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Introduction to Programming
with Java, for Beginners
Recursion
CIS
1
Meaning of “Recursive”
^
“Recursive” means “self referencing” ^
When a class has an instance variable whose type isitself, we say it is “recursively defined”. It’s an example of“structural recursion”. ^
Notice that the class has subparts that look like the whole.
Person
public class Person{
private String name;private Person mother;private Person father; }
CIS
2
Recursive Methods
A recursive method is one that calls itself
Common Pattern:
public
type
foo(
parameters
if (
condition
return
value
else return foo(
arguments
CIS
3
Why Use Recursive Methods?
Many things we model have recursive structures(where the subparts look like the whole):
^
Mathematical formulas•
Power: x^y == x * x ^ (y-1)• Factorial: n! == n * (n-1)!• Fibonacci series: fib(n) == fib(n-1) + fib(n-2)• Fractal geometry (Julia, Mandelbrot sets) ^
Languages•
Programming languages:
-^
An expression can contain expressions
-^
A statement can contain other statements
-^
HTML tags in a web page
-^
XML (extensible markup language), for storing semi-structured data
^
Hierarchical Entities (often stored as “trees”)•
A “family ancestral tree”• An operating system’s folder/directory hierarchy ^
Graphs•
Social networks (Facebook)• Computer networks• Airline travel networks Recursive methods are frequently used to process such structures
CIS
4
Write a Recursive Method
^
Rewrite it as a recursive method^
Instead of having a loop, have it call itself
^
How do you get it to stop when it should?
^
Can we generalize the steps we took as a way toapproach the coding of recursive methods?
^
Consider this method:
public static void countDown(int num){
if (num <= 0)
return; for (int i = num; i >= 1; i--){
System.out.println(num); } }
CIS
5
Example: print down to 1
/ Recursive method that prints**
num, num-1, num-2, ... 1.
*** Assumes num is positive./public static void printDownTo1(int num){*
if (num == 0) // base case
return; System.out.println("num is " + num);printDownTo1(num - 1);
}
CIS
6
Recursion Recipe1)^
Handle the “base case”, which is when a recursive callshould
not
be made because the process should stop.
For other cases, make a recursive call (the recursive“leap of faith”), which
must make progress towards a
goal
(towards the base case).
If the base case is not handled, or the recursive call doesnot progress towards the base case, then the method islikely to call itself infinitely (it will “diverge”), and you’ll get a“stack overrun” error.
CIS
7
Example: sum numbers /*
A
recursive
method
that
returns
the
sum
of
the
numbers
from
start
to
end
public static int sum(int start, int end){
if (start > end) // base case
return 0; return start + sum(start + 1, end); }
