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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 Challenge
Warm Up Debugging Challenge

Let’s warm up with another debugging challenge!

Create a method named countEqualToEitherChild that accepts a single BinaryTree<*>? and counts the number of nodes in the tree where the value at that node is equal to either the value at its right child or the value at its left child. Keep in mind that not every node has a right or left child, so you'll need to check for null carefully. (Or use try-catch!) However, you can assume that all of the values in the tree are non-null.

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

Tree Depth
Tree 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 Count
Tree 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 Tree
Binary 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[0])
private fun add(newValue: T) {
if (Random.nextBoolean()) {
if (right == null) {
right = BinaryTree(newValue)
} else {
right!!.add(newValue)
}
} else {
if (left == null) {
left = BinaryTree(newValue)
} else {
left!!.add(newValue)
}
}
}

Practice: Binary Tree Search Path

Created By: Geoffrey Challen
/ 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!

import cs125.trees.BinaryTree
fun pathToValue(tree: BinaryTree<Any>, value: Any): List<Any>? {
val path = mutableListOf<Any>()
return if (pathToValue(tree, value, path)) {
path
} else {
null
}
}
private fun pathToValue(tree: BinaryTree<Any>?, value: Any, path: MutableList<Any>): Boolean {
return false
}

Homework: BinaryTree to Map

Created By: Geoffrey Challen
/ 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.

import cs125.trees.BinaryTree
fun toMap(tree: BinaryTree<*>): Map<Any, Int>? {
// Create your map
// Call the helper method to populate the map
// Return the map
return null
}
// Helper method
private fun toMap(tree: BinaryTree<*>?, values: MutableMap<Any, Int>) {
// Add to mutableMap<Any, Int> by casting to Any
}

More Practice

Need more practice? Head over to the practice page.