> For the complete documentation index, see [llms.txt](https://cs61b-2.gitbook.io/cs61b-textbook/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://cs61b-2.gitbook.io/cs61b-textbook/17.-b-trees/17.7-exercises.md).

# 17.7 Exercises

## Factual

1. Which of the following are valid 2-3 trees?

 

<figure><img src="/files/VYqU3npB4MbNnkzuQfC0" alt=""><figcaption></figcaption></figure>

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<summary>Problem 1</summary>

Only (a).

A 2-3 tree only allows up to 3 children, which means a node can only have at most 2 values. (b) has an extra value in the rightmost node.

A 2-3 tree must also be perfectly balanced. (c) is imbalanced.

A B-Tree node always has one more child than the number of values. So in a 2-3 tree, a node with 1 value has 2 children, and a node with 2 values has 3 children. (d) violates this with the node `21`, which has one value but 3 children.

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## Procedural

1. Draw the 2-3 tree that results from inserting `1, 2, 3, 4, 5, 6, 7` in order.
2. [Problem 1](https://drive.google.com/file/d/1Vo8p4vbOGt7eY5TtalvAEnk4ignpTVvm/view?usp=sharing) of the Spring 2018 Midterm 2

<details>

<summary>Problem 1</summary>

Check your answers using this [interactive visualizer.](https://www.cs.usfca.edu/~galles/visualization/BTree.html)

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<details>

<summary>Problem 2</summary>

[Solutions](https://drive.google.com/file/d/1LIyFXwHYCWXNqIgKTsTyKiOYnB79_ykk/view?usp=sharing) and [walkthrough](https://www.youtube.com/watch?v=nMZn4EV0gGw) are linked here and on the course website.

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