This lecture is essentially all about some shortcuts that make it easier to write certain kinds of loops. As with our other shortcuts, these aren't technically needed, but they make our code much easier to write and understand, and that's pretty important!
for
-loopsn
, and you need to go
through a loop n
times. Consider, for example, the
very simple problem of writing a program that reads in
double
x
and int
n
from the user and prints out x
to the
n
th power. (Forget, for the moment, that
cmath
contains a function to do this.) Here's how
we'd do it with while-loops:
|
If you think the test "i < n
" looks strange,
remember this: the variable i
counts the number
of times we've gone through the loop body. We start having gone
through 0 times, and we want to stop when we've gone through
n
times. In other words, while we've looped fewer
than n
times, keep looping!
Any time we count our way through a loop like this, we'll have three basic pieces of code:
for
loop.
The previous code would be written as follows with a for loop:
power = 1.0; i = 0; while (i < n) { power = power * x; i = i + 1; } |
BECOMES | power = 1.0; for(i = 0; i < n; i = i + 1) { power = power * x; } |
The for
-loop is just a compact way of writing a
while loop which has the three steps outlined above:
initialization, test-condition, and update. A
for
-loop can always be written as a while
loop in the following way:
for(A; B; C) { statement1 statement2 . . statementk } |
is the same as | { A; while (B) { statement1 statement2 . . statementk C; } } |
As I said before, we usually use for-loops to loop
n
times, where n
is some value we know
from earlier on in the program. This for
-statment
will usually look like this:
|
Making sense of this brings up 2 more C++ shortcuts that we've ignored 'til now.
= value
" after
the variable's name in the declaration. For example:
double x = 1.0;
... both declares the variable x
and gives it an
inital value of 1.0
. When you declare several
variables in one statement, you can initialize some and leave
others, e.g.
string A, B = "doosey", C;
In the context of a for
loop this is nice, because
something like the counter i
in
for(int i = 0; i < n; i++) // int i = 0; => i is declared and initialized with 0
{
...
}
really only gets introduced for the for
-loop. Thus, it's nice to
be able to declare it and initialize it all in one statment, so it fits in the
first slot of the for
-statement.
x++
sets
x
to x + 1
, and x--
sets
x
to x - 1
.
+=
and -=
operators,
which are defined like this:
a += b |
is equivalent to | a = a + b |
a -= b |
is equivalent to | a = a - b |
℗
we have the operator
℗=
defined by
a ℗= b |
is equivalent to | a = a ℗ b |
for(int i = 0; i <= 100; i += 5)
cout << i << endl;
x++
is an expression
(its value is the value of x
before the
increment), it also has a side effect, namely that it
changes the value of the variable x
.
Thus we have:
code fragment | output |
|
5 6 |
x = x + 1
. This is because you have to be careful about which
value you get in the expression - is it the value before or after the
increment. It's confusing to read such things, and let's just avoid the
confusion. Remember, it's not a contest to see who can write a program with
the fewest keystrokes! (Though admittedly, that's kind of fun.)
Note: The name C++ is a pun on the ++ operator: It's the C
language, incremented!
Note: ++x
and --x
are also allowed. The
difference is that the value of the expression is the value after rather than
before the increment/decrement operation.
for
-statement goes out of scope after you leave the for-loop.
Thus, something like:
for(int i = 0; i < 12; i++)
{
cout << i << endl;
}
cout << i << endl;
shouldn't compile - after all, the i
doesn't exist as far as that
second cout
is concerned. This is usually a nice feature.
After all, you only introdced the new variable i
to iterative
through the numbers 0 up to 11. After you're done with that iteration, there's
no point to having i
around.
Here's a code that illustrates how that can be nice.
#include <iostream>
using namespace std;
int main()
{
for(int i = 0; i < 25; i++)
cout << '*';
cout << endl << " H E L L O W O R L D !" << endl;
for(int i = 0; i < 25; i++)
cout << '*';
cout << endl;
return 0;
}
See how we didn't need to use a different variable for the two
for-loops? That's because their scope does not extend beyond
the for-loop itself.
n
*'s - this is very
easy!
f(x)
by simple end-point
approximation - Simple end-point integration approximates the area under a
curve between x = 1
and x = b
by the sum of
n
evenly spaced rectangles whose hieghts are the function values
at x
-values given by the left endpoints of the bases. To remind
your self of how this works I've drawn this
picture.