Design a nonrecursive implementation of a binary tree that maintains node data in a Vector, data. In this implementation, element 0 of data references the root (if it exists). Every non-null element i of data finds its left and right children at locations 2i + 1 and 2(i + 1), respectively. (The inverse of these index relations suggests the parent of a nonroot node at i is found at location b(i − 1)/2c.) Any element of data that is not used to represent a node should maintain a null reference.

Question 3  Construct a Btree for the following set of key values: (12, 75, 10, 99, 25, 21, 9, 19, 22, 74, 82). Assume that the tree is initially empty and values are added in the presenting order. Draw the steps for builing the Btree for the case where the number of pointers, not values, that will fit in one node is five or 2d = 4.  Full explain this question and text typing work only thanks

For a single binary tree whose in-order traversal is HDIAJTURP M S and whose post-order traversal is HIDJUTA PS M R a. Draw the binary tree.

Match the term with each definition:   In a binary tree, the left child (if any) of a node plus its descendants   The number of nodes on the longest path from the root to a leaf   A node on a path from a node to a leaf   Set of nodes, T, such that either T is empty or T is partitioned into three disjoint sets (a single node r, called the root, and two (possibly empty) sets that are binary trees, called left and right subtrees of T).   A binary tree such that for any given data item, x, in the tree, every node in the left subtree of x contains only items less than x. Every node in the right subtree of x contain only items greater than x.   Nodes which have the same parent   A node on the path from the root to a node   A node directly "above" a node in the tree   The node in a tree that has no parent   If the node is the root, then the value is one. Otherwise, it's the value of one greater…

Create a function that checks whether a binary tree is balanced. For the sake of this issue, a balanced tree is one in which the heights of the two subtrees of each node never deviate by more than one.

You are given both the Post-order traversal and an in-order traversal for aunique binary tree.Post-order traversal: F A C D B EIn-order traversal: A F E C B D • Draw the unique tree defined by those traversals.• Write down the corresponding pre-order traversal for that tree.

A Binary Search Tree (BST) can be used to efficiently implement a sorted set. It stores uniquevalues and offers an efficient membership method (contains).A binary search tree (BST) is a binary tree with the additional binary search tree property.The binary search tree property states that for every node n in the tree1. n.data is greater than the data value of all nodes in the sub-tree rooted with n.left.2. n.data is less than the data value of all nodes in the sub-tree rooted with n.right.As we are implementing a set, all data (strings) in the tree will be unique. Every node in the treewill have its own distinct string. Strings will be compared using the canonical way (as defined bythe compareTo() method in the String class).For example, the binary tree on the left (below) IS a binary search tree and the one on the rightis NOT.You will implement several methods in the BinaryTree and BST classes. The BST class mustextend the BinaryTree class. Methods that you must complete (implement or…

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