I want to make a recursive function that sums all the digits in a number

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katherine keogh 2020-10-21

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评论： Sri sai teja Palisetti 2020-11-6

So this is the actual question

Write a recursive function that computes the sum of the digits provided as an input argumenet. No need to check the input. Not allowed to use loops or string conversion like str2num. e.g. a number 12345 = 1+2+3+4+5 = 15. There is a hint: consider a mathematical operaion how to get the last digit of a base 10 number.

So far my plan is basically take the last digit of the input 12345

last digit =5

takeaway this value from the orignal number

12345-5=12340

divide by 10

12340/10=1234

add the last digit to the output

output=last digit + prev output

and recall the function till input = 0 at which point output the output

Below is what I currently have and being my first recursion problem quite holey. I am not sure of the base case but also if I define output as 0 then everytime I call the function the output will be 0, so I don't really know how to solve this

function [output]=digit_sum(input)
a = mod(input,10) 
output=a+output
    input=input-a
    input=input/10
    if input==0
        output=output
        return
    else
    [output]=digit_sum(input)
    end
end

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Answer 1

John D'Errico 2020-10-21

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编辑：John D'Errico 2020-10-21

在 MATLAB Online 中打开

The "last" digit? A little ambiguously stated. In the number 12345, is 5 the last digit you are asking about?

It looks like you already know that you can divide by 10. What happens to that last digit then? Could you find the greatest integer that does not exceed the result? How would that help you? Do you know of a function that can convert a floating point number to an integer, still in a double form? (Yes, I suppose you could also decide to cast a number to an integer class, then back into a double. That would work too.)

There are other tools you might consider too.

Perhaps the best way to learn about them would be to do this in MATLAB:

help elfun

This will give you the first line of the help blocks of every function in MATLAB in the directory of elementary mathematical functions. So any of them seem like they would be helpful?

You can find the solution yourself, and if you do, you will be much farther ahead than if I tell it to you on platter. So take a look at the results of the help command I suggested. This will also teach you a way to learn other things in MATLAB. Do some exploring. I promise the solution can be found in elfun. (It is not just elves they hide in there.)

Edit: The problem has moved forward a bit. The question is now how to step foward.

My first comment is digit_sum must know when to terminate the recursion. The step forward will actually begin with knowing when to stop the recursion. Every recursive function typically has a test in the beginning, testing to see if it is done.

The logic could look like this:

function outsum = digit_sum(innum)
   if innum == 0
     % this is the case where it can quit
     outsum = 0;
   else
     % we need to work more deeply here
     % compute a, using mod
     a = ...
     
     % you already know how to modify the input
     % subtract off a from innum, then divide by 10
     innum = ...
     outsum = a + digit_sum(innum);
   end

I've not done the actual work there, just giving you the flow. You already know the rest.

digit_sum cannot escape the recursion until it gets to the end, until the input number has nothing left to it. At that point, the recursion folds back up, one level after another.

Take a shot at that. I think you will have working code now pretty quickly. Ask again if you get closer, but still feel stuck.

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John D'Errico 2020-10-21

编辑：John D'Errico 2020-10-21

在 MATLAB Online 中打开

MOD!!!!!! And that is indeed the perfect solution. That you found it yourself is even better! WELL DONE!

Honestly, the help trick is something I use to this day. Yes, I've been using MATLAB since the pyramids were built. So I should know every function in it. But I don't always remember every function - sometimes my memory fails me. And with every release, they add new functions. Sigh.

So I'll find a function that is close to what I need. I'll figure out which directory it lives in. Then do help on that directory name.

So if I know I need a function in the symbolic toolbox, or the statistics toolbox, then I do help for

help stats
help symbolic

etc. For example, you know that something must exist to solve a problem in linear algebra. And we know the cholesky decomposition is in the linear algebra tools. So where does it live?

>> which chol
built-in (/Applications/MATLAB_R2020b.app/toolbox/matlab/matfun/chol)

It lives in matfun. So now I could do this

help matfun

Now I might look at the functions contained in there. Surely one of them would solve my problem.

If you need a function that works with strings,

help strfun

will give you a boost up.

When all else fails, another trick is to glance at the output of the path function.

path

This will list out every directory supplied with MATLAB, and the associated toolboxes you have. Take a scan through them using help. Yes, many of them will seem pretty boring, But some might be interesting. Take a scan through them if you need some particular function.

Again though, well done to find mod. Rem would also have worked as well, The main difference is in how they handle negative numbers, and in this context that difference is not relevent.

katherine keogh 2020-10-21

在 MATLAB Online 中打开

I got this one too! Your clue on the other post complety unlocked it for me! Here was my solution, I'm sure someone as clever as you can solve it in basically no lines BUT I UNDERSTAND IT NOW!

function [output]=digit_sum(input)
if input==0
        output=0
else
        a = mod(input,10) 
    input=input-a
    input=input/10
    w=[a,digit_sum(input)]
    output=sum(w)
end
end

Sri sai teja Palisetti 2020-11-6

@katherine keogh tq so much it helped me to complete my assignment

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