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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the initial condition for T(0)?
💡 Hint: Think about the number of ways to form a triangulation when there are no sides.
Question 2
Easy
How many structurally different full binary trees are there with three leaves?
💡 Hint: Consider the arrangements of branches.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
How many full binary trees exist with 4 leaves?
- 1
- 2
- 5
💡 Hint: Think about how arrangements can change.
Question 2
True or False: The 3rd Catalan number is 5.
- True
- False
💡 Hint: Recall the list of Catalan numbers.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the number of triangulations of a convex polygon with n sides corresponds to the nth Catalan number.
💡 Hint: Start by showing simple cases and building up.
Question 2
If a polygon's triangulation patterns were altered, hypothesize how the changes could affect the corresponding Catalan number.
💡 Hint: Think about howpolygonal shapes change the arrangement.
Challenge and get performance evaluation