1. Computer Science 4 Mr. Gerb
When to use recursion
Computer Science 4
Mr. Gerb
Reference:
Objective: Understand when recursion is useful and how to remove it.

2. Three rules of thumb: Use recursion only when:
The depth of recursive calls is relatively “shallow” compared to the size of the problem.
The recursive version does about the same amount of work as the nonrecursive version.
The recursive version is shorter and simpler than the nonrecursive solution.

3. Shallow recursive calls: First Example
Supposed you were to use recursion to search a very large linked list with N elements.
O(N) stack frames might exist at one time
Bad if N is large
Most compilers have a limited amount of space set aside for the stack
Likely to cause a stack overflow

4. Shallow Recursive Calls: Second Example
Suppose you were to use recursion to binary search an array of N elements
O(LogN) stack frames will exist at one time
OK even if N is large
E.g. for 16 billion elements, only need 34 stack frames!
I.e. depth of recursion not a problem for binary search

5. Recursive Version Works Same as Non-Recursive Version
Example: Nth fibonacci number:
public static int fib(int n){
if (n<=2)
return 1;
else
return fib(n-1)+fib(n-2); }
How many recursive calls does fib make?

6. Fibonacci Example Cont’d
fib(1) and fib(2) both take none
fib(3) takes two:
fib(1)
fib(2)
fib(4) takes 4
fib(3) fib(1) fib(2) fib(2)
fib(5) takes 8
fib(4) fib(3) fib(1) fib(2)
fib(2) fib(3) fib(1) fib(2)

7. Fibonacci Example Cont’d
fib(6) takes 14
fib(5) fib(4) fib(3) fib(1)
fib(2) fib(2) fib(3) fib(1)
fib(2) fib(4) fib(3) fib(1)
fib(2) fib(2)
fib(7) takes 24
fib(6) fib(5) fib(4) fib(3)
fib(1) fib(2) fib(2) fib(3)
fib(1) fib(2) fib(4) fib(3)
fib(1) fib(2) fib(2) fib(5)
fib(4) fib(3) fib(1) fib(2)
fib(2) fib(3) fib(1) fib(2)

8. Fibonacci Example Cont’d
fib(8) takes 40
fib(6) fib(5) fib(4) fib(3)
fib(1) fib(2) fib(2) fib(3)
fib(1) fib(2) fib(4) fib(3)
fib(1) fib(2) fib(2) fib(7)
fib(1) fib(2) fib(2) fib(5)
fib(4) fib(3) fib(1) fib(2)
fib(2) fib(3) fib(1) fib(2)

9. Non-Recursive Fibonacci
public static void fib(int n){
int back1=1, back2=1,fib=1;
for (int ctr=3;ctr<=n;ctr++){
fib=back1+back2;
back2=back1;
back1=fib; }
return fib;

10. Recursive vs. Non-Recursive Fibonacci
Non-recursive Fibonacci equires n-2 runs through the loop
fib(3) once through the loop
fib(4) twice through the loop
fib(8) six times through the loop
Recursive Fibonacci requires an exponential number of recursive calls
Therefore computing Fibonacci numbers is not a good candidate for recursion.

11. Recursive Function Shorter and Simpler
Many recursive algorithms would require creating your own stack to implement non-recursively
Merge Sort
Quick Sort
Search
Much simpler to express, understand, implement and maintain using recursion

12. Two ways to remove recursion
Use a stack
Keep your own stack frames
Rarely an improvement on the recursive solution
Tail recursion
When a function contains only one recursive call and it is the last statement to be executed, that is called tail recursion
Tail recursion can be replaced by iteration to remove recursion.

13. Example: Search an array for an item
public boolean fnd(int[] a, int n, int st){
if (st>a.length)
return false;
else if (a[st]==n)
return true;
else
return fnd(a,n,st+1); }
int found = false;
while (!found &&
st<=a.length){
if (a[st]==n)
found = true;
st++ }

14. Summary Use recursion only when
Recursion is not deep
Doesn’t slow the algorithm down
Easier to understand or implement
Can remove recursion with a stack or tail recursion
Tail recursion
One recursive call, last statement executed
Recursion can be replaced with iteration