# Practice with Recursion

import cs125.trees.BinaryTree
fun treeDepth(tree: BinaryTree<*>?): Int {
return 0
}
assert(treeDepth(BinaryTree(0, 1, 2)) == 1)

Guess what? In this lesson we’ll be doing more practice with binary trees! And recursion! What could be more fun?

## Warm Up Debugging ChallengeWarm Up Debugging Challenge

But, would we want to miss out on another debugging challenge? No way!

## Tree DepthTree Depth

As a warm up let’s write a recursive function to determine the depth or height of a tree. As a reminder, the depth is defined as the distance from the root node to the farthest leaf node. (The depth is not defined for a empty tree, since it has no root.)

// Tree Depth

## Tree Node CountTree Node Count

Next, let’s look at an example of a recursive function that passes another data structure around. We’ll write a recursive method that returns an array with counts of the number of nodes that have zero, one, or two children. This will also prepare you for this lesson’s homework problem—which is a tricky one!

// Tree Child Count

## Binary Search TreeBinary Search Tree

Finally, let’s look again at the problem of locating a node in a binary tree. We’ll start with code from our previous answer, redesign it to be more efficient, and then analyze the performance of our new approach.

import kotlin.random.Random
class BinaryTree<T>(
var value: T,
var left: BinaryTree<T>? = null,
var right: BinaryTree<T>? = null
) {
constructor(values: List<T>) : this(values)
if (Random.nextBoolean()) {
if (right == null) {
right = BinaryTree(newValue)
} else {
}
} else {
if (left == null) {
left = BinaryTree(newValue)
} else {
}
}
}

## Practice: Binary Tree Search Path

Created By: CS 124 Staff / Version: 2020.11.0

Let's continue exploring recursion on binary trees. However, this problem takes a significant step forward in difficulty, so be prepared!

We've provided a method `pathToValue` that accepts a `BinaryTree<Any>` as its first parameter and an `Any` as its second. It returns a `List<Any>` containing all the values in the tree on the way to the first node with a value equal to the passed `Any`, or `null` if the tree does not contain the passed `Any`. We've handled this case already for you in the starter code.

Our wrapper method initializes the list properly and then calls a private helper method which performs the recursion. The helper should return `true` if the tree contains the value, and if it does also manipulate the list properly. If the tree does not contain the value it should return `false`. You will want to use ```add(int index, Any value)``` to add values to the front of the list as you work your way through the tree.

This problem is hard! Here's an outline of a solution to help get you started:

• If you reach an empty tree, you can return `false`, since an empty tree does not contain the value
• Otherwise, if this node contains the value, add yourself to the list, stop recursing, and return `true`.
• Otherwise, first search your right subtree. If that succeeds, then this node is also part of the path and should be added. If not, try the left subtree.
• If neither the right nor left subtree contains the node, you should return false and not modify the list, since this node is not on the path to the desired node.

Good luck and have fun!

## Homework: BinaryTree to Map

Created By: CS 124 Staff / Version: 2021.4.0

Create a method `toMap` that accepts a `BinaryTree<*>` and returns a `Map<Any, Int>` mapping the values in the tree to the count of the times that the value appears.

Our suggestion is to have `toMap` create the map and then call a private recursive helper method to populate it. You will need to import `cs125.trees.BinaryTree`. We've provided some code to get you started.

For reference, `cs125.trees.BinaryTree` is defined like this:

Note that you may need to cast `tree.value` to `Any` so that you can add it to your map.

## More Practice

Need more practice? Head over to the practice page.

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