Lab: Tree Traversal

Summary

In this laboratory, you will explore the traversal of trees. Although tree traversal can be used for all sorts of trees, you will ground your exploration in binary search trees.

Repository

https://github.com/Grinnell-CSC207/lab-tree-traversal-2019

Preparation

a. Fork and clone the specified respository.

b. Import the repository into Eclipse.

c. Skim the code to make sure that you understand the structure of the tree data structure.

Exercises

Exercise 1: Building a tree

Consider the following set of instructions.

    String[] strings = {"aardvark", "billygoat", "chinchilla", "dingo", "emu",
        "frog", "gnu", "hippo", "iguana", "jackalope", "koala", "llama"};
    BinaryTree<String> tree = new BinaryTree<String>(strings);

a. What tree do you expect these instructions to produce?

b. Run BinaryTreeExperiment to check your answer.

c. What do you expect to happen to the tree if we use an array with two more animals?

d. Check your answer experimentally.

Exercise 2: Alternate output

Suppose instead of printing the tree in the deeply nested form, we want to print the elements of the tree on a single (very long) line, but in more or less the same order that we get from dump.

gnu dingo billygoat aardvark chinchilla frog emu jackalope iguana hippo llama koala

a. Write a procedure, elements01(PrintWriter pen), that creates that output.

b. In what order does that method traverse the tree?

c. Suppose we traversed the tree using a depth-first, left-to-right, in-order traversal. What output would you expect?

d. Write a new procedure, elements02(PrintWriter pen), that prints the tree using a depth-first, left-to-right, in-order traversal.

Exercise 3: Avoiding recursion

You have likely written recursive procedures to generate that output. What if we can’t use recursion? For example, if we’re implementing an iterator, it will be almost impossible to stop the recursion at each stage.

Sketch, but do not implement, an algorithm to print all the values in the tree without using explicit recursion. You can use either depth-first, left-to-right, preorder traversal or depth-first, left-to-right, in-order traversal.

If you get stuck after two minutes, look at the notes at the end of this lab.

Spend no more than five minutes on this problem!

Exercise 4: Printing elements

Consider the following potential solution to the previous exercise.

/**
 * Print all of the elements in some order or other.
 * 
 * Note: We are trying to avoid recursion.
 */
public void print(PrintWriter pen) {
  // A collection of the remaining things to print
  Stack<Object> remaining = new Stack<Object>();
  remaining.push(this.root);
  // Invariants: 
  //   remaining only contains Strings or Nodes
  //   All values in the tree are either
  //     (a) already printed
  //     (b) in remaining
  //     (c) in or below a node in remaining
  while (!remaining.isEmpty()) {
    Object next = remaining.pop();
    if (next instanceof BinaryTreeNode<?>) {
      @SuppressWarnings("unchecked")
      BinaryTreeNode<T> node = (BinaryTreeNode<T>) next;
      if (node.right!= null) {
        remaining.push(node.right);
      } // if (node.right!= null)
      if (node.left != null) {
        remaining.push(node.left);
      } // if (node.left != null)
      remaining.push(node.value);
    } else {
      pen.print(next);
      pen.print(" ");
    } // if/else
  } // while
  pen.println();
} // print(PrintWriter)

a. How does this code achieve the goal of achieving recursive traversal without actually recursing?

b. In what order do you expect it to print the values in the tree?

c. Add this code to your program and verify that it works. If it does not, fix it.

Exercise 5: Other orderings

The print method prints the tree using a depth-first, left-to-right, pre-order strategy.

a. What changes would you have to make in order to have the print method traverse the tree using a depth-first, left-to-right, in-order strategy?

b. Check your answer experimentally.

c. What changes would you have to make in order to have the print method traverse the tree using a depth-first, left-to-right, postorder strategy?

d. Check your answer experimentally.

e. What changes would you have to make in order to have the `print method traverse the tree using a depth-first, right-to-left, inorder strategy?

f. Check your answer experimentally.

Exercise 6: Iterating trees

Using the ideas from the print method, implement the iterator method. (You should not implement remove.)

You may iterate the tree in any order you consider reasonable.

Exercise 7: Breadth-first traversal

So far, we’ve only explored depth-first traversal. But what if we want to do breadth-first traveral, wherein we visit/print all of the values at a particular level before going on to the next level?

a. Sketch what changes you would make to print to get it to print the values in a top-down, preorder, left-to-right, breadth-first traversal. (Hint: You probably don’t want to use a stack any more.)

b. Implement those changes.

For those with extra time

If you find that you have extra time, try any of the following problems.

Extra 1: Numbering levels

Extend your breadth-first traversal algorithm so that each time it reaches a new level, it prints a new line and the level number 0 for the root, 1 for the children of the root, 2 for the grandchildren, etc.). (It’s okay if you print one extra level number at the end, even if there are no values at that level.)

0: monkey
1: gibbon snake
2: dingo koala python viper
...

Extra 2: Bottom-up traversal

Your breadth-first traversal algorithm should start at the top and work its way down. Rewrite the algorithm so that it prints the tree from the bottom up.

Notes

If you need to simulate a recursive method without recursion, the most common strategy is to use a stack.