General Computer Science
for Engineers
CISC 106
Lecture 06
James Atlas
Computer and Information Sciences
06/24/2009
Lecture Overview

Recursion
◦
◦
◦
◦
-
Definition
Characteristics
Details
Examples
Recursive Function Definition

Definition
◦ The process where a function can call itself.

Characteristics
◦ Allows breaking big problems into smaller and
smaller problems.
◦ One must ensure recursion stops
When you call a function…

Matlab creates a ‘record’ to store the
variables from the new function
◦ Record is pushed on the “stack”

When function done, result passed back
to calling function
◦ Record is popped off
stack.
When you call a function…
function bar2 executing
function bar2
function foo2 calls bar2
function foo2
function bar1 calls foo2
function bar1
function foo1 calls bar1
function foo1
function main calls foo1
function main
In recursion these would all same function!!
Why Can a Function Call Itself?
Calling a function creates a an ‘instance’ of
the function!
 When a function calls itself it creates a
new ‘instance’ of itself
 Each instance pushed on stack

◦ At top of stack is instance of function
currently executing
Recursion requires 3 things

Terminating condition to stop!
◦ Force creation of new instances of a function

Function must call itself
◦ With different inputs!

Terminating condition must eventually be true
Example
How many CEO’s at this table?
A recursive approach……
Taken from http://cache.daylife.com/imageserve/0dgm32v6aYgv6/610x.jpg
Example
How many CEO’s at this table?
A recursive approach……
How
many
CEOs
to my
left?
Taken from http://cache.daylife.com/imageserve/0dgm32v6aYgv6/610x.jpg
Example
How many CEO’s at this table?
A recursive approach……
I don’t
know
how
many
to your
left?
Taken from http://cache.daylife.com/imageserve/0dgm32v6aYgv6/610x.jpg
Example
How many CEO’s at this table?
A recursive approach……
I don’t
know
either
how
many
to your
left?
Taken from http://cache.daylife.com/imageserve/0dgm32v6aYgv6/610x.jpg
Example
How many CEO’s at this table?
A recursive approach……
None….
Just angry
senators….
Taken from http://cache.daylife.com/imageserve/0dgm32v6aYgv6/610x.jpg
Example
How many CEO’s at this table?
A recursive approach……
It’s
just
Bob
next to
me
Taken from http://cache.daylife.com/imageserve/0dgm32v6aYgv6/610x.jpg
Example
How many CEO’s at this table?
A recursive approach……
It’s
just
Bob
and
Jim
next to
me
Taken from http://cache.daylife.com/imageserve/0dgm32v6aYgv6/610x.jpg
Example
How many CEO’s at this table?
A recursive approach……
Why am
I stuck
with Bob,
Jim and
Frank?
Taken from http://cache.daylife.com/imageserve/0dgm32v6aYgv6/610x.jpg
Example
How many CEO’s at this table?
A recursive approach……
Just the
4 of us…
Taken from http://cache.daylife.com/imageserve/0dgm32v6aYgv6/610x.jpg
Sequence, selection, repetition
•
•
•
•
Sequence (statements are ordered, 1, 2, 3…etc.)
Selection (logical control, IF statement)
Repetition (iteration and recursion)
With these three control structures, you can program
anything
Subarrays
It is possible to select and use subsets of
MATLAB arrays.
arr1 = [1.1 -2.2 3.3 -4.4 5.5];
arr1(3) is 3.3
arr1([1 4]) is the array [1.1 -4.4]
arr1(1 : 2 : 5) is the array [1.1 3.3 5.5]

Linear search
Searching, extremely important in
computer science
If we have a list of unsorted numbers,
how could we search them?
Iterative strategy

Given [5 4 2 10 6 7] find which position 6
occupies

Alternatively, does the array contain the
number 6?
Recursive strategy
Break
Binary search
Now, what if the list is sorted, can we
search it faster?
Group exercise:
Speed up our search process if we
know the list is already sorted
(smallest to greatest)
Binary Search
Find N in list
 Pick a number X halfway between the
start and end of the list
 If X == N we are done
else if X < N search top half of list
else search bottom half of list

Let’s do this in Matlab

Recursive solution
Binary Search
Flowchart diagram of the
algorithm
Note the two stopping
conditions (Exits)
Note the one loop
(Note: flowchart is equivalent to
pseudocode)
How much faster is this than linear
search?
If linear search takes roughly n steps for
n things,
Then binary search takes roughly
log2(n) steps for n things. This is
because we divide the n things by 2
each time.