Answers to Self-Study Questions

Test Yourself #1

Question 1 

    (1)               (2)             (3)               (4)

     A                10              cat               15
    / \              /               /   \             /  \
   B   C            5              bat   rat          5    22
                   /              /                    \     \
                 -3             ant                     20    30
Tree 1 is not a BST because B is greater than A, yet B is in the left subtree of the node with key A (all keys in a node's left subtree should have keys that are less than the key in that node).
Tree 4 is not a BST because 20 is greater than 15, yet 20 is in the left subtree of the node with key 15.

Question 2

Test Yourself #2

The BST that results from inserting the values 5 3 7 6 2 1 4 in that order is: 

           5
         /   \
        3     7
       / \   /
      2   4 6
     /
    1

The BST that results from inserting the values 1 2 3 4 5 6 7 in that order is: 

       1
        \
         2
          \
           3
            \
             4
              \
               5
                \
                 6
                  \
                   7

The BST that results from inserting the values 4 3 5 2 6 1 7 in that order is: 

           4
          / \
         3   5
        /     \
       2       6
      /         \
     1           7

Test Yourself #3

private K smallest(BSTnode<K> n)
// precondition: n is not null
// postcondition: return the smallest value in the subtree rooted at n

{
    if (n.getLeft() == null) {
        return n.getKey();
    } else {
        return smallest(n.getLeft());
    }
}