[Tutor] recursive function example

[Alan Gauld]

On 12/12/13 04:18, ugajin at talktalk.net wrote:
>
> In a way,it may help to identify the issue
> def multiply(a,b)
>   return a*b
> clearly returns the product of the two arguments, a and b
> I presume it returns a+a rather than b+b+b

It depends on how multiplication is implemented in the CPU microcode.
But thats none of our concern, it uses Python multiplication.

> mult(a, b-1) also has two arguments.
> and rest takes the value of the two arguments,

No it doesn't.
I don't know why you think that but rest takes the
*return* value of mult(). It is no different to the
multiply() case.

> I do not see an instruction to multiply the arguments

That's what mult() is. It is a function that multiplies
it's arguments by successive addition. It just happens
to do that using recursion. But you have to "trust"
that it will multiply the two arguments.

> How in the original def mult(a, b) . . .,
> does mult(a, b-1) say return the product of a and b-1?

It says return 'value'. And value is the addition of
the first argument and the product of (a * b-1)

Let's go back a couple of steps.

Do you understand how it works for this case:

mult(3,0)

It returns zero because b is zero, right?

Now consider what it does for

mult(3,1)

It checks if b is zero, it's not, so it executes

rest = 3 + mult(3,0)

But you know that mult(3,0) returns zero, so

rest = 3 + 0

ie rest = 3.

Do you understand this far?


-- 
Alan G
Author of the Learn to Program web site
http://www.alan-g.me.uk/
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