Enrol to start learning
Reading is open to everyone. Enrolling is free, and it is what unlocks the audio lessons, practice tests and progress tracking.
23. Full Binary Tree Definition
The chapter discusses important concepts related to combinatorial structures such as full binary trees, paths in a grid, diagonals in convex polygons, triangulations, and derangements. It emphasizes the relationships between these structures and the nth Catalan number, illustrating how they can be derived or counted using various mathematical techniques, including bijections and recurrence relations.
Sections
This section introduces key concepts in discrete mathematics, focusing on full binary trees, catalan numbers, valid paths in grids, triangulations of polygons, and derangements.
This section discusses the number of valid paths in a square grid from the origin (0,0) to (n,n) using only upward and rightward movements.
This section explores the method to calculate the number of diagonals in a convex polygon based on its number of sides.
This section covers the concept of triangulations of convex polygons, exploring the relationship between the number of triangulations and the nth Catalan number.
The section discusses the concept of derangements, exploring the categorization and recursive relationships involved in determining the number of derangements for a given set of n objects.
A full binary tree is defined as a binary tree where every internal node has either 0 or 2 children, and the number of such trees relates to Catalan numbers.
The number of valid paths on a square grid from (0, 0) to (n, n) can be established using a bijection between paths and strings consisting of 'R' and 'T' movements.
The number of diagonals in a convex polygon can be computed directly by considering the vertices involved, leading to the formula for the number of diagonals.
Full Binary Tree
A binary tree where every internal node has either 0 or 2 children.
Catalan Number
A sequence of natural numbers that occur in various counting problems, often involving recursively defined objects.
Derangement
A permutation of a set where none of the elements appear in their original position.
Practice Exercises
Total Questions
2
Estimated Time
4 min
Passing Score
70%
Instructions
- Read each question carefully
- You can use hints if you need help
- Complete all questions before submitting
3 more questions available
Enrol free