The Binary Tree is one of the best ways to organize data when you need fast access. For this assignment, we will organize a list of names and perform various operations on those names. Build and show a binary tree based on the following names inserted into the binary tree in order listed: John, Eddie, Kim, Derrick, Ethan, Lonny, Mark, Curly, Donny, Nancy, Patricia, Oscar.
•Show the order to names for a preorder traversal
•Show the order to names for a postorder traversal
•Show the order to names for a inorder traversal
Is this tree balanced? Why or why not?
How would the tree need to look for it to be more balanced if it is not?
If we deleted Eddie from the tree, what would the new tree look like (use one of the current names to replace Eddie and the tree redone)?
I do not know where to start...Please point me in the right direction so I know how to do this on my own? Thanks
To build a binary tree and perform the operations on the given list of names, you can follow these steps:
1. Start by creating the root node of the binary tree with the first name in the list, which is "John".
2. For each subsequent name in the list, compare it with the current node's name to determine whether it should go to the left or right subtree of the current node.
3. If the name is less than the current node's name, move to the left child of the current node. If the left child is empty, insert the name as the left child. Otherwise, repeat step 2 for the left subtree.
4. If the name is greater than or equal to the current node's name, move to the right child of the current node. If the right child is empty, insert the name as the right child. Otherwise, repeat step 2 for the right subtree.
5. Repeat steps 2-4 for all the names in the list.
To visualize the binary tree, you can use ASCII art or draw it on paper. Each node will contain the name value and have a left child pointer and a right child pointer.
Preorder Traversal: In a preorder traversal, you visit the current node, then recursively traverse the left subtree, followed by the right subtree. For the given list of names, the preorder traversal order would be:
John, Eddie, Curly, Donny, Kim, Derrick, Ethan, Lonny, Mark, Nancy, Oscar, Patricia
Postorder Traversal: In a postorder traversal, you recursively visit the left subtree, followed by the right subtree, and finally the current node. For the given list of names, the postorder traversal order would be:
Donny, Curly, Eddie, Ethan, Lonny, Mark, Nancy, Oscar, Patricia, Kim, Derrick, John
Inorder Traversal: In an inorder traversal, you recursively traverse the left subtree, visit the current node, and then traverse the right subtree. For the given list of names, the inorder traversal order would be:
Curly, Donny, Eddie, Ethan, John, Kim, Lonny, Mark, Nancy, Oscar, Patricia, Derrick
To determine if the tree is balanced, you need to compare the height of the left and right subtrees of each node. If the height difference is greater than 1 for any node, the tree is not balanced. In this case, you can see that the given tree is not balanced because the height difference of the left and right subtree of the root node "John" is 2.
To make the tree more balanced, you can use a self-balancing binary tree algorithm like AVL tree or Red-Black tree. These algorithms automatically maintain balance during insertions and deletions by performing tree rotations.
If you delete "Eddie" from the given tree, you can replace it with the next name in the preorder traversal list, which is "Curly". The new tree would only differ in the position of "Curly" and its child nodes.
I hope this helps you get started with building and manipulating a binary tree!