1. Recursion Recursion is a math and programming tool
Technically, not necessary
Advantages of recursion
Some things are very easy to do with it, but difficult to do without it
Frequently results in very short programs/algorithms
Disadvantages of recursion
Somewhat difficult to understand at first
Often times less efficient than non-recursive counterparts
Presents new opportunities for errors and misunderstanding
Tempting to use, even when not necessary
Recommendation – use with caution, and only if necessary
=> Read section 2.3

2. Recursive Mathematical Definitions
Factorial - Non-Recursive Definition
N! = N * (N-1) * (N-2) * … * 2 * 1
*Note that a corresponding Java program is easy to write
public static int fact(int n) :

3. { Factorial - Recursive Definition 1 if N=1 Basis Case
N * (N-1)! if N>=2 Recursive Case
Why is it called recursive?
Why do we need a basis case? {
N! =

4. Fibonacci - Non-Recursive Definition…
*Note that a corresponding Java program is easy to write…or is it?
public static int fib(int n) :

5. { Fibonacci - Recursive Definition 0 if N=1 Basis Case
fib(N-1) + fib(N-2) if N>=3 Recursive Case {
fib(N) =

6. Recursive Java Programs
Printing N Blank Lines – Non-Recursive
public static void NBlankLines(int n) {
for (int i=1; i<=n; i++)
System.out.println(); }

7. Printing N Blank Lines – Recursive
// NBlankLines outputs n blank lines, for n>=0
public static void NBlankLines(int n) {
if (n <= 0) Basis Case
return;
else {
System.out.println();
NBlankLines(n-1); Recursive Case }

8. Another Version // NBlankLines outputs n blank lines, for n>=0
public static void NBlankLines(int n) {
if (n > 0) {
System.out.println();
NBlankLines(n-1); }

9. public static void main(String[] pars) {:
NBlankLines(3); }
public static void NBlankLines(int n) { n=3
if (n > 0) {
System.out.println();
NBlankLines(n-1);
public static void NBlankLines(int n) { n=2
public static void NBlankLines(int n) { n=1
public static void NBlankLines(int n) { n=0

10. A Similar Method: public static void TwoNBlankLines(int n) {
if (n > 0) {
System.out.println();
TwoNBlankLines(n-1); }

11. public static void main(String[] pars) {:
TwoNBlankLines(2); }
public static void TwoNBlankLines(int n) { n=2
if (n > 0) {
System.out.println();
TwoNBlankLines(n-1);
public static void TwoNBlankLines(int n) { n=1
public static void TwoNBlankLines(int n) { n=0

12. Are the Following Methods the Same or Different?
public static void TwoNBlankLines(int n) {
if (n > 0) {
System.out.println();
TwoNBlankLines(n-1); }

13. { Recursive Factorial Definition 1 if N=1 Basis Case
N * (N-1)! if N>=2 Recursive Case
Recursive Factorial Program
public static int fact (int n) {
if (n==1)
return 1; Basis Case
else {
int x; Recursive Case
x = fact (n-1);
return x*n; } {
N! =

14. Another Version public static int fact (int n) { if (n==1)
return 1; Basis Case
else
return n*fact (n-1); Recursive Case }

15. { Recursive Fibonacci Definition 0 if N=1 Basis Case
fib(N-1) + fib(N-2) if N>=3 Recursive Case
Recursive Fibonacci Program
public static int fib (int n) {
if (n==1)
return 0; Basis Case
else if (n==2)
return 1; Basis Case
else {
int x,y; Recursive Case
x = fib (n-1);
y = fib (n-2);
return x+y; } {
fib(N) =

16. Another Version
public static int fib (int n) {
if (n==1)
return 0;
else if (n==2)
return 1;
else
return fib(n-1) + fib(n-2); }

17. Recursion & The Run-Time Stack
How does recursion related to stack frames and the run time stack?
Note that stack frames are sometimes called allocation records or activation records
Why might a recursive program be less efficient than non-recursive counterpart?
Why is the recursive fibonnaci function especially inefficient?