11. From the following trees, select the balanced BSTS: (A BST is balanced if the height of its left and right sub-trees are different by at most one, recursively applied.) A. M D R J B. A 6 10 38 55 64 P 72 91 W 92 Z 123
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- 5. Design an recursive algorithm that uses a tree traversal algorithm on a proper binary tree to check if the tree satisfies some property.A binomial tree is a special type of rooted tree, defined recursively as follows: Basis Step: The Oth binomial tree, Bo, is a single vertex. Recursive Step: For k > 1, the kth binomial tree, B, consists of two copies of B-1 and an additional edge making the root of one copy the child of the root of the other. a) Draw B2 b) Find a (non-recursive) formula for the number of vertices in B, and prove your formula correct. c) Prove that there are C(k, l) vertices at level l of Be (You may find Pascal's identity useful: C(n + 1, k) = C(n, k – 1) + C(n, k))Computer Science Binary Search Tree Implement Binary search Tree (BST) and perform the following operations a. Insert the keys 11,66, 6,9,40,28,5, 88,125,90 b. Print the keys in sorted order using suitable traversal method. C. Search for a key x and prints its address if it is present. d. Compute height of the BST e. Print successor/predecessor of a given key f. Delete the keys 40 and 88 one by one and print the tree in level order after each delete. Note: use only recursive functions for all the operations. Write the c code with proper comments.
- Create a binary linked tree, and traverse the tree by using the recursive function. The structure of the tree is as follow: You should input the nodes in pre-order sequence. If a child of a node is NULL, input a space. Write the function of create binary tree, pre-order to print the nodes, in-order to print the nodes and post-order to print the nodes. Count the height of the tree. Header file typedef char ElemType; typedef struct node//define the type of binary tree node { }BTnode; Source file #include <stdio.h> #include <stdlib.h> #include "tree.h" BTnode * createTree()//create the binary tree,return the root { BTnode *tnode;// tnode is the root char elem; ;//input the character //if the input is a space,set the pointer as NULL Else// if the input is not a space,generate the binary node and create its left sub-tree and right…Create a binary linked tree, and traverse the tree by using the recursive function. The structure of the tree is as follow: //PICTURE// You should input the nodes in pre-order sequence. If a child of a node is NULL, input a space. Write the function of create binary tree, pre-order to print the nodes, in-order to print the nodes and post-order to print the nodes. Count the height of the tree.A tree can be represented using lists as follows. (root listOfSubTrees ) tree listOfSubTrees tree = root listOfSubTrees = tree Consider the tree defined by: (FD (G (AHI) C) E B) Give the order of letters visited in when using a pre-order traversal implemented recursively as seen in class. (separate each element with a space where the left is the first element visited and the right is the last element visited, example: A B C D E F)
- Create a binary linked tree, and traverse the tree by using the recursive function. The structure of the tree is as follows: //check pic// You should input the nodes in pre-order sequence. If a child of a node is NULL, input a space. Write the function of create binary tree, pre-order to print the nodes, in-order to print the nodes and post-order to print the nodes. Count the height of the tree. Hints: Header file typedef char ElemType; typedef struct node//define the type of binary tree node { }BTnode; Source file #include <stdio.h> #include <stdlib.h> #include "tree.h" BTnode * createTree()//create the binary tree,return the root { BTnode *tnode;// tnode is the root char elem; ;//input the character //if the input is a space,set the pointer as NULL Else// if the input is not a space,generate the binary node and create its left…9. A binary tree is symmetric if for every internal node the number of nodes in its left subtree is the same as the number of nodes in its right subtree. Given a node p, let p.size() return the number of nodes in the subtree with root p, and p.getLeftChild() and p.getRight Child() return the left and right children of p, respectively. Write a recursive algorithm public boolean isSymmetric (Binary TreeNode r) that receives as parameter the root r of a binary tree and it returns true if the tree is symmetric and it returns false otherwise. For example for the tree below with root r the algorithm must return true, but for the tree with root s it must return false. $8,89 Figure 3For the following tree, give the postorder traversal 1 4 6 7 Select one: a. 4257631 O b. 2465371 c. 2456371 O d. 7654321 3. 2.
- 24. What sequence of nodes from the tree A DEF G would be printed if the following recursive procedure were applied to it? def printTree (Tree): if (Tree is not None): printTree (Tree.Left) print (Tree.Value) printTree (Tree.Right)12. How many recursive calls needed to build this perfect binary tree? Please show the detailed step by step calculation from the following recursive definition in the box. Base Case: If a single node has no children, it is a perfect binary tree of height h = 0 If a node has h> 0, it is a perfect binary tree if both of its subtrees are of height h- 1 and are non-overlapping or in other words- "If T is a perfect binary tree, then a new perfect binary tree T' can be constructed by taking two copies of T, adding a new vertex y and adding edges between v and the roots of each copy of T. The new vertex v is the root of T" 1. 2.3. Given the binary tree, please describe the Inorder traversal algorithm and output the binary tree's Inorder traversal sequence. 10 1 40 1 20 1 1 50 30