UNIVERSITY OF TEXAS AT DALLAS DEPARTMENT OF COMPUTER SCIENCE Exam 3 Instructor: Daniel Uribe Student Name: May 4, 2021 1 LINEAR HOMOGENEOUS RECURRENCE RELATIONS (20 POINTS) Solve these recurrence...

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UNIVERSITY OF TEXAS AT DALLAS DEPARTMENT OF COMPUTER SCIENCE Exam 3 Instructor: Daniel Uribe Student Name: May 4, 2021 1 LINEAR HOMOGENEOUS RECURRENCE RELATIONS (20 POINTS) Solve these recurrence relations together with the initial conditions given. Recall that the solu- tion to a second order recurrence relation an = c1an−1 + c2an−2 will be of the form f (n) =α1r n1 +α2r n2 . Where r1,r2 are roots to the characteristic equation of an and α1 = k1 −k0r2 r1 − r2 , α2 = k0r1 −k1 r1 − r2 with k0 = a0 and k1 = a1. Or if the roots are repeated, it will be of the form f (n) =α1r n +α2nr n . where α1 = a0. 1. (10 pts) Find the solution for an = 8an−1 −16an−2 for n ≥ 2 and a0 = 1, a1 = 2. 2. (10 pts) Find the solution for an = 8an−1 −16an−2 for n ≥ 2 and a0 = 5, a1 = 7. Note: This differs from the previous problem only by its initial conditions. 1 2 ADVANCED COUNTING (20 POINTS) 1. (10 pts) Use the definition of an r -permutation, or the product rule to determine the number of trifectas possible in a race with 9 horses. A trifecta is the correct ordering of the first three horses to finish the race, i.e. an individual correctly picks the winner of the race, the second place finisher (place), and the third place finisher (show). The result may be left in product notation, i.e. a1 ·a2 · · · . 2. (10 pts) In a deck with 52 cards, what are the chances that five cards selected randomly from the deck (or straight from the top of a shuffled deck) will yield a 2-6 straight flush of hearts. That is, what is the probability that one of the first five cards dealt will be a 2 of hearts and that one of the first five cards dealt will be a 3 of hearts and . . . . Again, the result may be left in product notation. 2 3 RELATIONS (20 POINTS) WizardId WizardName UsesWand IsDark 1001 Gandalf 0 0 1002 Saruman 0 1 1003 Hermione 1 0 1004 Albus 1 0 1005 Gellert 1 1 1006 Tom 1 1 1. (10 pts) Use the Wizards table defined above to list the tuples in the following SELECT statement. SELECT WizardId, WizardName FROM Wizards WHERE IsDark = 1 Answer: 2. (10 pts) Use the Wizards table defined above to list the tuples in the following SELECT statement. SELECT WizardId, WizardName FROM Wizards WHERE IsDark = 0 AND UsesWand = 1 Answer: 3 4 GRAPHS (20 POINTS) 1. (20 pts) Give the adjacency matrix for the following graph. A B C D E F G H 6 8 6 4 6 6 3 1 6 6 5 6 6 Use this matrix as a template for your solution.  A B C D E F G H A B C D E F G H  . 4 5 TREES (20 POINTS) html head body meta title div script 1. (10 pts) Use the tree defined above to give the subtree rooted at body. Answer: 2. (10 pts) Use the tree defined above to give the subtree rooted at head. Answer: 5 6 BONUS: CODING & PRIME NUMBERS (5 POINTS) Use https://rextester.com to implement the sieve of Eratosthenes. Write a function which accepts a positive integer n >= 2. When invoked the function should print all prime numbers less than or equal to the input parameter n. Attach the file separately with the appropriate file extension to indicate the language (e.g. sieve.js). 6 https://rextester.com Linear Homogeneous Recurrence Relations (20 points) Advanced Counting (20 points) Relations (20 points) Graphs (20 points) Trees (20 points) Bonus: Coding & Prime Numbers (5 points)
Answered 5 days AfterMay 05, 2021

Answer To: UNIVERSITY OF TEXAS AT DALLAS DEPARTMENT OF COMPUTER SCIENCE Exam 3 Instructor: Daniel Uribe Student...

Swapnil answered on May 07 2021
125 Votes
1) LINEAR HOMOGENEOUS RECURRENCE RELATIONS
2) ADVANCED COUNTING
3) RELATIONS
Create table Wizards
with below attributes, respective data types, not null constarints and primary key
create table Wizards(
   WizardId int primary key not null,
   WizardName varchar(50),
   UsesWand bit,
   IsDark bit
);
-- insert values into Wizards table
insert into Wizards (WizardId, WizardName, UsesWand, IsDark) values (1001, 'Gandalf', 0, 0);
insert into Wizards (WizardId, WizardName, UsesWand, IsDark) values (1002, 'Saruman', 0, 1);
insert into Wizards...
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