为什么.to_s会破坏此代码？

Question

I'm working on a Codewars Ruby problem, and don't understand the error I'm seeing. Here are the instructions:

Coding decimal numbers with factorials is a way of writing out numbers in a base system that depends on factorials, rather than powers of numbers. In this system, the last digit is always 0 and is in base 0!. The digit before that is either 0 or 1 and is in base 1!. The digit before that is either 0, 1, or 2 and is in base 2!. More generally, the nth-to-last digit in always 0, 1, 2, ..., or n and is in base n!.

Example : decimal number 463 is coded as "341010"

because 463 (base 10) = 3×5! + 4×4! + 1×3! + 0×2! + 1×1! + 0×0!

If we are limited to digits 0...9 the biggest number we can code is 10! - 1.

So we extend 0..9 with letters A to Z. With these 36 digits we can code up to 36! − 1 = 37199332678990121746799944815083519999999910 (base 10)

We code two functions, the first one will code a decimal number and return a string with the factorial representation : "dec2FactString(nb)"

the second one will decode a string with a factorial representation and produce the decimal representation : "factString2Dec(str)".

Given numbers will be positive.

Note

You can hope tests with Big Integers in Clojure, Python, Ruby, Haskel but not with Java and others where the number "nb" in "dec2FactString(nb)" is at most a long.

Ref: http://en.wikipedia.org/wiki/Factorial_number_system

def dec2FactString(nb)
  if nb <= 0 then
    num = 1
  else
    num = (nb * dec2FactString(nb - 1))
  end
  return num
end

Note that this method is only the first half of the problem. This code appears to work inasmuch as it returns the correct factorial, as a Fixnum when using this test:

Test.assert_equals(dec2FactString(4), "24") 

Since the instructions ask for a string, I'd normally think that just adding ".to_s" to the num variable would take care of that, but instead I'm seeing a consistent "String can't be coerced into Fixnum (TypeError)" error message. I've tried pushing the output to an array and printing from there, but saw the same error.

I read up on Fixnum a little, and I understand the error in terms of adding a Fixnum to a string won't work, but I don't think I'm doing that in this case - I just want to convert the Fixnum output into a string. Am I missing something?

Observe - this code breaks and produces the error below it:

def dec2FactString(nb)
  if nb <= 0 then
    num = 1
  else
    num = (nb * dec2FactString(nb - 1))
  end
  return num.to_s
end

Example from description
 `*': String can't be coerced into Fixnum (TypeError)
    from `dec2FactString'
    from  `dec2FactString'
    from  `dec2FactString'
    from  `dec2FactString'
    from  `block in 
'
    from  `block in describe'
    from  `measure'
    from  `describe'
    from  `
'

Answer 1

You're calling this function recursively. If you calculated the factorial of 1 and left to_s in there, it'd be fine since you're not reusing the variable.

However, if you do place to_s in there, what would you expect the result of num = (nb * dec2FactString(nb - 1)) to be? dec2FactString would be returning a str instead of a Fixnum , and you can't/shouldn't be able to do multiplication between a number and a string.

What you could do is split the responsibilities of stringification and calculation by creating two methods - one that delegates to the recursive function, and one that coerces its result into a string.

def dec2FactString(nb)
    return fact(nb).to_s
end

def fact(nb)
    if nb <= 0 then
        1
    else
        nb * fact(nb - 1)
    end
end

Answer 2

Firstly, Factorial is only defined on non-negative numbers and so your first test is incorrect (if nb <= 0). The recursion should stop when the number is 0 and should return 1 at that point.

Because your recursion returns a string and not a number, you cannot multiply the string by a Fixnum in the next round of recursion. Your recursion can be expanded via the substitution method to the following.

dec2FactString(5)
5 * dec2FactString(4)
5 * 4 * dec2FactString(3)
5 * 4 * 3 * dec2FactString(2)
5 * 4 * 3 * 2 * dec2FactString(1)
5 * 4 * 3 * 2 * 1 * dec2FactString(0)
5 * 4 * 3 * 2 * 1 * "1"

... That is the point where the recursion ends in an error since dec2FactString(0) returns "1"

It would be far better to break it into two functions. One that calculates factorial recursively and one that converts the final answer to a string. Also, you don't need to explicitly return a value in Ruby. The last line of a function is the return value.

I won't give you the complete code as you won't learn anything. As a few hints, do some research on tail call optimisation, recursion and return values in Ruby. This will allow you to craft a better implementation of the recursive function.

Happy coding!