Problem with factorial recursive function

Whenever I run the code for a matrix of n values, like n=1:10, only the last 2 factorials are displayed while the rest are 0's. Would anyone be able to tell me where I have gone wrong?

Code:

 function x = fact(n)

    if n<=1
       x = 1;    
    else
       x = n .* fact(n-1) ;
    end

 end

Answer 1

[Titus Edelhofer]

Hi Arun,

your code does not work for arrays because of the "if n<=1". You would need to do something like

idx = (n>1);
x(~idx) = 1;
x(idx) = n(idx).* ...

Titus

[Stu145]

Hi Tidus,

I am now getting a 'Maximum recursion limit error....' for even single values now when using the following code. I have tried to implement what you said, but it's the final equation that is now causing me an issue.

function x = fact(n)

 idx = (n>1);

 x(~idx)=1;

 x(idx) = n(idx).*fact(n(idx)-1);

 end

[John D'Errico]

For how large of a value are you trying to compute the factorial? Be careful, as this could be important, since that too would blow up the recursion limits.

Regardless, as you have written it, the code will still run forever. What happens when all values of n are <= 1?

The function as you wrote it will still call fact, but with an empty array for n. so you will have fact calling fact, each time with an empty argument n.

I would add a test to stop that from happening.

[Shubham Tyagi]

I'm compiling this code with a 2*4 matrix but (dimensions doesn't match in val(i)=r(i).*fact(r(i)-1);) type error is coming.

function val=fact(r)

i=(r>1); val(~i)=1; if r==1 return end val(i)=r(i).*fact(r(i)-1); end

Answer 2

[Image Analyst]

Not sure what you did, but it worked fine for me. I put all this (both functions) into test.m

function test
clc;
for k = 1 : 10
  kFactorial = fact(k);
  fprintf('%d! = %d\n', k, kFactorial);
end

function x = fact(n)
if n<=1
  x = 1;
else
  x = n .* fact(n-1) ;
end

In the command window you'll see:

1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040
8! = 40320
9! = 362880
10! = 3628800

[Titus Edelhofer]

Hi,

the problem arises if you want to call fact in vectorized form, i.e.,

kFact = fact(1:10);

Then you need to switch from "if" to logical indexing. And, as John indicated, you must make sure that you protect the recursion with

if any(idx)
  x(idx) = n(idx).*fact(n(idx)-1);
end

Titus

[Shubham Tyagi]

what about m*n matrix rather than a vector??

[Image Analyst]

I don't know what matrix you're talking about. Please give the code you are going to run to call your function, and show what output you'd expect to see.

If you want fact n to print out an array from the first integer to the last integer, the fact() function will need to be modified since now it's just expecting a single number, not a vector or matrix.

[Torsten]

Reshape everything to vectors and reshape back to matrices, if necessary.

Best wishes

Torsten.

Answer 3

[Titus Edelhofer]

Hi,

two minor changes are needed:

function x = fact(n)
x = ones(size(n));
idx = (n>1);
if any(idx)
  x(idx) = n(idx).*fact(n(idx)-1);
end

First, you need to initialize x as an array of the same size as n (because for fact(n-1) otherwise the array could be smaller), giving the error you observed.

Second, protect the recursive call to fact(n-1) by doing this only if there is anything to do...

Titus

[Titus Edelhofer]

Calling for a matrix works fine, btw.:

fact([2 3 4; 5 6 7])
ans =
         2           6          24
       120         720        5040

Answer 4

[Anil Sarode]

sorry i copied your code :

this is the one way to solve your problem :

function file: from where you make function call each time using for loop :

n=1:10;
y=[];
for i=1:length(n)
 y(i)=fact(i) ;  
 end

function: which do desire task

   function [x] = fact(n)

    if n<=1
       x = 1;    
    else
       x = n .* fact(n-1) ;
    end
 end