CS106X
Handout 13
Autumn 2009
October 5
th
, 2009
Recursion
Today we'll start working with one of CS106X’s neatest ideas: recursion.
Recursion often does
the trick whenever the problem to be solved can be broken down into virtually identical
(though smaller) subproblems.
The classic introductory example employing recursion is an
implementation of the
factorial
function:
int factorial(int n)
{
if (n == 0) return 1;
return n * factorial(n  1);
}
Every recursive function lists a sequence of base cases, and then one or more recursive cases.
Occasionally, the problem to be solved is so simple that we can return or terminate execution
without any further computation.
The first of the two lines in
factorial
is an example of
such a base case—
factorial(0)
is always
1
and is easily understood.
However, whenever
the specified integer
n
is larger than
0
, it helps to calculate
factorial(n1)
and multiply the
result of that computation by
n
itself.
That's precisely what the recursive call is doing.
We'll be spending the rest of this week and all of next week learning recursion.
Recursion is
difficult to understand the first time you see it, so be patient if it doesn’t
click right away.
I’ll be covering many of the examples covered in the
reader, but I don’t reproduce those here.
I do, however, have a
good number of examples that aren’t in the reader, and
that’s what this handout is all about.
Go ahead and start reading through Chapters 5 and
6.
Your third assignment is going out on Friday,
and it’s all about recursion and recursive
backtracking, so read!
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Fractals I [Courtesy of Eric Roberts]
Although fractals have been a mathematical curiosity for more than a century, modern interest
in fractals as a practical tool can be traced largely to Benoit Mandelbrot, a researcher at IBM
who made an extensive study of the field.
As a way of getting people to understand the
concept, Mandelbrot posed the following question: How long is the coastline of England?
You
can look up an answer in an encyclopedia, but that answer turns out to be meaningless unless
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 Spring '09
 SelimAksoy
 Computer Science, Periodic Table, Recursion, Chemical element

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