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.

A tree that is rooted and has a maximum of two children per node is commonly known as a binary tree. The purpose of this demonstration is to establish that the quantity of nodes present in a binary tree that are accountable for generating two children is precisely one unit less than the quantity of leaves in the same tree.

Design an recursive algorithm that uses a treetraversal algorithm on a proper binary tree to check if the tree satisfies someproperty.

Look at the B tree of order 5 given below and insert 12, 56, 9, and 14 into it. Do this on scratch paper. no coding necessary

A "balanced" tree, in general, has leaf nodes that are all the same height.

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

Choose the correct option: Group of answer choices In a perfect binary tree each internal node has 0 to 2 maximum child nodes In a full binary tree each internal node has either 0 or 2 child nodes In a perfect binary tree each leaf node is at different level None of the choices

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

Recursively, a complete binary tree is a graph. Basis step: One vertex forms a binary tree. Inductive step: If T1 and T2 are disjoint complete binary trees with roots r1, r2, respectively, the graph produced by starting with a root r and adding an edge from r to each of the vertices r1, r2 is also complete. Recursively define a complete binary tree's leaves. Base step: The full binary tree has one root, r. Inductive step: T's leaves are the union of T1's and T2's.       Class defines binary tree height h(T). Use structural induction to prove that `(T), the number of leaves of a complete binary tree T, is less than 2 h(T).