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(10 points) Recall that the set of full binary trees is defined as follows: Basis: A...
Binary Trees Problem 4. Binary Trees. [15 marks total Recall that a binary tree is defined as a fintie set of nodes that is either empty or consists of a root and two disjoint binary trees T and TR, respectively, the left and right subtree of the root. Since the definition itself divides a binary tree into two smaller structures of the same type, the left and the right subtree, many problems about binary trees can be solved by applying...
2. A complete binary tree is defined inductively as follows. A complete binary tree of height 0 consists of 1 node which is the root. A complete binary tree of height h +1 consists of two complete binary trees of height h whose roots are connected to a new root. Let T be a complete binary tree of height h. Prove that the number of leaves of the tree is 2" and the size of the tree (number of nodes...
Recall from Assignment 2 the definition of a binary tree data structure: either an empty tree, or a node with two children that are trees. Let T(n) denote the number of binary trees with n nodes. For example T(3) 5 because there are five binary trees with three nodes: (a) Using the recursive definition of a binary tree structure, or otherwise, derive a recurrence equation for T(n). (8 marks) A full binary tree is a non-empty binary tree where every...
Problem 2 [35 points (155 15)]: Let Ti and T2 be two binary search trees containing the same elements. In this problem, you will show how to transform Ti into T2 (i.e. Ti is altered to now have the same structure as T2) through a series of rotation operations. (a) Define a binary tree to be a right-going chain if no node in the tree has a left child (in other words, the tree is a linked list formed through...
(b.) Huffman code is a way to encode information using variable-length binary strings to represent symbols depending on the frequency of each individual letter. Specifically, letters that appear more frequently can be encoded into strings of shorter lengths, while rarer letters can be turned into longer binary strings. On average, Huffman code is a more efficient way to encode a message as the number of bits in the output string will be shorter than if a fixed-length code was used....
Problem 3: Bounded-Degree Spanning Trees (10 points). Recall the minimum spanning tree problem studied in class. We define a variant of the problem in which we are no longer concerned with the total cost of the spanning tree, but rather with the maximum degree of any vertex in the tree. Formally, given an undirected graph G = (V,E) and T ⊆ E, we say T is a k-degree spanning tree of G if T is a spanning tree of G,...
. Huffman Encoding (a.) (6 points) Suppose a certain file contains only the following letters with the corresponding frequencies 1 AİB 73 9 30 44 130 28 16 In a fixed-length encoding scheme, cach character is given a binary representation with the same number of bits. What is the minimum number of bits required to represent each letter of this file under fixed-length encoding scheme? Describe how to encode all seven letters in this file using the number of bits...
Please answer question 2. Introduction to Trees Thank you 1. Graphs (11 points) (1) (3 points) How many strongly connected components are in the three graphs below? List the vertices associated with each one. 00 (2) (4 points) For the graph G5: (a) (0.5 points) Specify the set of vertices V. (b) (0.5 points) Specify the set of edges E. (c) (1 point) Give the degree for each vertex. (d) (1 point) Give the adjacency matrix representation for this graph....
Binary Search Tree Part A: The code attached in this document is a sample code to demonstrate insert operation in binary search tree. Please fill in the missing part for the insert method to make the program work. The expected output should be as follows. 20 30 40 50 60 70 80 Part B: Find Lowest Common Ancestor (LCA) of a Binary Search Tree. According to WikiPedia definition , The lowest common ancestor is defined between two nodes v and...