15.1. Finding the Minimum

Try these first

1. 1.

   What is the minimum value in the tree that looks like this: 10 ↘ 5 ↘ 20?

   Hint

   Look for the leftmost node.

2. 2.

   True or False: The maximum value of a BST can be found at a left child.

   Hint

   Think about how the values are organized in the tree.

3. 3.

   What is the primary method for finding the minimum value in a BST?

   • Go right
   • Go left
   • Go up

   Hint

   Think about which direction you travel for smaller values.

4. 4.

   True or False: In a BST, the predecessor of a node will always be its left child.

   • True
   • False

   Hint

   Consider how to find the predecessor in the absence of a left child.

5. 5.

   Given a BST with the following structure, find the predecessor and successor of the node with value 7.

   - python

   Try it yourself

       5
      / \
     3   8
    / \   \
   1   4   9
        \ 
         6

   Show the path taken.

   Hint

   Think about moving up the tree and checking right/left children.

6. 6.

   Write an algorithm to remove a node from a BST and then find the minimum and maximum values afterwards. Describe each step clearly.

   Hint

   Consider if the node has children and how that impacts the structure.