Robots Slice Apples?

Computer Science Level 1

Robots are used to prepare bags of sliced apples. One particularly bad robot gets tired as his power starts to run low, so making the $k$ th bag takes the robot $k+4$ actions.

For example, the robot can make the 1st bag with just 5 actions, but by the 100th bag, it takes the robot 104 actions. The total number of actions needed to make $n$ bags of sliced apples (for large $n$ ) is:

\Theta(n^4)

\Theta(n)

\Theta(n^3)

\Theta(n^2)

1 solution

Eli Ross Staff
Oct 29, 2015

In total, $n$ bags will take $(1+4)+(2+4)+(3+4)+\ldots+(n+4)$ actions by the robot. We can take out the $n$ copies of 4, and see that this is $4n + (1+2+3+\ldots+n)$ actions by the robot. Since $1+2+3+\ldots+n = \frac{n(n+1)}{2} \approx \frac{n^2}{2}$ , the robot uses $\approx 4n+\frac{1}{2}n^2 = \Theta (n^2)$ actions.

It probably wouldn't be a bad idea to explicitly define the theta function (maybe its not a function, i have no idea) . I had no idea what any of the answers meant but I could have easily found a function for the number of cuts.

McKay Holmes - 5 years, 6 months ago

I agree with Mckay.

Ethan Sharp - 5 years, 3 months ago

I found the actions to cuts or whatever confusing. I had nothing to work with except 2 seemingly Un related variables

Alex Williams - 5 years, 1 month ago

This idea is called big O notation, and deals with the complexity of different algorithms. How long it takes to process basically.

Hope Haugstad - 4 years, 6 months ago

It would be useful if there was a lesson first and then the questions! At the moment this app isn't teaching much, just testing what you already know.

Christian Morgan - 3 years, 11 months ago

Yeah, I definitely agree there...

RandomInkknight III - 2 years, 10 months ago

What's the symbol that looks like an O called

Katie Chen - 4 years, 7 months ago

Capital (or "big") theta

Victoria Vasys - 4 years, 6 months ago

https://rob-bell.net/2009/06/a-beginners-guide-to-big-o-notation/

Emily Falces - 3 years, 2 months ago

You can't factor out 4n, but you can factor out 4. Other than that, Eli's explanation w/ (1+2+3+...+n) approx (n^2/2) is good.

Caleb Kelley - 2 years, 7 months ago

Robots Slice Apples?

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