Tl and T2 are two very huge binary trees, with Tl being much larger than T2. Develop an algorithm to detect whether T2 is a subtree of Tl. A tree T2 is a subtree of Tl if and only if there is a node n in Tl whose subtree is identical to T2. That is, if the tree were severed at node n, the two trees would be identical.

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.

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…

Problem 3 Recall from lecture that a binary tree T is either: 1. null (the empty tree); or 2. a root noder with two subtrees T₁ and TR, both of which are binary trees. Consider the following algorithm numLeaves (T) that takes as input a binary tree T and returns the number of leaves in the tree. numLeaves (T): 1: if T == null then return 0 2: 3: else 4: 5: 6: 7: 8: TL, TR the left and right subtrees of T, respectively if T₁ == null and TR == null then return 1 else return numLeaves (TL) + numLeaves (TR) Prove by structural induction that for every binary tree T, numLeaves (T) returns the number of leaves of T.