The following questions will be based on the recurrence relation: T(n) = 2T(|n/2])+ n² for n > 2 T(n) = 1 if n < 2 Master.Method.4.a.b.k: What is the value of a, b, and k? Variable Coefficient a b k Master.Method.4.simplified: Does the simplified master method apply? Master.Method.4.case: What case of the Master Method applies? Master.Method.4.Asymptotic: What is the asymptotically tight bound? Enter an expression

Java Code: Below are the methods for parser.java. Make sure to use the existing Parser.java file to add in all the methods and show the output.    OperationNode: Has enum, left and Optional right members, good constructors and ToString is good  VariableReferenceNode: Has name and Optional index, good constructors and ToString is good  Constant & Node Pattern: Have name, good constructor and ToString is good  ParseLValue - variables: Accepts a variable name and creates an appropriate Variable Reference Node ParseLValue - arrays: Accepts a name, appropriately gets an index and creates an appropriate Variable Reference Node  ParseLValue - dollar: Creates an operation node, gets the value of the $ operator appropriately  ParseBottomLevel – constants & patterns: Detects strings, numbers and patterns and creates appropriate nodes  ParseBottomLevel – parenthesis: Creates an operation node AND gets the contents of the parenthesis appropriately  ParseBottomLevel – unary operators: All…

The following questions will be based on the recurrence relation: T(n) = 16T([n/4])+ n! if n > 4 T(n) = 1 if n < 4 Master.Method.5.a.b.k: What is the value of a, b, and k? Variable Coefficient b k Master.Method.5.simplified: Does the simplified master method apply? Master.Method.5.case: What case of the Master Method applies? Master.Method.5.Asymptotic: What is the asymptotically tight bound? Enter an expression

Q1. Let’s play a dice game with a pair of dice following these rules:1. At the beginning, you throw a pair of dice. If the two numbers add up to 5, 6, 7, 8, or 9, thegame immediately stops.2. If your first throw does not meet those 5 totals, you would continue until you get either 11 or12.Get 1000 simulations of this paired dice game. What is the average number of dice throw per game?You can use the sample() function to simulate the dice.