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    • Sorting Algorithms : 51

    • Practice with Recursion : 50

    • Trees and Recursion : 49

    • Trees : 48

    • Recursion : 47

    • Lists Review and Performance : 46

    • Linked Lists : 45

    • Algorithms and Lists : 44

    • Lambda Expressions : 43

    • Anonymous Classes : 42

    • Practice with Interfaces : 41

    • Implementing Interfaces : 40

    • Using Interfaces : 39

    • Working with Exceptions : 38

    • Throwing Exceptions : 37

    • Catching Exceptions : 36

    • References and Polymorphism : 35

    • References : 34

    • Data Modeling 2 : 33

    • Equality and Object Copying : 32

    • Polymorphism : 31

    • Inheritance : 30

    • Data Modeling 1 : 29

    • Static : 28

    • Encapsulation : 27

    • Constructors : 26

    • Objects, Continued : 25

    • Introduction to Objects : 24

    • Compilation and Type Inference : 23

    • Practice with Collections : 22

    • Maps and Sets : 21

    • Lists and Type Parameters : 20

    • Imports and Libraries : 19

    • Multidimensional Arrays : 18

    • Practice with Strings : 17

    • null : 16

    • Algorithms and Strings : 15

    • Strings : 14

    • Functions and Algorithms : 13

    • Practice with Functions : 12

    • More About Functions : 11

    • Errors and Debugging : 10

    • Functions : 9

    • Practice with Loops and Algorithms : 8

    • Algorithms I : 7

    • Loops : 6

    • Arrays : 5

    • Compound Conditionals : 4

    • Conditional Expressions and Statements : 3

    • Operations on Variables : 2

    • Variables and Types : 1

    • Hello, world! : 0

    Practice with Recursion

    import cs125.trees.BinaryTree;
    int treeDepth(BinaryTree tree) {
    return 0;
    assert treeDepth(new BinaryTree<Integer>(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!

    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 java.util.Random;
    // Binary Search Tree
    public class BinaryTree {
    private Object value;
    private BinaryTree right;
    private BinaryTree left;
    private Random random = new Random();
    public BinaryTree(Object setValue) {
    value = setValue;
    public BinaryTree(Object[] values) {
    assert values.length > 0;
    value = values[0];
    for (int i = 1; i < values.length; i++) {
    private void add(Object newValue) {
    if (random.nextBoolean()) {
    if (right == null) {
    right = new BinaryTree(newValue);
    } else {

    Solve: Binary Tree Search Path (Practice)

    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 public class BinaryTreePath with a single class method pathToValue. pathToValue accepts a BinaryTree<Object> as its first parameter and an Object as its second. It returns a List<Object> containing all the values in the tree on the way to the first node with a value equal to the passed Object, or null if the tree does not contain the passed Object. We've handled this case already for you in the starter code. However, you should fix pathToValue so that it throws an IllegalArgumentException if either the passed tree or the passed value is null.

    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, Object 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;
    import java.util.ArrayList;
    import java.util.List;
    public class BinaryTreePath {
    public static List<Object> pathToValue(BinaryTree<Object> tree, Object value) {
    List<Object> path = new ArrayList<>();
    if (pathToValue(tree, value, path)) {
    return path;
    } else {
    return null;
    private static boolean pathToValue(BinaryTree<Object> tree, Object value, List<Object> path) {
    return false;

    Solve: BinaryTree to Map

    Created By: Geoffrey Challen
    / Version: 2021.4.0

    Create a public class BinaryTreeToMap that provides a single static method toMap. toMap accepts a BinaryTree<?> and returns a Map<Object, Integer> 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. If the tree passed to toMap is null you should throw an IllegalArgumentException. You will need to import cs125.trees.BinaryTree, as well as Map and a Map implementation (probably HashMap) from java.util. We've provided some code to get you started.

    For reference, cs125.trees.BinaryTree has the following public properties:

    import cs125.trees.BinaryTree;
    import java.util.Map;
    public class BinaryTreeToMap {
    public static Map<Object, Integer> toMap(BinaryTree<?> tree) {
    // Check for null
    // Create your map
    // Call the helper method to populate the map
    // Return the map
    return null;
    // Helper method
    private static void toMap(BinaryTree<?> tree, Map<Object, Integer> values) {}

    More Practice

    Need more practice? Head over to the practice page.