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Lucas Ackerknecht
615 Pointsfactorials question
def factorial(n) if n == 0 1 elsif n < 0 "NAN" elsif n*factorial(n-1) end
I think this is somewhat right. I don't understand what n*factorial(n-1) does, though. So if I were to just type factorial(4) in the command line, how does n*factorial(n-1) know to loop until it gets to 1*(1-1). Also, isn't factorial(n-1) a new variable? How does Ruby know factorial(n-1) is the same as factorial(n) - 1?
Is it doing: 4*3 3*2 2*1 1*0 then summing? What's triggering the loop?
3 Answers
Mike Costa
Courses Plus Student 26,362 PointsHey Lucas,
I'm not too familiar with Ruby, so I wrote this in PHP to help you explain factorials.
function factorial($n){
if($n == 0) {
return 1;
} elseif($n < 0) {
echo "NAN";
} else {
return $n * factorial($n-1);
}
}
Let's call the function with a parameter of 5.
This type of function is a recursive function, meaning that you can call the function within itself. With this factorial function, you're giving it a parameter (in my case, the parameter is $n). The program then reads the first line of the function when you call it, which is the if statement. If $n equals 0, return 1 (or true). Being that $n equals 5, it skips this if block and goes to the first else if, if $n < 0. (this is here in case the parameter happens to be a negative number.) 5 isn't a negative number, so it skips to the last else if block of code. Using the parameter 5, the last block of code reads:
5 * factorial(5 - 1)
..which calls the function again (causing the loop to have a new parameter, which will now be 4). This function loops itself taking the product of $n * factorial and keeps multiplying as it loops in the last line of the function.
5 * factorial(5 - 1) //$n is now 4
20 * factorial(4 - 1) // $n is now 3
60 * factorial(3 - 1) // $n is now 2
120 * factorial(2 - 1) // $n is now 1
120 * factorial(1 - 1) // $n is now 0
Now that $n equals 0, when the function calls itself, the first if statement is true. So the returned product of the function is the 5 factorial ( 5! == 5*4*3*2*1).
Hope this helps. :)
Lucas Ackerknecht
615 PointsAwesome, thank you so much!
So if I were to change
return $n * factorial($n-1);
to
return $n * factorial($n+1);
Would the computer know it was a recursive function and keep on spitting out new n's until it triggers an "if" clause (let's say instead of 0 I put an upper limit of 100 on it. If I don't put an upper limit, would it go to infinity?
I guess I'm just not sure how the computer knows what's a recursive function.
Like, would
return $n * factorial($n) - 1;
Not be recursive? If $n = 3, then would it just be 3*3 - 1 = 8. The end?
Mike Costa
Courses Plus Student 26,362 PointsIf you changed it to
return $n * factorial($n + 1);
it would go until you set an upper limit like you said, however, I think it reaches infinity around 170.
The reason its recursive is it keeps calling itself until it reaches a statement that causes it to not do so.
For instance, lets say we created a function called addition and set it to add numbers between 1 and 20 together.
function addition($n) {
if ($n == 20) {
return 1;
} else if ($n < 0) {
echo "NAN";
} else {
return $n + addition($n+1);
}
}
The reason recursion happens is because your calling the "addition" function WITHIN the "addition" function. You're making it call itself until you don't want it to. Without a breakpoint/limit, it becomes an infinite loop. Technically the computer doesn't know its recursive, it's just doing what its told.
When I tried this statement:
return $n * factorial($n) - 1;
I got a this error:
Fatal error: Allowed memory size of 33554432 bytes exhausted
Fun fact: If you google the word recursion, the search page asks "Did you mean: recursion". Sometimes, google has jokes! :D
Lucas Ackerknecht
615 Points"Mind blown"
Thanks! I get it now.
Mike Costa
Courses Plus Student 26,362 PointsGlad I can help! :)