1. Recursion Method calling itself (circular definition)
A recurrence formula for evaluation
A recurrence terminating condition
Is easier and natural to write.
Is more ‘expensive’ than iterative computation

2. factorial class fact { public static int factorial(int n){ int fact;
if (n==0) fact = 1;
else fact = n * factorial(n-1);
return fact; }
public static void main (String args[]) {
System.out.println(factorial(7));

3. Reverse a string class reversestring {
public static String reverse1(String S){
if (S.length() == 1 ) return S;
else return (reverse1(S.substring(1)) + S.charAt(0)); }
public static String reverse2(String S){
else return (S.charAt(S.length()-1) + reverse2(S.substring(0,S.length()-1)) );
public static void main(String args[]){
String s = "This is a headline";
System.out.println(s);
String r1 = reverse1(s);
System.out.println(r1);
//String r2 = reverse2(r1);
//System.out.println(r2);
System.out.println(reverse1(reverse2(s)));

4. GCD revisited Recall that gcd (a, b) = gcd (a-b, b) assuming a > b.
Directly defines a recurrence
public static int gcd (int a, int b) {
if ((a==1) || (b==1)) return 1;
if (a==b) return a;
if (a < b) return gcd (a, b-a);
if (a > b) return gcd (a-b, b); }

5. GCD revisited
Refinement: gcd (a, b) = gcd (a-nb, b) for any positive integer n such that a >= nb, in particular n = a/b, assuming a > b
public static int gcd (int a, int b) {
if (0==a) return b;
if (0==b) return a;
if (a < b) return gcd (a, b%a);
if (a > b) return gcd (a%b, b); }