Exercises - Lecture 9

9A

1. Which of the following are binary search trees?

2. Write the values printed by an in-order traversal of each of the following BSTs. What do you notice about the resulting sequences?

   

3. Draw the binary tree resulting from the following sequence of insertions:

   t = new BST();
   t.insert(10)
   t.insert(15)
   t.insert(16)
   t.insert(8)
   t.insert(16)
   t.insert(9)
   t.insert(11)
   t.insert(-1)

4. Draw the binary tree resulting from the following sequence of insertions:

   t = new BST();
   t.insert(-1)
   t.insert(8)
   t.insert(9)
   t.insert(10)
   t.insert(11)
   t.insert(15)
   t.insert(16)
   t.insert(16)

5. Implement the minimum method in the following BST class, which finds the smallest value in a BST:

   /** BST: a binary tree, in which:
    * - all values in left are < value
    * - all values in right are > value
    * - left and right are BSTs */
   public class BST {
     int value;
     BST left;
     BST right;
   
     /** Returns the minimum value in BST n.
       * pre: n is not null */
    public static int minimum(Node n) {
      // your code here
    }
   }

9B

6. T / F Searching a binary search tree has a better worst-case runtime than searching a linked list.
7. T / F Searching a binary search tree has a better best-case runtime than searching a linked list if the element is not in the list/tree.

9C

8. Perform the following operations in sequence on the tree given below. Draw the resulting tree after each operation.

remove(9)
remove(4)
remove(10)