Python Coding Test Course, Traversing Trees

Introduction

Solving algorithm problems is a very important process for software developers. In particular, trees are used as a core structure in many problems, and understanding how to traverse trees is essential for effectively utilizing this structure. In this article, we will explain the basic concepts of trees and various traversal methods using Python, and connect theory to practice by solving actual algorithm problems.

Basics of Trees

A tree is a non-linear data structure consisting of nodes and the connections between them.
Each node can have child nodes, making this structure suitable for representing hierarchies.
The topmost node is called the root node, and there are various traversal methods that define the relationships between nodes.

Types of Trees

– Binary Tree: A tree where each node can have at most two child nodes.
– Binary Search Tree: A sorted binary tree where the left child is smaller than the parent node, and the right child is larger.
– AVL Tree: A balanced binary search tree that maintains a height difference of 1 or less.

Tree Traversal Methods

Tree traversal defines the order in which nodes are visited. The main traversal methods are as follows.

1. Pre-Order Traversal

Pre-order traversal visits the node itself first, then recursively visits the left child node, and finally visits the right child node.
In other words, the visiting order is: Node → Left → Right

2. In-Order Traversal

In-order traversal visits the left child node first, then the node, and finally the right child node.
The order is: Left → Node → Right

3. Post-Order Traversal

Post-order traversal visits the left child node first, then the right child node, and finally the node itself.
The order is: Left → Right → Node

Problem: Print the Results of Binary Tree Traversal

The following is a problem that takes nodes of a binary tree as input and outputs the results of pre-order, in-order, and post-order traversals.
Given a list containing the values of each node, you need to return the results of the tree traversal.

Problem Description

Based on the given list, construct a binary tree and return a list containing the results using each traversal method.
For example, if the list is [1, 2, 3, 4, 5], the following tree can be constructed:

Input / Output Format

Input: A list containing each node.
Output: Lists of results from pre-order, in-order, and post-order traversals.

Problem-Solving Process

Step 1: Define the Tree Structure

To construct the tree, we will first define a class that represents a node.

class TreeNode:
    def __init__(self, value):
        self.value = value
        self.left = None
        self.right = None

Step 2: Build the Tree

We will write a function that constructs the tree based on the given list.
In this example, we simply set the first value of the list as the root node and place the rest as the left and right children.

def build_tree(values):
    if not values:
        return None
    root = TreeNode(values[0])
    for value in values[1:]:
        insert_node(root, value)
    return root

def insert_node(root, value):
    if value < root.value:
        if root.left is None:
            root.left = TreeNode(value)
        else:
            insert_node(root.left, value)
    else:
        if root.right is None:
            root.right = TreeNode(value)
        else:
            insert_node(root.right, value)

Step 3: Write the Traversal Functions

We will implement each traversal method. The tree will be explored recursively and nodes will be stored in a list.

def preorder_traversal(root):
    result = []
    if root:
        result.append(root.value)
        result.extend(preorder_traversal(root.left))
        result.extend(preorder_traversal(root.right))
    return result

def inorder_traversal(root):
    result = []
    if root:
        result.extend(inorder_traversal(root.left))
        result.append(root.value)
        result.extend(inorder_traversal(root.right))
    return result

def postorder_traversal(root):
    result = []
    if root:
        result.extend(postorder_traversal(root.left))
        result.extend(postorder_traversal(root.right))
        result.append(root.value)
    return result

Step 4: Integrate and Call

Finally, we integrate all of the above functions to solve the problem.

def traverse_tree(values):
    root = build_tree(values)
    return {
        'preorder': preorder_traversal(root),
        'inorder': inorder_traversal(root),
        'postorder': postorder_traversal(root),
    }

# Example usage
input_values = [1, 2, 3, 4, 5]
result = traverse_tree(input_values)
print(result)  # Print the results

Final Results and Summary

Through the above process, we can traverse the given binary tree list and derive the results of pre-order, in-order, and post-order traversals.
This problem has taught us the concept of tree traversal and how to implement it efficiently.
Additionally, we encourage you to experience and practice with various tree structures and traversal methods.