Recursion!
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Recursion!
Can a method call another
method?
Can a method call another
method?YES
Can a method itself?
Also YES
Rules:
1. Recursive call must be to a smaller
version of the problem.
2. Recursion must be heading for the
base case.
public static int fact(int n)
{
if (n == 0) return 1;
else return n*fact(n-1);
}
public static void main(String[] args)
{
int f;
f = fact(4);
System.out.println(f);
}
Call to fact(4)
public static int fact(int n)
{
if (n == 0) return 1;
else return n *fact(n -1);
}
public static int fact(int 4)
{
if (4 == 0) return 1;
else return 4 *fact(4 -1);
}
Call to fact(3)
public static int fact(int 4)
{
if (4 == 0) return 1;
else return 4 *fact(4 -1);
}
public static int fact(int 3)
{
if (3 == 0) return 1;
else return 3 *fact(3 -1);
}
Call to fact(2)
public static int fact(int 4)
{
if (4 == 0) return 1;
else return 4 *fact(4 -1);
}
public static int fact(int 3)
{
if (3 == 0) return 1;
else return 3 *fact(3 -1);
}
public static int fact(int 2)
{
if (2 == 0) return 1;
else return 2 *fact(2 -1);
}
Call to fact(1)
public static int fact(int 4)
{
if (4 == 0) return 1;
else return 4 *fact(4 -1);
}
public static int fact(int 3)
{
if (3 == 0) return 1;
else return 3 *fact(3 -1);
}
public static int fact(int 2)
{
if (2 == 0) return 1;
else return 2 *fact(2 -1);
}
public static int fact(int 1)
{
if (1 == 0) return 1;
else return 1 *fact(1 -1);
}
Call to fact(0)
public static int fact(int 4)
{
if (4 == 0) return 1;
else return 4 *fact(4 -1);
}
public static int fact(int 3)
{
if (3 == 0) return 1;
else return 3 *fact(3 -1);
}
public static int fact(int 2)
{
if (2 == 0) return 1;
else return 2 *fact(2 -1);
}
public static int fact(int 1)
{
if (1 == 0) return 1;
else return 1 *fact(1 -1);
}
public static int fact(int 0)
{
if (0 == 0) return 1;
else return 0 *fact(0 -1);
}
public static int fact(int 4)
{
if (4 == 0) return 1;
else return 4 *fact(4 -1);
}
public static int fact(int 3)
{
if (3 == 0) return 1;
else return 3 *fact(3 -1);
}
public static int fact(int 2)
{
if (2 == 0) return 1;
else return 2 *fact(2 -1);
}
public static int fact(int 1)
{
if (1 == 0) return 1;
else return 1 *fact(1 -1);
}
public static int fact(int 0)
{
if (0 == 0) return 1;
else return 0 *fact(0 -1);
}
public static int fact(int 4)
{
if (4 == 0) return 1;
else return 4 *fact(4 -1);
}
public static int fact(int 3)
{
if (3 == 0) return 1;
else return 3 *fact(3 -1);
}
public static int fact(int 2)
{
if (2 == 0) return 1;
else return 2 *fact(2 -1);
}
public static int fact(int 1)
{
if (1 == 0) return 1;
else return 1 *fact(1 -1);
}
Returned 1
public static int fact(int 4)
{
if (4 == 0) return 1;
else return 4 *fact(4 -1);
}
public static int fact(int 3)
{
if (3 == 0) return 1;
else return 3 *fact(3 -1);
}
public static int fact(int 2)
{
if (2 == 0) return 1;
else return 2 *fact(2 -1);
}
Returned 1
public static int fact(int 4)
{
if (4 == 0) return 1;
else return 4 *fact(4 -1);
}
public static int fact(int 3)
{
if (3 == 0) return 1;
else return 3 *fact(3 -1);
}
Returned 2
public static int fact(int 4)
{
if (4 == 0) return 1;
else return 4 *fact(4 -1);
}
Returned 6
public static void main(String[] args)
{
int f;
f = fact(4);
System.out.println(f);
}
Returned 24
public static void main(String[] args)
{
int f;
f = fact(4);
System.out.println(f);
}
Displays 24
?
Comments about recursion
1. Recursion is never necessary. Can always be done iteratively.
2. Can hide inefficiency.
3. But may be the easiest, clearest, shortest way to write a program.
public static int fib(int n)
{ // pre: n>=0
// post: returned value is fib(n)
if (n==0 || n==1) return n;
else return fib(n-1)+fib(n-2);
}
Fib(8)
Fib(8)
Fib(6)Fib(7)
Fib(8)
Fib(6)
Fib(5)Fib(6)
Fib(7)
Fib(8)
Fib(4)Fib(5)
Fib(6)
Fib(5)
Fib(5)
Fib(6)
Fib(7)
Fib(4)
Yadda yadda yadda
Fib(8)
Fib(4)Fib(5)
Fib(6)
Fib(5)
Fib(5)
Fib(6)
Fib(7)
Fib(2)Fib(3)Fib(3)Fib(4)Fib(3)Fib(4)Fib(4)
Fib(8)
Fib(4)Fib(5)
Fib(6)
Fib(5)
Fib(5)
Fib(6)
Fib(7)
Fib(2)Fib(3)Fib(3)Fib(4)Fib(3)Fib(4)Fib(4)
To compute fib(8), we call:
fib(8) 1 time
fib(7) 1 times
fib(6) 2 times
fib(5) 3 times
fib(4) 5 times
fib(3) 8 times
fib(2) 13 times
fib(1) 21 times
fib(0) 13 times
A total of 67 method calls!
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