Directions Clearly write the formulas you are using to get y

Directions: Clearly write the formulas you are using to get your answers. Put a box around your final answer. What is the minimum height of a binary tree that has 1000 vertices? What is the maximum number of vertices that a binary tree of height 10 could have? What is the maximum number of terminal vertices that a binary tree of height 6 could have? If a single elimination tournament has 102 teams, how many games get played? If a single elimination tournament has 512 teams, what is the minimum height of the tree? If a single elimination tournament has 513 teams, what is the minimum height of the tree? If a full binary tree has 75 total vertices, how many internal vertices does it have? If a full binary tree has 90 internal vertices, how many terminal vertices does it have? If a full binary tree has 400 terminal vertices, how many total vertices does it have?

Solution

1) The minimum height of a binary tree = log₂(n+1) 1

Given n = 1000

Minimum height of tree = log₂(1000+1) 1 = 9.967 - 1 = 8.967 = 9

2) h = 10

log₂(n+1) - 1 = 10

log₂(n+1) = 11

n = 2¹¹ - 1 = 2047