Table of contents
1 Introduction
Binary Search Tree (Binary Search Tree), also known as binary search tree or binary search tree, is a commonly used data structure for storing and finding ordered data sets. Its characteristic is that for each node in the tree, the values of all nodes in its left subtree are less than the value of the node, and the values of all nodes in the right subtree are greater than the value of the node. This property makes binary sorting trees efficient for search and insertion operations.
This article will introduce the concept and nature of binary sorting trees, discuss common traversal algorithms (preorder traversal, inorder traversal, postorder traversal), and give code examples for implementing binary sorting trees.
2. The concept and properties of binary sorting tree
A binary sort tree is a binary tree that satisfies the following properties:
For each node in the tree, all nodes in its left subtree have values less than that node's value.
For each node in the tree, all nodes in its right subtree have a value greater than that node's value.
The left and right subtrees are also binary sorted trees.
These properties make the search operation of the binary sorting tree very efficient, with an average time complexity of O(log n). At the same time, the binary sorting tree can also support operations such as insertion, deletion, and traversal.
3. Binary sort tree traversal
The traversal of a binary sorted tree refers to visiting all nodes in the tree in a certain order. Commonly used traversal methods include pre-order traversal, in-order traversal, and post-order traversal.
Preorder Traversal: Visit the root node first, then traverse the left subtree according to the preorder traversal method, and finally traverse the right subtree according to the preorder traversal method.
Inorder traversal (Inorder Traversal): Traverse the left subtree according to the inorder traversal method, then visit the root node, and finally traverse the right subtree according to the inorder traversal method.
Postorder traversal (Postorder Traversal): traverse the left subtree according to postorder traversal, then traverse the right subtree according to postorder traversal, and finally visit the root node.
Different traversal methods can obtain different node access sequences, which are suitable for different scenarios and problems.
4. Implementation of binary sorting tree
下面是使用C++语言实现二叉排序树的代码示例：
#include <iostream>
struct TreeNode {
int val;
TreeNode* left;
TreeNode* right;
TreeNode(int value) : val(value), left(nullptr), right(nullptr) {
}
};
class BinarySearchTree {
private:
TreeNode* root;
public:
BinarySearchTree() : root(nullptr) {
}
void insert(int value) {
root = insertNode(root, value);
}
TreeNode* insertNode(TreeNode* node, int value) {
if (node == nullptr) {
return new TreeNode(value);
}
if (value < node->val) {
node->left = insertNode(node->left, value);
} else {
node->right = insertNode(node->right, value);
}
return node;
}
void inorderTraversal() {
inorder(root);
}
void inorder(TreeNode* node) {
if (node == nullptr) {
return;
}
inorder(node->left);
std::cout << node->val << " ";
inorder(node->right);
}
};
int main() {
BinarySearchTree bst;
bst.insert(5);
bst.insert(3);
bst.insert(8);
bst.insert(1);
bst.insert(4);
std::cout << "Inorder traversal: ";
bst.inorderTraversal();
return 0;
}
The above code implements the insertion operation and in-order traversal operation of a binary sort tree. Insert nodes by calling the insert method, and use the inorderTraversal method for inorder traversal. In the above example, the order of inserting nodes is 5, 3, 8, 1, 4, and the inorder traversal result is 1 3 4 5 8.
5. Summary
This article introduces the concept, properties and traversal algorithm of binary sorting tree. A binary sort tree is an ordered data structure that enables efficient search and sort by exploiting the size relationship between nodes. In practical applications, binary sorting trees are widely used in scenarios such as database indexes and dictionaries. By understanding and mastering the principles and operations of binary sorting trees, we can better solve related problems and optimize algorithms.