Math Problem Statement

Add the following elements into a Binary Search Tree and upload an image of the tree you've created. Do not balance the tree.

67, 25, 36, 90, 18, -2, 50, 9

Give the in-order, pre-order, and post-order traversals of the tree you created

Solution

Here is the binary search tree (BST) created using the elements: 67, 25, 36, 90, 18, -2, 50, and 9.

The traversal results are:

  • In-order traversal: [-2, 9, 18, 25, 36, 50, 67, 90]
  • Pre-order traversal: [67, 25, 18, -2, 9, 36, 50, 90]
  • Post-order traversal: [9, -2, 18, 50, 36, 25, 90, 67]

Would you like further details or have any questions?

Here are 5 related questions for further exploration:

  1. How does in-order traversal work in a binary search tree?
  2. What are the applications of pre-order traversal in tree structures?
  3. Why is the post-order traversal useful for deleting a binary tree?
  4. How does the structure of a BST depend on the order of insertion of elements?
  5. What are the advantages of using a self-balancing binary search tree?

Tip: In a binary search tree, the in-order traversal always results in a sorted sequence of elements.

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Math Problem Analysis

Mathematical Concepts

Data Structures
Binary Search Tree
Tree Traversals

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12