23.1.3. Bijection with Parenthesizing

Try these first

1. 1.

   Define a Full Binary Tree.

   Hint

   Focus on the characteristics of internal nodes.

2. 2.

   How many full binary trees are there with 2 leaves?

   Hint

   Consider the simplest case.

3. 3.

   What defines a Full Binary Tree?

   • Every node has one child
   • Every node has two children
   • Internal nodes have 0 or 2 children

   Hint

   Think about what each node can have.

4. 4.

   Catalan numbers count which of the following?

   • True
   • False

   Hint

   Consider their application in combinatorics.

5. 5.

   Devise a formula based on the recurrence relation for the number of full binary trees with arbitrary n leaves.

   Hint

   Consider breaking it down into smaller tree components.

6. 6.

   How would you visualize the Catalan number application in a real-world scenario, like expression grouping?

   Hint

   Visualize with drawings and labels to clarify the concept.