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Lecture
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-loopsOne of the most common looping situations you'll
come across is this: You've got a number n,
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 nth power. (Forget,
for the moment, that cmath
contains a function to do this.) Here's how we'd do it with while-loops:
power = 1.0;i = 0;while (i < n){ power = power * x; i = i + 1;} |
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:
1. the initialization of our
loop counter before the loop begins
2. the test-condition that determines whether we keep
looping
3. the update (i.e. increment) of our loop counter at the
end of each loop iteration
This set-up is so common that C++ has a special
syntax allowing us to express it more succinctly, the 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-statement
will usually look like this:
for(int i = 0; i < n; i++){ CODE} |
Making sense of this brings up 2 more C++ shortcuts that we've ignored 'til now...
Up 'til now, we've made declaring a
variable and initializing that variable (i.e. giving the variable it's
initial value in the program) separate steps. However, in C++ you may give a
variable it's initial value at the same time you declare it by simply putting
"= 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;
if the context of a for loop this is nice, because something like the counter
i in
for(int i = 0; i < n; i++){ CODE}
really only gets introduced for the for-loop. Thus, it's nice to be able to
declare it and initialize it all in one statement, so it fits in the first slot
of the for-statement.
Incrementing (adding 1) and decrementing
(subtracting 1) variables is something that goes on all the time in
programming.
Therefore, C++ has a shortcut: x++
sets x to x + 1, and x-- sets x
to x - 1.
The trick here is that while 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. For
the moment, let's just say this: Don't use ++
and -- in expressions, just use them as
standalone statements that provide a shortcut to something like 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.
If you look back at the correspondence between for-loops and while-loops, you'll see that the corresponding while loop is encased in a block of it's own. The point is that any variable you declare in the first slot of the 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;
doesn’t compile - after all, the i doesn't exist as far as that second cout is concerned. Unfortunately, some
compilers don’t implement this correcty, so the i is still in scope. Watch out. Fortunately, the compiler
we are using does work properly.
1.
Write
n *'s - this is very
easy!
2.
Integration
of 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.
Last modified by LT M. Johnson 08/15/2007 04:49 PM
