-1
votes
1answer
48 views

Number of Different AVL Tree

I studying the related question. http://stackoverflow.com/questions/13500560/number-of-ways-to-create-an-avl-tree-with-n-nodes-and-l-leaf-node but it's not so general. In-fact, We want to know ...
0
votes
1answer
124 views

Find largest chromatic number of a full binary tree [closed]

This is a Discrete Math/Combinatorics Question from my hw…but I don't really understand the question. Find largest chromatic number of a full binary tree given the following depths: (Check all ...
1
vote
0answers
53 views

Proving that a BST with N>=1 nodes will have log(N+1) levels

I am trying to prove by induction the following theorem: Use Induction to prove the following fact: for every integer, $N\ge 1$ , a BST with $N$ nodes must have at least $\log( N + 1)$ levels. I've ...
2
votes
1answer
383 views

Height of a full binary tree

A full binary tree seems to be a binary tree in which every node is either a leaf or has 2 children. I have been trying to prove that its height is O(logn) unsuccessfully. Here is my work so far: I ...
11
votes
1answer
627 views

How many max heaps are there?

How many different max-heaps can I form using a list of $n$ integers. Example: list [1,2,3,4] and max-heap is 4 3 2 1 or ...
8
votes
2answers
877 views

What is the average height of a binary tree?

Is there any formal definition about the average height of a binary tree? I have a tutorial question about finding the average height of a binary tree using the following two methods: The natural ...
3
votes
2answers
550 views

How can I prove that a complete binary tree has $\lceil n/2 \rceil$ leaves?

Given a complete binary tree with $n$ nodes. I'm trying to prove that a complete binary tree has exactly $\lceil n/2 \rceil$ leaves. I think I can do this by induction. For $h(t)=0$, the tree is ...
10
votes
2answers
1k views

Proving a binary tree has at most $\lceil n/2 \rceil$ leaves

I'm trying to prove that a binary tree with $n$ nodes has at most $\left\lceil \frac{n}{2} \right\rceil$ leaves. How would I go about doing this with induction? For people who were following in the ...