What is a Binary Tree? How many classifications are there? What is a node?

A node without a daughter tree is a leaf node.

The degree of a node refers to the number of subtrees of the node, and there is no node with a degree greater than 2 in the binary tree. That is, each node can have a maximum of two subtrees.

In computer science, a binary tree is an ordered tree with up to two subtrees per node. Usually the root of the subtree is called the "left" subtree

subtree) and the right

subtree）。Binary trees are often used as binary lookup trees and binary heaps.

1) Complete binary tree - only the bottom two layers of the binary tree with a node degree less than 2, and the nodes of the bottom layer are concentrated in several positions on the far left of the layer;

2) Full binary tree - except for the leaf nodes, each node has left and right children, and the leaf nodes are at the bottom of the binary tree.

Node: A noun used to describe a "tree" structure in a data structure.

This structure resembles an upside-down tree.

Each leaf grows on a node, and this node is called the parent node of the leaf, and this leaf is called the child node of your node, and it is also called the leaf node of the tree, and it has no child node. And the parent node of the leaf must have the parent node above, so that the root node will be reached one level at a time, it is like the root of a tree, and there is no "fork" on it.

A complete binary tree with a height of h.

There is a maximum of (2 to the hth power-1) nodes.

There are at least (2 to the (h-1) power) nodes.

When there is only one node in the last layer, the total number of complete binary tree nodes is the least, then we can know that there are (2 h-1)-1 in the first h-1 layer, and the total number of (2 h-1)-1+1 ==2 h-1 is added to the last layer.

The degree of a binary tree represents the number of subtrees or direct successors of a node, and the degree of a binary tree is a subtree or monad. 2 degrees is two children, or the left and right subtrees have two forks with a maximum degree of 2.

A child node is a child of a node's subtree, the root of which is called the node; A parent node is a child whose B node is a node, and a node is the parent of a node.

The characteristic of a binary tree is that the number of nodes on each layer is the maximum number of nodes, and in a binary sock tree, if all but the last layer is full, and either the last layer is full, or there is a lack of continuous nodes on the right, then the binary tree is a complete binary tree.

A full binary tree with n nodes has a depth of floor(log2n)+1. A complete binary tree with a depth of k, with at least 2k-1 leaf nodes and at most 2k-1 nodes.

Summary. And the leaf nodes are arranged from left to right, which is a complete binary tree.

What are the forms of a three-node binary tree (please illustrate) There are five forms of kissing.

1. Complete binary tree: If the height of the binary tree is h, except for the h layer.

The number of nodes in the other layers (1 h-1) reached the maximum, and the hth layer had leaf nodes.

And the leaf nodes are arranged from left to right, which is a complete binary tree.

Kiss is one of these five types.

1. Node: Each element in the binary tree is called a node.

2. Degree: The degree of the binary tree represents the number of children or direct successors of a node, and 1 degree is only one child or monad tree. 2 degrees is a binary tree that both children or left and right subtrees have, and the maximum degree is 2.

3. Leaves: Leaves are the abbreviation of leaf nodes. The leaf, or leaf, refers to certain computers in the network structure that receive signals from computers that are closer to the center and do not transmit signals to computers that are farther away.

The leaf node is the lowest node in the tree, and the leaf node has no child nodes. The structure of formatting leaf nodes is slightly more complex than that of intermediate nodes. To be able to save multiple entries in one formatted leaf node.

According to the classification, it can be divided into the following types:

A binary tree is a commonly used structure in trees, and it has the following characteristics (assuming that the number of layers i starts at 1):

Binary trees are further divided into the following types:

Note: Note:

If the height of a complete binary tree is h(h >=1) and the number of points is n, it has the following important characteristics:

A complete binary tree with n nodes (n > 0), numbering nodes from top to bottom, left to right, starting from 1, to any ith node.

If a complete binary tree has 768 nodes, what is the number of leaf nodes?

Suppose the number of nodes with a leaf degree of 0 is n0, the number of nodes with a degree of 1 is n1, and the number of nodes with a degree of 2 is n2, then the number of summary points has the following relationship:

Since the number of complete binary trees with a degree of 1 is either 0 or 1, there are two cases here:

It can also be concluded that if the total number of nodes is odd, then the number of leaf nodes n0 = n + 1) 2 , and if it is an even number, the number of leaf nodes is n0 = n 2

The two cases can be simplified when calculating, because the final content is an integer, so if the two behaviors are unified, you can choose to use the odd case uniformly, that is, n0 = n + 1) 2. This calculation method is no problem in the case of an odd number of nodes, but if it is an even number, the result will be a decimals, and the extra parallel decimal is actually not needed in the case of an even number, in order to tolerate faults, so at this time you can take the way of rounding down to discard the decimals, and then carry out the fault tolerance of even numbers, so as to achieve the purpose of compatibility between the two situations.

Therefore, the final method can be used to calculate the number of nodes with a degree of 0 in the following way:

floor((n + 1) >1)

Answer]: There is a binary tree of cn nodes (n>=2).

This is 1 summing formula.

n=0, which is an empty tree, and has only 1 form of brigade, i.e. a[0]=1.

n=1, which is a single-node ridge point tree, with only one morphology. i.e. a[1] = 1.

When n>=2, a[n] is the sum of a[n]a[n-m-1], m from 0 n-1.

For example, when n=2, m=0 n-1=0 1, a[2]=a[0] a[2-0-1]+a[1] a[2-1-1]=a[0] a[1]+a[1] a[0]=2;

When n=3, m=0 n-1=0 2,a[3]=a[0] a[3-0-1]+a[1] a[3-1-1]+a[2] a[3-2-1].

a[0]×a[2]+a[1]×a[1]+a[2]a[0]=1×2+1×1+2×1=5。Split the middle accompaniment.

A binary tree is an important type of tree structure.

The abstracted data structure of many practical problems is often in the form of binary trees, even ordinary trees can be easily converted into binary trees, and the storage structure and algorithm of binary trees are relatively simple, so binary trees are particularly important. Binary trees are characterized by a maximum of two sub-trees per node, and there are left and right points.

A binary tree is a set of n finite elements, which is either empty or consists of an element called a root and two disjoint binary trees called left and right subtrees, respectively, which are ordered trees. When the set is empty, the binary tree is called an empty binary tree. In a binary tree, an element is also called a node.

1. Full binary tree: If a binary tree only has nodes with degree 0 and nodes with degree 2, and the nodes with degree 0 are on the same layer, then the binary tree is full binary.

2. Complete binary tree: A binary tree with a depth of k and n nodes is called a complete binary tree if and only if each of its nodes corresponds to the nodes numbered from 1 to n in a full binary tree with depth k.

A complete binary tree is characterized by the fact that leaf nodes can only appear on the two largest sequences, and that the largest sequence of descendants under the left branch of a node is equal to or larger than the largest sequence of descendants under the right branch1.