Re: "that programming concept is new" < Destiny Sparks: Do you meant it is unanswerable? -Thanks >

COMP 1900 - Spring 2021

Lab 4: Loops

Please explain as best you can, I want to understand not just get the answer. Thank you so much!

1.

Write a program named

Warmup.java

that prints the following sequences of numbers on the

screen. Start by writing a loop that runs for the desired number of iterations, then think about

what each iteration should do.

(a)

(2 points) The first 20 terms of -11, -8, -5, -2, 1, ...

(b)

(2 points) The first 50 terms of 100.0, 102.0, 104.04, 106.1208, 108.243216, ... (Hint:

Each term is 2 percent more than the previous term.)

(c)

(3 points) The first 100 terms of 3840, 3838, 3835, 3831, 3826, ... (Hint: Make a variable

to store how much you should subtract to get to the next term. That variable changes its

value with each loop iteration.)

(d)

(3 points) The first 997 terms of 1000, -997, 994, -991, 988, ... (Hint: One way to do this is

to include conditional statements within your loop.)

2.

(6 points) Consider the sequence of integers defined as follows:

The first term is any positive integer.

For each term

n

in the sequence, the next term is computed like this: If

n

is even, the next

term is

n/

2. If

n

is odd, the next term is 3

n

+ 1.

Stop once the sequence reaches 1.

Here are a few examples of this sequence for different values of the first term:

8, 4, 2, 1

12, 6, 3, 10, 5, 16, 8, 4, 2, 1

19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2

Note that all three of these eventually do reach 1. In fact, it is believed (but not known) that

the sequence will

always

reach 1, regardless of the first term chosen. This is known as the

Collatz conjecture

. Despite its apparent simplicity, it has so far eluded all attempts at a proof.

Mathematician Jeffrey Lagarias at the University of Michigan has claimed that this is an

extraordinarily difficult problem, completely out of reach of present day mathematics.

We might not be able to prove the Collatz conjecture here, but we can experiment

computationally with it! Write a program named

Collatz.java

that allows the user to enter any

positive integer. The program should then compute and list all the terms of the sequence until

it reaches 1. At the end, show how many terms it took to get to 1 (including 1 itself).

Include input validation to ensure that the users input is positive. If its not positive, show an

error message and allow the user to re-enter the input as many times as necessary.

Example program run (underlined parts indicate what the user enters)

Enter starting value (must be a positive integer):

12

12

6

3

10

5

16

8

4

2

1

Number of terms: 10

Example program run (underlined parts indicate what the user enters)

Enter starting value (must be a positive integer):

1

1

Number of terms: 1

Example program run (underlined parts indicate what the user enters)

Enter starting value (must be a positive integer):

-5

Must be a positive integer! Try again:

0

Must be a positive integer! Try again:

5

5

16

8

4

2

1

Number of terms: 6