Algorithm Factorialize A Number

Recursion

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🏁 Problem Explanation:

Return the factorial of the provided integer. If the integer is represented with the letter n, a factorial is the product of all positive integers less than or equal to n.

Factorials are often represented with the shorthand notation n!

For example: 5! = 1 * 2 * 3 * 4 * 5 = 120

💬 Hint: 1

This one starts easily since 0! = 1, so you can go ahead and simply return 1 there.

We can use that as an if in order to break the loop we’re going to create using a recursive function. It will check if the number you gave the function is 0 (which would be the end of your factorial chain). Functions “end” when they return anything. In fact, all functions without an explicit return statement will return undefined.

This is also why instead of having “finished”, a function is always said to “have returned”. And now this…

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💬 Hint: 2

Understanding recursion

Recursion refers to a function repeating (calling) itself. In this case we are basically returning the given number (i.e. 5), multiplied by the function itself but this time the value passed to the num parameter is num-1 (which initially translates to 4). The very function is going to run inside itself interesting, eh?

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💬 Hint: 3

Understanding the flow

The first returned value can be visualized better if you think about those parenthesis operations you did in secondary school where you do the math inside every parenthesis from inside out, bracket and square bracket until you get a final result (a total). This time it’s the same thing, look at the program flow:

During the first execution of the function:

[num = 5]

Is 5 equal to 1 or 0? No —> Oki doki, let’s continue…

Returns:

(5 _(second execution: 4 _(third execution: 3 _(fourth execution: 2 _fifth execution: 1))))

What it returns can be viewed as (5*(4*(3*(2*1)))) or just 5 * 4 * 3 * 2 * 1, and the function will return the result of that operation: 120. Now, let’s check what the rest of the executions do:

During the rest of the executions:

Second Execution: num = 5-1 = 4 -> is num 0 or 1? No
–> return the multiplication between 4 and the next result when num is now 4-1.

Third Execution: num = 4 - 1 = 3 -> is num 0 or 1? No
–> return the multiplication between 3 and the next result when num is now 3-1.

Fourth Execution: num = 3-1 = 2 -> is num 0 or 1? No
–> return the multiplication between 2 and the next result when num is now 2-1.

Fifth Execution: num = 2-1 = 1 -> is num 0 or 1? Yep
–> return 1. And this is where the recursion stops because there are no more executions.

Got it? ;)

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Spoiler Alert!

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Solution ahead!

🔰 Code Solution:

function factorialize(num) {
  if (num === 0) { return 1; }
  return num * factorialize(num-1);
}

factorialize(5);

🚀 Run Code

Code Explanation:

Notice at the first line we have the terminal condition, i.e a condition to check the end of the recursion. If num == 0, then we return 1, i.e. effectively ending the recursion and informing the stack to propagate this value to the upper levels. If we do not have this condition, the recursion would go on until the stack space gets consumed, thereby resulting in a Stack Overflow.

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🏆 Credits:

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Thanks @luishendrix92 @Rafase282 @hallaathrad for your help with Algorithm: Factorialize a Number

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