Practice Discrete Mathematics (23.1) - Full Binary Tree Definition - Discrete Mathematics

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6 sample questions

Question 1.
How many full binary trees can be formed with 2 leaves?
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Consider the definition of a full binary tree.
Question 2.
What is a valid path from (2,2) to (0,0) in a grid?
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Think about how many times you will move right and upward.
3Question 3.
How many leaves does a full binary tree with 3 internal nodes have?
- 3
- 4
- 5
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Think about how the structure of full binary trees works.
4Question 4.
True or False: All vertices of a polygon can form diagonals.
- True
- False
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Consider the definition of what a diagonal is.
Question 5.
Formulate and prove a relationship between the number of full binary trees and the Catalan sequence.
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Consider how binary trees can represent multiplication.
Question 6.
Provide a rigorous mathematical proof for the formula calculating diagonals in a polygon.
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Break down sides and verify with smaller polygons.

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