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tree structure

Tree structure is a very common and important data structure, which simulates trees in nature. The tree structure consists of nodes (node) and edges (edge), one of which is designated as the root node (root), and other nodes are connected together according to the hierarchical relationship. Each node can have zero or more child nodes, and each child node can have its own child nodes, forming a hierarchical structure.

Basic concept of tree structure

root node

The root node in the tree structure is the starting node of the entire tree. It has no parent node and is the only entry of the tree.

child node

A child node in a tree structure is the direct successor node of a node, and a node can have zero or more child nodes.

parent node

The parent node in the tree structure is the direct predecessor node of a certain node, and a node can only have one parent node.

leaf node

A leaf node in a tree structure is a node that has no children, also known as a terminal node.

sibling node

Nodes in a tree structure that have the same parent node are called sibling nodes.

subtree

A subtree in a tree structure is a tree composed of a node and all its descendant nodes, and each node can be regarded as the root node of a subtree. A subtree is a tree structure consisting of a node and all its descendant nodes. A subtree can be part of a tree structure or the entire tree structure itself.

depth

The depth of a node in a tree structure refers to the length of the path from the root node to that node.

high

The height of a node in a tree structure is the length of the path from that node to the furthest leaf node.

Features of the tree structure

The tree structure has the following characteristics:

Hierarchy : There is a clear hierarchical relationship between nodes in a tree structure, and each node has a unique parent node (except the root node) and zero or more child nodes.
Uniqueness : Each node in the tree structure has a unique parent node and a unique position.
Acyclicity : There is no cycle in the tree structure, that is, there is no path back to the node after going through several edges from a certain node.
Orderedness : The child nodes in the tree structure are ordered, that is, the order of the child nodes is determined.

binary tree

A binary tree is a special tree structure in which each node has at most two child nodes, called left child and right child. A binary tree can be empty, or a non-empty tree with the following properties:

Each node has at most two child nodes.
The value of the left child node is less than or equal to the value of the parent node.
The value of the right child node is greater than or equal to the value of the parent node.
This property of a binary tree makes it very efficient in operations such as searching, sorting, and traversal.

forest

A forest is a collection of disjoint tree structures. Each tree structure is a subtree of the forest. In other words, a forest is composed of multiple independent tree structures.
Every binary tree can be viewed as a forest, where the left subtree of each node is a binary tree, and the right subtree is also a binary tree.
Conversely, each forest can be viewed as a binary tree where the left subtree of the root node of each tree is empty and the right subtree is the next tree in the forest.

Find and traverse methods

look up

In the tree structure, commonly used search methods are depth-first search (DFS) and breadth-first search (BFS).

depth-first search

Starting from the root node, follow each branch as far as you can until you reach the target node or go no further. Depth-first search can be implemented using recursion or a stack.

breadth first search

Starting from the root node, traverse layer by layer in hierarchical order until the target node is found or all nodes are traversed. Breadth-first search can be implemented using queues.

traverse

Tree structure traversal methods include pre-order traversal, in-order traversal and post-order traversal.

preorder traversal

First visit the root node, and then recursively traverse the subtrees in the order of left subtree and right subtree.

Inorder traversal

First recursively traverse the subtrees in the order of the left subtree, then visit the root node, and finally traverse the subtrees recursively in the order of the right subtree.

post order traversal

First traverse the subtree recursively in the order of left subtree and right subtree, and then visit the root node.

Application Scenario

Tree structure has a wide range of application scenarios in computer science and information technology, including but not limited to the following aspects:

File system : File systems usually use a tree structure to organize the hierarchical relationship of files and directories.
Database : The index structure in the database often uses a tree structure to improve the efficiency of data retrieval.
Compilation principle : The syntax analysis stage in the compiler uses a tree structure to represent the syntax structure of the source code.
Artificial Intelligence : Tree structures are used in machine learning algorithms such as decision trees and neural networks to represent and process data.
Network Routing : Routing tables usually use a tree structure to determine the forwarding path of packets.

As a flexible and efficient data structure, the tree structure plays an important role in the fields of computer science and information technology, and is widely used in various scenarios.

Trees, Forests, and Binary Trees