Introduction to Java Programming and Data Structures, Comprehensive Version, Student Value Edition (11th Edition)
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Chapter 26.2, Problem 26.2.3CP
Program Plan Intro

Adelson-Velskii and Landis (AVL) tree:

  • Adelson-Velskii and Landis tree is a well-balanced binary tree which is named after scientists G. M. Adelson-Velsky and E. M. Landis.
  • In this tree, the difference between the heights of two different sub trees for every node may be 0 or 1.
  • The process of insertion and deletion of an element in an AVL tree is same as in binary search tree except the concept of rebalancing the tree again after insertion and deletion.

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[5 marks] Give a recursive definition for the language anb2n where n = 1, 2, 3, ... over the alphabet Ó={a, b}. 2) [12 marks] Consider the following languages over the alphabet ƒ={a ,b}, (i) The language of all words that begin and end an a (ii) The language where every a in a word is immediately followed by at least one b. (a) Express each as a Regular Expression (b) Draw an FA for each language (c) For Language (i), draw a TG using at most 3 states (d) For Language (ii), construct a CFG.
Question 1 Generate a random sample of standard lognormal data (rlnorm()) for sample size n = 100. Construct histogram estimates of density for this sample using Sturges’ Rule, Scott’s Normal Reference Rule, and the FD Rule. Question 2 Construct a frequency polygon density estimate for the sample in Question 1, using bin width determined by Sturges’ Rule.
Generate a random sample of standard lognormal data (rlnorm()) for sample size n = 100. Construct histogram estimates of density for this sample using Sturges’ Rule, Scott’s Normal Reference Rule, and the FD Rule.
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