Question

If your first name starts with a letter from A-J inclusively: Design the algorithm and method following operations for a binary tree T: • preorderNext(p): Return the position visited after p in a preorder traversal of T (or null if p is the last node visited). • inorderNext(p): Return the position visited after p in an inorder traversal of T (or null if p is the last node visited). Write a Java/Python to test your solution. What

Answer 1

The question involves designing algorithms for finding the successors of a node in preorder and inorder traversals of a binary tree. PreorderNext and inorderNext successors are found by understanding the specific properties of each traversal method. The Java skeleton code provided outlines the class structure and the methods to be completed with the traversal logic.

Step-by-step explanation:

Algorithm and Java Code for Preorder and Inorder Successor in a Binary Tree

To design algorithms for finding the preorderNext and inorderNext of a given node p in a binary tree T, we will utilize the properties of preorder and inorder traversals.

Preorder Traversal

For preorder traversal (root-left-right), the preorderNext of a node p is:

• If p has a left child, then it is the left child.
• If p does not have a left child but has a right child, then it is the right child.
• If p has neither, we go to p's parent (provided that we store parent pointers) and continue moving up until we find a node that is the left child of its parent and also has a right sibling. That right sibling is our preorderNext.
• If no such node exists, return null.

Inorder Traversal

For inorder traversal (left-root-right), the inorderNext of a node p is:

• If p has a right child, we go to the leftmost node of that right subtree.
• If p does not have a right child, we move up to the parents until we find a node that is the left child of its parent. The parent is our inorderNext.
• If we reach the root without finding such a node, return null.

Here is a simplified Java code that uses the above logic to find the preorder and inorder successors:

class Node {
int data;
Node left, right, parent;

Node(int item) {
data = item;
left = right = parent = null;
}
}

public class BinaryTree {
Node preorderNext(Node p) {
// Implement the above algorithm
}

Node inorderNext(Node p) {
// Implement the above algorithm
}

public static void main(String[] args) {
// Create a binary tree and test the methods
}
}

Replace the comment 'Implement the above algorithm' with the actual logic based on the given algorithms for preorderNext and inorderNext.