Design an recursive algorithm that uses a tree traversal algorithm on a proper binary tree to check if the tree satisfies some property.

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.

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).

Determine the preorder traversal of the tree, Determine the inorder traversal of the tree, Determine the postorder traversal of the tree.

Using python programming language.  Design a function to check if a binary tree is balanced. A balanced tree is defined to be a tree such that the heights of the two subtrees of any node never differ 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…

Given the following binary tree below, find the Inorder, Postorder and Preorder traversals. Also state which graph traversal algorithm was used in all three traversals