# Recursion Challenge help

Tell us what’s happening:
How does multiply(arr, n) == multiply(arr, n - 1) * arr[n - 1]?
I’m trying to understand how this line of code works and how it does the same thing as the example loop provided.

function sum(arr, n) {
// Only change code below this line

// Only change code above this line
}

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Challenge: Replace Loops using Recursion

This line says, in words, that “the product of the first n elements in the arr is the same as the product of the first n - 1 elements in arr multiplied by the nth item in arr (which is arr[n - 1])”.

Does that help or can I explain better?

If you could simplify that it would be greatly appreciated. I am able to complete the challenge based on the example code provided, I just don’t fully understand what all the code is doing. If you could include another example and break down how it works that would be awesome.

the multiply(arr, n - 1) is the part I’m having trouble understanding. What does this do the first time the function is being called and how is it not the same as the arr[n-1] value?

So, let’s look at an example.

arr = [3, 2, 4]
n = 3

with the function

function multiply(arr, n) {
if (n === 0) {
let result = 1;
return result;
} else {
let smallerCase = multiply(arr, n - 1);
let result = smallerCase * arr[n - 1];
return result;
}
}

Now, in the case above, we

1. Call multiply(arr, 3)
a) if test: 3 !== 0
b) else: so we call multiply(arr, 2)
2. Calling multiply(arr, 2)
a) if test: 2 !== 0
b) else: so we call multiply(arr, 1)
3. Calling multiply(arr, 1)
a) if test: 1 !== 0
b) else: so we call multiply(arr, 0)
4. Calling multiply(arr, 0)
a) if test: 3 !== 0, we return result = 1

Now we can finish 3)
3)
c) smallerCase = 1 and result = 1 * 3
d) we return result = 3

Now we can finish 2)
2)
c) smallerCase = 3 and result = 3 * 2
d) we return result = 6

Now we can finish 1)
1)
c) smallerCase = 6 and result = 6 * 4
d) we return result = 24

Whew, that was a lot. The big picture is that in recursion, we make a smaller version of the problem until we get down to the smallest version of the problem.

Thanks so much for your help, for future reference I could not find the 5 minute video on recursion that is stated on the watch a video link. The provided articles somewhat helped but being able to watch that video would of probably helped me tremendously. Thanks again.