Tree Traversals

Table of Contents

Based on Lenhart and Jannen (https://williams-cs.github.io/cs136-f20-www/slides/treeTraversals.pdf)

1 Reading

Read Bailey 12.6.

2 Learning Goals

After this lesson you will be able to

  1. Describe and implement the four primary tree traverals

3 Slides

You can download the slides that were the basis for the lecture in pdf or PowerPoint.

4 Practice Problems1

  1. In code that recursively traverses binary trees, how many recursive calls are usually found within the code?

  2. For the following binary tree give the order nodes are visited for a pre-order, an in-order, a post-order traversal, and a level-order traversal.

    binary-tree.png

  3. What does this code do? 

    public void mystery(BinaryTreeNode<String> node) {
    if (node == null) {
        return;
    }
    mystery(node.right);
    mystery(node.left);
    System.out.println(node.data);
}
  4. Write a method public void printExpr(BinaryTreeNode<String> expr) that uses an in-order traversal to print out a correctly parenthesized version of the expression represented by the tree rooted at expr.

Footnotes:

1

Solutions:

  1. Usually 2. Each call handles one subtree.
  2. When nothing else is said, a left-to-right traversal is assumed.
    • Pre-order traversal: GEBDFKMR
    • In-order traversal: BDEFGKMR
    • Post-order traversal: DBFERMKG
    • Level-order traversal: GEKBFMDR
  3. The code implements a right-to-left post-order traversal (i.e., the right subtree is traversed before the left subtree).
  4. public void printExpr(BinaryTreeNode<String> expr) {
    if (expr == null) {
        return;
    }
    if (expr.isLeaf()) {
        System.out.print(expr.data);
        return;
    }
    System.out.print("(");
    printExpr(expr.left);
    System.out.print(expr.data);
    printExpr(expr.right);
    System.out.print(")");
}