CMPS 1371Introduction to

Computing for Engineers

RECURSION

Recursion

Simple definition: When a function calls itself

Why: Simple reason: often a problem can

reduce to exactly the same problem but on a slightly simpler task

Recursion

Examples:

Factorial n! = (n)(n-1)(n-2)...(3)(2)(1)

Fibonacci F

n = F

n-1 + F

n-2

A "stack"

Last one in is first one out (LIFO)Takes the element on top

regardless of sizeNot too hard to get to recent

ones…

A stack is used for functions to get space for it's arguments, internal data, and it's return location

Each call to a function gets the room it needs on the stack ("pushed" onto the stack).

Allows calling function over and over…

Recursion vs Iteration

Iteration for loops and while loops that solve a

problem by iterating through steps Recursion

functions that call themselves, moving towards one or more base cases

Sum function

As you may know, finding the sum of a vector in MATLAB is easy—we can use the built-in MATLAB function sum():

<< x = [1 2 3];<< sum(x)ans = 6

However, it is an important programming skill to know how to find the sum of a vector (or an array) without using a built-in function, because many languages do not have such a function.

Iteration for sum function

function result = sum1(x)

for i=1:length(x) result = x(i) + result;

end

Adds each element to result

Recursion for sum function

There are only three possibilities for a vector x:

x is an empty vector, which has the sum 0 x is really just a single element—hence x is already

the sum of the vector x

x is vector with at least two elements, and can thus be divided into two parts;

the first element, x(1) the rest of the vector, x(2:end)

Recursion for sum function

function result = sum2(x)

if ( isempty(x) ) result = 0;elseif ( length(x) == 1) result = x;else

result = x(1) + sum2 (x(2:end)); end

Calls the function over again till it reads all elements

Factorial Function

Create a function to calculate the factorial amount

Result should be as follows:

>> fact(5)ans = 120

Factorial Recursion

Try this:first make a new function “fact”

function y = fact(x)if x==1

y=1;else

y=x*fact(x-1);end

This function calls itself. It’s recursive. How does this work?

Palindromes

Palindrome is a word or sentence that is spelled the same forwards and backwards

Examples: level radar toot i prefer pi Napolean's classic lament:

able was i ere i saw elba

eye kayak racecar

Palindromes

Create a function to determine if a word is a palindrome

How would we do it recursively?

If start and end are the same and the middle is a palindrome, then is true

What are the terminating conditions? if length == 1, yes if length == 2, then

if strcmp(str(1),str(2)), then yes

Palindrome code

function ans = isPal(str)

% is str a palindrome?

% isPal(‘ enter your word ’)

str = lower(str);

if length(str) < 2

ans = true;

disp('your word is a palindrome')

elseif str(1) ~= str(end)

ans = false;

disp('your word is not a palindrome')

else

ans = isPal(str(2:end-1));

end

Recursion Characteristics

There are three necessary characteristics of all recursive functions

1. There must be a terminating condition to stop the process

2. The function must call a clone of itself3. The parameters to that call must move the

function toward the terminating condition

A recursive function does not really call itself because it passes different parameters to the function