the root node , Branch nodes also become internal nodes .

（5） The degree of a tree is the maximum value of the degree of each node in the tree .

3、 ... and 、 The relationship between nodes

（1） The root of a node's subtree is called the child of the node (Child), Accordingly , This node is called the parents of children (Parent).

（2） Children of the same parents call each other brothers (Sibling). The ancestor of a node is all nodes from the root to the branch it passes through .
（3） Any node in a subtree with a node as its root is called the descendant of the node .

Four 、 Layer and depth of tree

（1） The hierarchy of nodes (Level) Define from the root node , The root is the first layer , The child of root is the second layer .

（2） If a node is at i layer , Then the root of its subtree is i+1 layer .

（3） Their parents are cousins at the same level .

（4） Of nodes in a tree The biggest level Called the depth of the tree (Depth) Or height .

5、 ... and 、 Binary tree
        Binary tree (Binary) yes n(n≥0) A finite set of nodes , It has at most two subtrees per node . It may be an empty set , Or it is composed of a root node and two disjoint binary trees called the left subtree and the right subtree of this root respectively .

6、 ... and 、 Five basic forms of binary trees  

（1） Empty binary tree （ There is no node ）

（2） There is only one root node

（3） The root node has only the left subtree

（4） The root node has only right subtrees

（5） The root node has both left and right subtrees

7、 ... and 、 The special form of binary tree

（1） Oblique tree

 （2） Full binary tree

（3） Perfect binary tree

8、 ... and 、 Properties of binary trees