Transcript gcd( 0,6)

1.00/1.001 Lecture 10
Recursion
Recursion
• Recursion is a divide-and-conquer (or divideand-combine) approach to solving problems:
method Recurse(Arguments)
if (SmallEnough(Arguments))
return Answer
else
// Termination
// “Divide”
Identity= Combine( SomeFunc(Arguments),
Recurse(SmallerArguments))
return Identity
// “Combine”
• If you can write a problem as the
combination of smaller problems, you can
implement it as a recursive algorithm in Java®
Finding maximum of array
Assume we can only find max of 2 numbers at a time. Suppose
we want to find the max of a set of numbers, say 8 of them.
35 74 32 92
53 28 50 62
Our recursive max method calls itself:
max(0,7)
max(0,3)
max(4,7)
Greatest common divisor
Given two non negative integers a < b,
the greatest common divisor of a and
b is:
b if a == 0
Greatest common divisor of
b%a and a
Example
gcd (12,18) = gcd (18%12, 12) =
gcd (6,12) = gcd(12%6, 6)
gcd(0, 6) =
6
import javax.swing.*;
// To support simple input
public class GCD {
public static void main(String[] args) {
String input= JOptionPane.showInputDialog("Enter a");
int a= Integer.parseInt(input);
input= JOptionPane.showInputDialog("Enter b");
int b= Integer.parseInt(input);
System.out.println("gcd is " + gcd(a,b));
}
public static int gcd(int a, int b) {
if(a == 0)
return b;
else
return gcd(b%a,a);
}
}
Call Sequence
main( ) calls gcd(12, 18)
returns 6
gcd(12, 18 ) calls gcd(6, 12)
returns 6
gcd(6, 12 ) calls gcd(0, 6)
6
gcd( 0,6) returns 6
Summary
• Recursive method calls itself, directly or
indirectly (almost always directly in practice)
• Recursion is based on divide and conquer:
– Reduce an original problem to a sequence of
smaller instances, until they are small enough to
solve directly
– Then, combine the subproblem solutions to
construct the solution to the original problem
• Recursion is one aspect of how a group of
nonprocedural languages work
– Java® is procedural: you tell computer what to do
and how to do it (like C++, Visual Basic, …)
– Nonprocedural languages: you tell computer
what to do and it figures out how to do it (Prolog)
Java® is a trademark or registered trademark of Sun Microsystems, Inc. In the United States and other countries.