You have invited a group of friends over for breakfast and need to make n ≥ 1 pancakes using a skillet that can hold only two pancakes at a time. Each pancake has to be cooked on both sides; cooking one side of a pancake takes 1 minute, regardless of whether one or two pancakes are cooked at the same time.

Design an algorithm to do this job in the minimum amount of time. Also, determine the minimum amount of time it takes as a function of n.

Question

You have invited a group of friends over for breakfast and need to make n ≥ 1 pancakes using a skillet that can hold only two pancakes at a time. Each pancake has to be cooked on both sides; cooking one side of a pancake takes 1 minute, regardless of whether one or two pancakes are cooked at the same time.

Design an algorithm to do this job in the minimum amount of time. Also, determine the minimum amount of time it takes as a function of n.

calculusxy · Answer

@phi

phi · Answer

this sounds like computer programming.  what class is this ?

calculusxy · Answer

Computer science

calculusxy · Answer

@phi

phi · Answer

if n is even, then you can cook them "normally"
two at a time
first cook the  bottoms
then cook the tops
then move to the next pair

phi · Answer

if n=3, you can cook them
A_bottom   B_bottom
take B out
then cook
A_top  C_bottom
take A out
cook
B_top  C_top

calculusxy · Answer

Since they didn't specify do I need to include both the even and the odd numbers?

phi · Answer

I assume you can make progress with that ?

calculusxy · Answer

I am still not sure of what to do since they didn't specify the numbers?

phi · Answer

the answer is a function of n
if n=1
just cook 1_top and 1_bottom, total time 2 minutes

calculusxy · Answer

So I want to clarify the algorithm with you.

calculusxy · Answer

Do I need to write that the procedures by saying if n=1 or n=2 or n=3?

phi · Answer

I'm thinking of using recursion

phi · Answer

it would look (something) like
if n=0  return;  (do nothing)
if n=1 then  cook 1 pancake, flip, cook other side, return
else if n is odd then   cook(3), cook(n-3), return
else  cook 2 pancakes, flip both, cook other side, cook(n-2), return

phi · Answer

the program could "print out" the instructions as it runs

phi · Answer

I think the min time will be
if n==1 then 2 else n
i.e. if you are cooking n pancakes, it will take n minutes
(except for the case of 1 pancake, which will take 2 minutes)

calculusxy · Answer

@Hero

calculusxy · Answer

Can you please elaborate on the steps that @phi showed? I am still confused.

hero · Answer

Just wait until @phi gets back. I don't want to interfere with his reasoning.

calculusxy · Answer

@Hero this is due tomorrow. Please help me!

hero · Answer

Here you go: You might find what you're looking for here: http://web.engr.illinois.edu/~jeffe/teaching/algorithms/all-algorithms.pdf

calculusxy · Answer

Can you actually help me with the function for finding the minimum amount of time?

calculusxy · Answer

I am pretty sure I will be able to get through to find an algorithm, but I am not sure by what they meant with the functions.

hero · Answer

Truth is, I have a host of other things on my plate that I need to do now. I don't really have the time to help you with this.