AP project Ideas?

I have to make a program using C++ for my AP class. There are a bunch of requirements for it though and one of them is that it needs to have an algorithm that has two algoritms inside of it, one of which has to function independently. It also has to have an abstraction, which I still don't understand (I'm not even sure if it was taught). The problem is that every idea I come up with for it doesn't need two algorithms. Please help?

(I'm uploading this again since no one responded to the first one)
As an European I dare to ask, 'AP' stands for Advanced Placement as described here: https://en.wikipedia.org/wiki/Advanced_Placement ?

BTW, the lower right corner of your post shows "Reported" and when I hoover the mouse cursor over it "This message has been reported" pops up. Do you have a clue what this signifies? Some relation to AP? Or do you use your spare time to fight for human rights of Tibetan Buddhists, muslim Uighurs and/or protestant minorities in China? -- "Reported" disappeared silently.

Edit: About the two independant algorithms nested in a third one -- take a look at ancient programmable pocket calculators, you could program a function like f(x) = sin2(x/2) that could be used independantly to calculate f(x), but also in conjunction with a root finder (Solve) as well with Integrate. It is even possible to use the solver to find limits of the integral to achieve a given result for integration. If you want to fiddle with you may do so with a free simulator: https://thomasokken.com/free42

Edit: strike through
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I am nosy which program using C++ would be adequate to satisfy your AP class level. Did you decide for one of the responses you got in this thread and over there -- http://www.cplusplus.com/forum/beginner/252507/#msg1111396 ?
Mike, AP classes are meant to replace a college class. So think 'first semester coding class' level of material (unless this is a very elite school, then it could be nearly 3rd year stuff if he has AP-5 level class but that seems unlikely, very few schools offer that).

Your idea seems about the right level to me, IF he has also had calc … he may not have.. I had AP programming but no calc until college.
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@jonnin
Thank you for clarification. Helps to adjust my expectations... wrong word, I expect nothing... classification is not much better... to have a better understanding/insight.

No calc? Today, emulators, simulations, virtual devices are the poor man's hardware. Most, even the best, are for nothing. Making excuses like no calc, no idea may be shortend: no idea (what is a bad certificate for the teachers).
I meant no calculus. as in he may not have a clue what you said yet.
As in math background to do the project, not what the computer can or can't do but what the programmer may or may not understand.
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How about a sudoku solver? The main "solve" algorithm could call several different sub algorithms, each of which tries a specific strategy to further the solution. I wrote one like this and found it a lot of fun.
I meant no calculus
Sorry for me misconceiving. Without calculus une calculette even with CAS is not of much help. :(
Dhayden

That might work but I don't even know the first thing about Sudoku
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