1. Recursion Recursive definitions Recursive methods
Run-time stack & activation records
=> Read section 2.3

2. Recursion is a math and programming tool
Technically, not necessary
Wasn’t available in early programming languages
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 helpful

3. Recursive 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) :

4. Recursive Definitions
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?
Note that the “recursive reference” is always on a smaller value. {
N! =

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

6. Recursive Definitions
Fibonacci - Recursive Definition:
0 if N=1 Basis Case
1 if N=2 Basis Case
fib(N-1) + fib(N-2) if N>=3 Recursive Case
Note there are two basis cases and two recursive references. {
fib(N) =

7. 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(); }

8. Recursive Java Programs
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 }
*Don’t ever write it this way; this is a simple, first example of recursion.

9. Recursive Java Programs
Another Equivalent Version (slightly restructured):
// NBlankLines outputs n blank lines, for n>=0
public static void NBlankLines(int n) {
if (n > 0) {
System.out.println();
NBlankLines(n-1); }

10. Recursive Java Programs
public static void main(String[] args) { :
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
if (n > 0) {
System.out.println();
NBlankLines(n-1); }
public static void NBlankLines(int n) { n=0

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

12. Recursive Java Programs
public static void main(String[] args) { :
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
if (n > 0) {
System.out.println();
TwoNBlankLines(n-1); }

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

14. { Recursive Factorial Definition: Recursive Factorial Program:
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! =

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

16. { Recursive Fibonacci Definition: Recursive Fibonacci Program:
0 if N=1 Basis Case
1 if N=2 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) =

17. 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); }

18. 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?