Practice Recurrence Relation For Triangulations (23.4.2)

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8 questions

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6 sample questions

Question 1.
What is the initial condition for T(0)?
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Think about the number of ways to form a triangulation when there are no sides.
Question 2.
How many structurally different full binary trees are there with three leaves?
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Consider the arrangements of branches.
3Question 3.
How many full binary trees exist with 4 leaves?
- 1
- 2
- 5
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Think about how arrangements can change.
4Question 4.
True or False: The 3rd Catalan number is 5.
- True
- False
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Recall the list of Catalan numbers.
Question 5.
Prove that the number of triangulations of a convex polygon with n sides corresponds to the nth Catalan number.
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Start by showing simple cases and building up.
Question 6.
If a polygon's triangulation patterns were altered, hypothesize how the changes could affect the corresponding Catalan number.
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Think about howpolygonal shapes change the arrangement.

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