A rooted binary tree has two children per node. Demonstrate that a binary tree has one fewer nodes that generate two offspring than leaves.

The binary search tree is great for storing information that allows efficient searching and/or retrieval of the data. It is designed as a collection of nodes, each with a single left node/child and a single right node/child, where at each node, the left child is always less than or equal to the parent value and the right node is always greater than the parent value. To find any item in a well-balanced tree has a best case of O(log2N) retrieval. However, binary search trees have a worst-case retrieval scenario of O(N). This can happen if you have a binary search tree of the form shown here. To find the E in the search tree, we must visit all 5 nodes, not very efficient. Fortunately, it is possible to guarantee that binary search trees never end up in this unfortunate form, so that there is a better chance of having this quick O(log2N) retrieval from all binary search trees. This process is called search tree balancing. One of these techniques is to use rotations. Rotations take a…

Topic: Binary Tree Graph

To find the kth smallest element in the tree, create a recursive algorithm that accepts a BST and an integer k as inputs. Remember that all the nodes in the right subtree are bigger than the root, while all the nodes in the left subtree are smaller.

Show all working explaining detailly each step

Insert the following words into a binary tree Luis, Pablo, Ana, Celia, Miguel

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.

Create an ordered, rooted tree that represents the infix form of the following equation. Then write out the prefix and postfix forms of the equation.  ((X*Y) + (Y * ((X+5) * (Y+7))))/3

Write algorithm Smallest(tree, k, num, v) pre-cond: tree is a binary search tree and k > 0 is a

ADT's – Tree, Binary Tree, and Binary Search Tree Given the following tree: B C G H D F a. Identify the children of node c? b. What is the degree of node d? c. What is the degree of node g? J K