No, I don’t think those two are the same, why would I? I don’t understand the question.
The question I am asking is why does multiply(arr, n) == multiply(arr, n - 1) * arr[n - 1]???
To try and make it simple:
This is one thing: multiply(arr, n)
This is another thing: multiply(arr, n - 1)
Why are they the same thing. ELI5
I don’t think I have a problem with indexing. I’ve just gone back and done those challenges and I have no problems.
Perhaps you could explain which concepts you think I’ve missed?
Those two loops in my snippets are using different indexing to do the exact same thing.
Nowhere is it being claimed that they are the same. Recursion depends upon them not being the same.
Sure
multiply(arr, n) == multiply(arr, n - 1) * arr[n - 1]
does not mean that
multiply(arr, n) is a function call that returns the product of the first n elements in arr.
multiply(arr, n - 1) is a function call that returns the product of the first n - 1 elements in arr.
Thus, multiply(arr, n - 1) * arr[n - 1] must be the product of the first n elements in arr.
What? How does it not mean that?
multiply(arr, n) and multiply(arr, n - 1) have different arguments. They should in general be different.
The statement says
multiply(arr, n) == multiply(arr, n - 1) * arr[n - 1]
This means that
multiply(arr, n)
and
multiply(arr, n - 1) * arr[n - 1]
are equivalent.
How is it a function call that returns the product of the first n elements in arr? Surely it’s a function declaration with two parameters?
I don’t think you’re getting what I’m asking. I don’t know how else to ask.
multiply() is a function. multiply(arr, n) returns a number which is the product of the first n entries of arr.
Function declaration:
function multiply(arr, n) {
if (n <= 0) {
return 1;
} else {
return multiply(arr, n - 1) * arr[n - 1];
}
}
Function call:
multiply(arr, n)
Thus,
multiply(arr, n) == multiply(arr, n - 1) * arr[n - 1]
means
theValueReturnedByMultiplyArrN == theValueReturnedByMultiplyArrNMinus1 * arr[n -1]
nowhere does the challenge say that theValueReturnedByMultiplyArrN and theValueReturnedByMultiplyArrNMinus1 are the same.
Your line ‘Thus’
This is the step I can’t follow! Why are they equal? !
multiply(arr, n) computes the product of the first n elements in arr.
multiply(arr, n - 1) computes the product of the first n - 1 elements in arr.
arr[n - 1] is the nth element in arr.
So, multiply(arr, n - 1) * arr[n - 1] is the product of the first n elements in arr and
multiply(arr, n) == multiply(arr, n - 1) * arr[n - 1]
Hi - please read through the comments above before repeating the same explanation that didn’t help before.
I did read the comments. I’m answering your question.
Let me start at the absolute beginning. Do you understand the distinction between a function definition and the result you get from calling the function?
Yes. Apparently my post has to be 20 characters so I’m padding it out a bit.
Ok.
Let’s look at the array arr = [2, 4, 1, 5].
When I call multiply(arr, 4), I should get 2 * 4 * 1 * 5 = 40.
When I call multiply(arr, 3), I should get 2 * 4 * 1 = 8.
We can write this as
multiply(arr, 4) == 40
and
multiply(arr, 3) == 8
Note that we are using == to mean that the left and right hand side of the comparator evaluate to the same value.
Notice that
40 == 8 * 5
and that
arr[3] == 5
This means that
40 == 8 * arr[3]
We are close here.
Now we can say that
40 == multiply(arr, 3) * arr[3]
Finally, we can say that
multiply(arr, 4) == multiply(arr, 3) * arr[3]
The last thing to notice is that n = 4 so
multiply(arr, n) == multiply(arr, n - 1) * arr[n - 1]
All of this was based on the return values of these functions.
I think I understand your explanation up until your final point.
n only = 4 because thats how you’ve called the function. How does that affect the fact that multiply(arr, n) == multiply(arr, n - 1) * arr[n - 1]?
In the explanation given in the challenge there is no array given, I’m confused as to whether you’re giving a generic explanation or specific to the challenge given.
It’s both. The exact same logic works for every size array. For every single array the product of every single value in the array is the same as the product of all but the last value and the last value.
Put symbolically
arr[0] * arr[1] * ... * arr[n - 1] == (arr[0] * arr[1] * ... arr[n - 2]) * arr[n - 1]
This is not a thread about radio buttons. I recommend you use the “get help” button on the challenge and start a new thread.