Scoping and Recursion CSC 171 FALL 2004 LECTURE

Scoping and Recursion CSC 171 FALL 2004 LECTURE 12

JAVADOC l Setting Documentation comments – Delimited by “/**” and “*/” in source l You can comment – Classes – Methods – Fields l Each comment is placed immediately above the feature it documents

Tagged Documentation l @param l @return l @throws l @deprecated l @see l @author l @version

Using Javadoc l Demo

Parameter Scoping public class my. Class { int x = 4; public static void main(String args[]){ int x = my. Method 1(5); System. out. println(“x ==“ + x); } public static int my. Method 1(int x) { my. Method 2(x); return x + 1; } public static int my. Method 2(int x) { x = 7; } }

Parameter Scoping public class my. Class { int y = 0 ; public static void main(String args[]){ int x = my. Method 1(5); y+=x; System. out. println(“x ==“ + x + “ y == “ + y); } public static int my. Method 1(int x) { y+= x; return my. Method 2(x) + 1; } public static int my. Method 2(int x) {y+=x; return x + 1; }

Recursion l l l Methods can call other methods Methods can also call themselves Consider the “factorial” method – – – 4! = 4*3*2*1 We can think of this as 4! = 4*3! 3! = 3*2! 2! = 2* 1! 1! = 1 l Recursion is when we think of things in terms of itself.

Recursion l We often think of recursion as a “programming technique” l Recursion is also a design pattern for data structures l Recursion is a way to think about problem solving

A Theological Aside Disclaimer: you don’t have to believe l Can computer science inform theology? l Christian notion of “Trinity”? l "A three-fold personality existing in one divine being or substance; the union in one God of Father, Son, and Holy Spirit as three infinite, co-equal, coeternal persons; one God in three persons. " l from about 400 AD to about 1800 AD, lots of people were put to death for refusing to believe in the idea of "one God in three persons. "

To this day l “Trinity is still largely incomprehensible to the mind of man. ” – J. Hampton Keathley, III , Th. M l But is it? How can something be “ 3 in 1”? l RECURSION!

Sierpinski Triangle This design is called Sierpinski's Triangle, after the Polish mathematician Waclaw Sierpinski who described it in 1916. Among these is its fractal or self-similar character. The large blue triangle consists of three smaller blue triangles, each of which itself consists of three smaller blue triangles, each of which. . . , a process of subdivision which could, with adequate screen resolution, be seen to continue indefinitely.

Serpinski Triangle What is a Serpinski Triangle? A Serpinski Triangle is a triangle made up of 3 Serpinski triangles.

Weiss’s fundamental rules of recursion Base case: always have at least one case that can be solved without recursion 2. Make progress: Any recursive call must progress toward the base case 3. “You gotta believe”: Always assume that the recursive call works. (In proofs “BTIH”). 4. Compound Interest rule: Never duplicate work by solving the same instance of a problem in separate recursive calls. 1.

Example : Fibonacci Number public static long fib (int n) { if (n <= 1) return n; else return fib (n-1) + fib(n-2); }

Recursion l Methods can call other methods l Methods can also call themselves public long factorial(long number) { if (number <=1) return 1; else return number * factorial(number – 1); }

Recursion vs. Iteration l GCD – Euclid’s (300 B. C. ) Algorithm – Oldest known non-trivial algorithm – If r is the remainder when a is divided by b – Then the common divisors of a and b are the same as the common divisors of b and r

Examples of Euclid’s Alg l l l GCD(206, 40) ==GCD(40, 6) ==GCD(6, 4) ==GDC(4, 2) ==GCD(2, 0) ==2 l l l GCD(154, 35) ==GCD(35, 14) ==GCD(14, 7) ==GCD(7, 0) ==7

In Class Excercise l Using Euclids algorithm write: public int GCD(int a, int b) l Partner up l 10 min l hand in on paper – two names

Iterative version public static int GCD 1(int a , int b) { while (b != 0){ int temp = a%b; a = b; b = temp; } return a; }

Recursive version public static int GCD 2(int a , int b) { if (b == 0 ) return a; else return GCD 2(b, a%b); }