Saturday, July 24, 2010

C++: more examples with functions

I think in order to understnad how functions works, it is crucial that we
try out some hands-on exercises with examples. But before the exercises,
here are quite a few more examples and notes. In this post, let us now
examine what happens if we write and call a regular function (those with
return type other than void).

First, let's consider a famous calculus problem: finding derivatives of
power functions. A derivative is the rate of change of a function over time,
usually denoted as F(x) prime or dy/dx. In our example, we want to calculate
the derivative of a power function (x^y) with the following algorithm, or
technically called specifications:
We want to return an integer value, so the return type would be an int. We
need two parameters: the function base, or f(x), and the exponent (^y),
denoted as base and power, respectively. We want to simply multiply the base
with power then return the multiple. For instance, if we want to find the
derivative of x^4, we would put 1 as base and 4 and power, then multiply
these two and return the result (4). The actual derivative is 4x^3.
Can you picture a possible problem? If you can picture it, I'll consider you
a genius (and perhaps add you as a Facebook friend...). But I will not touch
the problem yet, since the exercise here is to writing a functional
"function body." Then can do you have any idea on how you can help me
transform this English specs into C++?

The answer: the function signature, or the identifier that we use from a
host program to call this particular function goes something like this:
int derivative(int base, int power)
// The function signature with int as return type with arguments separated
by a comma.
int multiple; // The multiple of the base and power.
multiple = base * power; // The actual operation.
return (multiple);
Pay close attention to the "return (multiple);". This is the syntax that we
use when we are dealing with a function like this. in order for the host
program to process what we get here, the multiple must be used within a
method such as part of an output statement, or it needs to be assigned to
another integer variable. We'll see both examples in just a second.
Note: The derivative formula for power functions: multiply the base and
power and put this in front of the X, then bring the power down by one.

So, a more complete program which calculates a derivative is:
#include <iostream>
#include <string>
using namespace std;

// A function to calculate derivatives of power functions.
int derivative(int base, int power)
int multiple = base * power;
return (multiple);

// The actual program:
int main()
// a simple derivative calculator.
cout << "Welcome to Joslee's derivative calculator." << endl;
int func_base;
int func_power;
cout << "Please enter the base of your function:" << endl;
cin >> func_base;
cout << "Please enter the exponent of this function:" << endl;
cin >> func_power;
int dydx = derivative(func_base, func_power);
cout << "dy/dx " << func_base << "X^" << func_power << " = " dydx << "X^" <<
func_power-1 << endl;
return (0);
A bit complicated... But I'm sure you'll understand it better if I try this
program out:
Computer: Welcome to Joslee's derivative calculator.
Computer: Enter the function base:
Me: types "5".
Computer: Enter the exponent:
Me: types "3".
Computer: dy/dx 5X^3 = 15X^2.
Yes, and that's a bit better than writing the whole derivative operation in
the main() code.

As an added bonus, we can add conditional statements in our functions -
which allows me to answer the forseen problem of a user entering zero or 1
at the exponent prompt. To help us with this mess, we can add a useful
conditional statement (perhaps an if statement or two) to test whether the
entered value is zero or not. I cannot test for input of 1, as this
complicates matters worse (we need to create another function which is
called by the derivative function to sort this one out); right now, I don't
have enough time and space to try it out yet - perhaps next time. But the
point here was that we can do anything with a function, just like we can do
anything in main() (after all, main() is a function - a special one, after

Hope this gives you some picture of some basics in functions. There are more
things to be talked about, but I'll leave it up to more posts to do that. As
for what's ahead, I'm not even half way through - I still need to talk about
member functions, passing by value versus by reference and so on...

note: A member function is an action (or a function) that can be done with
that particular data type (technically an object). For instance, if we have
a vector and if we want to add new values, we can use push_back member
function under vector object (data) to do that. A member function has a form
of data.function where "data" is the actual data type that we are working
in, and the "function" is the member function of that data. So, in tech
language, the push_back is a member function (or a member) of vector object.
We'll come back to the notion of member functions much later when we talk
about designing our own data types.

P.S. Actually, under void functions, you can have a return statement like

I think that's enough for now. I'll come back with more practices with
functions. Again, if the content was not simple (or incorrect) for people to
understand, I apologize. As always, feel free to comment this post and
// JL P.S. Most of the notes come from CS010 class and various books.

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