需要帮助理解这个递归函数教程

Question

I came across this example of a recursive function in a textbook. I can see there are other threads on this site that ask a question about this very example from Eloquent JavaScript but that user's difficulty in understanding the example was to do with not understanding how functions are invoked in general.

function findSolution(target){
  function find(start, history){
    if(start == target)
      return history
    else if(start > target)
      return null
    else 
      return find(start + 5, "(" + history + " + 5)") ||
             find(start * 3, "(" + history + " * 3)") 
    }
    return find(1, "1");
  }

You supply a target number to the findSolution function, and it executes the inner function, find, which calls itself until it finds a way to reach the target number by adding 5 or multiplying by 3. Say I supply the number 13 as a target to reach. The parameters increment as follows.

Start = 1 + 5, History = "(1 + 5)"
Start = 6 + 5, History = "(1 + 5) + 5"
Start = 11 + 5, History = "(1 + 5) + 5) + 5"

Start becomes 16, and this is higher than 13, so this will return null. So the find function tries to multiply start by 3 instead of adding 5, going back to 11...

Start = 11 * 3, History = "(1 + 5) + 5) * 3"

This is also too high, and will so return null. Surely the function stops here, right??

When I test it out though, console logging the start values each time find recursively calls itself, it continues to call itself until it reaches number 13. The start values the function cycles through after 33 are:

18
3
8
13

But how is any of this possible? Shouldn't the function just return false after it reaches 16 and 33?

Answer 1

Console.log history just before the base case. That will help to understand how it works

Answer 2

There is a syntax error in your (the) example code. It should appear like this:

function findSolution(target){
    function find(start, history){
        if(start == target)
            return history
        else if(start > target)
            return null
        else 
            return (find(start + 5, "(" + history + " + 5)") ||
                    find(start * 3, "(" + history + " * 3)"))
    }
    return find(1, "1");
  }

(Note the structure of the last return in the inner function.)

When running the updated function with an input of 13, I see this in the console:

(((1 * 3) + 5) + 5)