Data Structure In Computer Science Using Jeliot Execution

Data Structure Computer Sciencusing Jeliot Execute The Following Tre

Data structure, Computer Scienc Using Jeliot, execute the following tree algorithm: import Prog1Tools.IOTools; class Node { Node left; Node right; int value; public Node(int value) { this.value = value; } } public class GeneralTreeTest { public static void main(String[] args) { // build a simple tree add 5 nodes to the tree Node root = new Node(5); System.out.println("Tree Example"); System.out.println("Building tree with root value " + root.value); insert(root, 1); insert(root, 8); insert(root, 6); insert(root, 3); insert(root, 9); System.out.println("Traversing tree "); printOrder(root); } public static void insert(Node node, int value) { if (value node.value) { if (node.right != null) { insert(node.right, value); } else { System.out.println(" Inserted " + value + " to right of " + node.value); node.right = new Node(value); } } } public static void printOrder(Node node) { if (node != null) { printOrder(node.left); System.out.println(" Traversed " + node.value); printOrder(node.right); } } } This algorithm first inserts five nodes into a tree structure and then traverses the tree.

Using the Jeliot environment, load, compile and execute this java algorithm to understand its operation. Determine the kind of tree structure that is being created and determine what kind of traversal the algorithm is conducting. Finally, conduct an Asymptotic analysis for the provided algorithm and report your analysis including Big O, Big Omega, or Big Theta as appropriate. Post your findings to the discussion forum and review and respond to the postings of your peers. If you have arrived at a different answer or analysis with your peers, discuss your findings with your peers and attempt to determine whose analysis is most accurate. You must post your initial response before being able to review other student’s responses. Once you have made your first response, you will be able to reply to other student’s posts. You are expected to make a minimum of 3 responses to your fellow student’s posts. WE THE PEOPLE WORKSHEET RESOURCES POS-301: We the People Essay Questions Respond to the following questions in words each. 1. Analyze the Declaration of Independence, the Articles of Confederation, and the U.S. Constitution. Explain the significance of these founding documents and how they altered the concept of government that had prevailed in society before their creation. 2. What does it mean to be a part of “We the Peopleâ€? What rights do “We the People†have and where do those rights come from? 3. How has the term “American†changed from the founding of the nation through today? References: © 2015. Grand Canyon University. All Rights Reserved.

Sample Paper For Above instruction

Introduction

This paper presents an analysis of a Java-based binary search tree algorithm, focusing on its structure, traversal method, and asymptotic complexity. The goal is to understand the nature of the tree generated by the code, identify the traversal type, and provide an asymptotic analysis to evaluate the algorithm's efficiency in terms of computational complexity.

Understanding the Tree Structure

The provided code constructs a binary search tree (BST), a hierarchical data structure in which each node has at most two children—left and right. When inserting nodes, the algorithm compares the value to the current node and then proceeds to insert into the left subtree if the value is less, or into the right subtree if greater. Given the sequence of insertions (5, 1, 8, 6, 3, 9), the resulting tree is a BST with the root node 5.

The insertion of values proceeds as follows:

- Node with value 1 becomes the left child of 5.

- Node with value 8 becomes the right child of 5.

- Node with value 6 becomes the left child of 8.

- Node with value 3 is inserted as the right child of 1 (since 3 > 1).

- Node with value 9 becomes the right child of 8.

The resulting structure is a binary search tree, where the left subtree of each node contains values less than the node's value, and the right subtree contains greater values, maintaining the BST property.

Type of Tree and Traversal Conducted

The tree created is a binary search tree. The traversal method used in the code is an in-order traversal, which visits the left subtree, then the node itself, and finally the right subtree. This in-order traversal outputs the nodes in ascending order for a BST.

The output sequence demonstrates the traversal:

- Visit leftmost nodes first, then the parent nodes,

- Producing a sorted sequence of node values.

Since the printOrder method in the code employs in-order traversal, the algorithm visits nodes following the sequence: left, node, right.

Asymptotic Analysis

The asymptotic complexity of the insertion and traversal algorithms depends on the height of the tree.

- Insertion: In the worst case, inserting a node requires traversing an entire branch of the tree, which can be as long as the height of the tree, h. Therefore, insertion has a time complexity of O(h).

- Traversal: The in-order traversal visits every node exactly once, resulting in a time complexity of O(n), where n is the total number of nodes.

In a balanced binary search tree, the height h is proportional to log n, leading to:

- Best/average case: O(log n) for insertion,

- Worst case: O(n) if the tree becomes skewed (like a linked list).

Overall, the total asymptotic complexity of inserting n nodes is O(n log n) in a balanced tree, or O(n^2) if the tree is highly unbalanced. The traversal complexity remains O(n).

As for the space complexity, it depends on the maximum height of the recursion stack during traversal or insertion, which is O(h). In a balanced tree, this is O(log n); in the worst case, O(n).

Conclusion

The Java algorithm constructs a binary search tree through sequential insertions, which is traversed in-order to output sorted node values. The structure supports efficient search operations when balanced, with insertion and traversal complexities varying according to the tree's height. The asymptotic analysis indicates that balanced trees yield logarithmic insertion complexity, but unbalanced trees degrade to linear performance, emphasizing the importance of maintaining balance in practical implementations.

References

1. Introduction to Algorithms (3rd ed.). MIT Press.
2. Algorithms (4th ed.). Addison-Wesley.
3. Data Structures and Algorithm Analysis in Java (3rd ed.). Addison-Wesley.
4. Data Structures and Algorithms in Java (6th ed.). Wiley.
5. The Algorithm Design Manual (2nd ed.). Springer.
6. Design and Analysis of Algorithms. PWS Publishing.
7. Cracking the Coding Interview. CareerCup.
8. The Art of Computer Programming, Volume 3: Sorting and Searching. Addison-Wesley.
9. The Art of Computer Programming, Volume 1: Fundamental Algorithms. Addison-Wesley.
10. Data Structures and Network Algorithms. SIAM.