Master the E - Complete Binary Tree in AtCoder Contest 321

Master the E - Complete Binary Tree in AtCoder Contest 321

Table of Contents

1. Introduction
2. Problem Statement
3. Understanding Complete Binary Trees
4. Finding the Number of Vertices with a Certain Distance
5. Solution Approach
6. Code Explanation
7. Complexity Analysis
8. Alternative Approaches
9. Conclusion
10. Additional Resources

Article

Introduction

In this article, we will Delve into the problem statement of "Compete Bity," which is the fifth problem of the ATOD Beginner Contest 321. We will discuss the nature of complete binary trees and explore a solution approach to finding the number of vertices with a certain distance. Additionally, we will provide a code explanation, analyze the complexity of the solution, and explore alternative approaches for solving the problem.

Problem Statement

The problem at HAND involves a complete binary tree with n vertices ranging from 1 to n. A complete binary tree follows specific rules, such as the left child being 2 times the parent's value and the right child being 2 times the parent's value plus 1. The levels of the tree, except for the last level, are expected to be full. The goal is to find the number of vertices that are a certain distance K away from a given vertex X.

Understanding Complete Binary Trees

Before diving into the solution approach, it is essential to understand the characteristics of complete binary trees. A complete binary tree is defined by the relationship between parent nodes and their respective left and right child nodes. By knowing the parent node I, the left child can be found using the formula 2 I, while the right child can be found using the formula 2 I + 1. Additionally, all levels of the tree, except the last level, are full.

Finding the Number of Vertices with a Certain Distance

To solve the problem, we need to determine the number of vertices that are at a distance K from a specific vertex X. This can be achieved by traversing each subtree and identifying the vertices at the desired distance. We can then explore the right subtree with a distance of K - 1 or the left subtree with a distance of K - 2, depending on the relationship of the previous node.

Solution Approach

To solve the problem, we utilize a recursive approach. Starting from the Current node, we find all the nodes at distance K in each subtree. We then move up to the parent node and find the nodes at distance K - 1 in its right subtree. By using a recursive function, we can traverse the tree efficiently.

Code Explanation

The code for solving the problem involves two functions. The first function handles the recursion and allows us to move to the parent of a given node, updating the necessary parameters. The Second function calculates the number of nodes in a subtree at a distance K. By finding the leftmost and rightmost nodes at the K level, we can determine the minimal number of nodes.

Complexity Analysis

When analyzing the complexity of the solution, we take into account the constraints in terms of the number of test cases (T) and the number of vertices (N). With the given constraints, an approach with a time complexity of O(log N) should suffice. The overall time complexity of the solution is O(T * log^2N).

Alternative Approaches

Although the discussed approach provides a simple and effective solution, other alternative approaches with a time complexity of O(log N) are possible. Exploring these alternatives can offer additional insights and approaches to solving the problem.

Conclusion

In conclusion, this article has explored the problem of "Compete Bity" in the Context of the ATOD Beginner Contest 321. We have discussed the nature of complete binary trees, presented a solution approach, explained the code, analyzed the complexity, and explored alternative approaches. By following these guidelines, You can efficiently solve the problem and tackle similar challenges.

Additional Resources

For further understanding and implementation of the "Compete Bity" problem, the following resources are recommended:

• Link to code implementation
• Detailed video explanation

Highlights

• Introduction to the "Compete Bity" problem in the ATOD Beginner Contest 321
• Understanding the properties of complete binary trees
• Solving the problem of finding the number of vertices with a certain distance from a given vertex
• Recursive solution approach for efficient tree traversal
• Code explanation and analysis of complexity
• Exploration of alternative approaches for the problem
• Additional resources for further understanding and implementation

FAQ

Q: Can you explain the concept of complete binary trees in more Detail? A: Certainly! Complete binary trees have specific rules for the relationship between parent nodes and their left and right child nodes. Each left child is 2 times the value of the parent, while each right child is 2 times the parent's value plus 1. Additionally, all levels of the tree, except for the last level, are expected to be full.

Q: How does the solution approach handle traversing the tree efficiently? A: The solution approach utilizes recursion to traverse each subtree and identify the nodes at the desired distance. By moving up to the parent node and exploring the right or left subtrees accordingly, we can efficiently find the desired number of vertices.

Q: Are there any alternative approaches to solving the problem? A: Yes, there are alternative approaches with a time complexity of O(log N) that can be explored. While the discussed approach is effective, it's always valuable to consider different strategies and apply them when appropriate.

Q: Where can I find additional resources for understanding and implementing the "Compete Bity" problem? A: You can find the code implementation and a detailed video explanation by following the provided links in the "Additional Resources" section of this article. These resources will provide a more in-depth understanding of the problem and its solution.