Assuming that a tree with one node has a height of 1, how many nodes may a balanced binary tree with 5 nodes have?

No node in a binary tree may produce more than two children. Exhibit that in any binary tree, the number of nodes producing two offspring is exactly one less than the number of leaves.

For a multi-node tree, explain what is the difference between a leaf of tree and sub-tree?

Remember, in our definition, the height of a binary tree means maximum number of nodes from the root to a leaf.       a) In a perfect binary tree of size n, what is the tree's exact height?  Justify your answer.       b) In a degenerate binary tree of size n, what is the tree's exact height?  Justify your answer.        c) What is the maximum height for a balanced binary tree of size 7? Justify your answer

True or False: 1. In 2-3 Trees, The leaf nodes are at different levels 2. Degree of node is not equal to the number of children that node has.  3. If the balance factor of a node is 1, then it means that the right sub tree of the tree is one level higher than that of the left sub tree . such a treee is called right-heavy tree

Topic: Binary Tree Graph

In a 5-ary tree, what is the maximum number of siblings a node x can have? What is the minimum number of siblings x can have?

A binary tree is a rooted tree with no more than two offspring per node. Show that in a binary tree, the number of nodes that produce two offspring is precisely one fewer than the number of leaves.

1. A complete binary tree of depth d is a tree where every node has two children, except for the nodes at depth d, which have no children. Such a tree has 2' nodes at depth j, where j = 0, 1, d. What is the minimal size of a vertex cover of a complete binary tree of depth 2m + 1, where m is a nonnegative integer?

No node in a binary tree may produce more than two children. Exhibit that in any binary tree, the number of nodes producing two offspring is exactly one less than the number of leaves.