Update a key by calling a recursive function, updating other keys during same sequence

Question

I'm excited to ask my first question here. I've run into some problems with recursion. I am coding with Python.

I am using a dictionary to store previously solved numbers in a mathematical sequence. I then check this dictionary when solving later sequences to make the program run faster. Each key represents solved 'starting numbers,' the value represents how long it took the sequence to take the starting number and take it down to 1 using a particular formula.

I'm solving the problem using recursion, which itself is very easy but there's more to it for me.

Each recursive step gives me the opportunity to update a different key in the library, but I am unable to find a way to do this.

So where a sequence might look like 13 -> x -> y -> z ... -> 1, what would you do to not only update the 13 key with value, but also the x, y, x values in the dictionary during the same recursive path? Right now I'm only able to update one number per sequence.

cache = {1:1}

def solve(number):

    if cache.has_key(number):
        return cache[number]
    else:           
      if condition one.. 
            return 1 + solve(number * formula 1)
      else condition two...
            return 1 + solve(number * formula 2)

for x in xrange(1,1000):

cache[x] = solve(x)   <-- right now only cache[x] is being updated.

Thank you!

Don't use use `dict.has_key`, it has been deprecated. Use `number in cache`. — Ashwini Chaudhary, Jul 03 '13 at 06:56
Your method isn't updating the dictionary (this is a basic issue), but what is the logic to get from 13 to 1, is it simple decrement? — Burhan Khalid, Jul 03 '13 at 06:58
@Inbar It does indeed. This SO entry might be useful here: http://stackoverflow.com/questions/1988804/what-is-memoization-and-how-can-i-use-it-in-python — Mattias Nilsson, Jul 03 '13 at 07:04
Thanks gents! You've given me a new topic to dive into in my studies. Memoization! — Jake Way, Jul 05 '13 at 05:41
@Burhan, I took it out because it might reveal an answer to a project euler problem. if its even we go n/2, if its odd we do 3n+1. — Jake Way, Jul 05 '13 at 05:43

score 1 · Accepted Answer · answered Jul 03 '13 at 06:57

1

Couldn't you just put it in cache before returning it for each recursive call?

instead of:

return 1 + solve(number * formula 1)

you'd do:

result = 1 + solve(number * formula 1)
cache[number] = result
return result

Or are you after something different?

answered Jul 03 '13 at 06:57

Mattias Nilsson

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Exactly what I was looking for, thank you so much for your time. – Jake Way Jul 05 '13 at 05:45

score 0 · Answer 2 · answered Jul 03 '13 at 06:57

0

In principle the dictionary.update() method is able to update several values of a dictionary in one shot. But I assume your problem lies in the fact, that you update cache[x] only in the caller, i. e. outside of the recursion.

answered Jul 03 '13 at 06:57

guidot

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score 0 · Answer 3 · answered Jul 03 '13 at 07:06

0

You can update another parameter of solve to contain all of the numbers in the sequence, like

def solve(number, valueList):
...
...
if condition one:
        valueList.append(number)
        return 1 + solve(number * formula 1, valueList)

etc. I'm assuming that what you mean by "the numbers in the sequence" are the ones that meet condition 1 or 2 before being accepted.

If you don't have a problem with Mattias' answer, his is more straightforward. I'm assuming that for whatever reason, you don't want to add to the cache until the recursion finishes.

Anyway, when the recursion finishes, you can iterate through valueList and add it to cache.

answered Jul 03 '13 at 07:06

vroomfondel

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Thank you so much, I just posted this yesterday and already have the answer to my question. Mattias answer was what I was looking for, I didn't realize I could use return/result in this way. – Jake Way Jul 05 '13 at 05:39
@JakeWay you should accept his answer then! Glad to hear you figured it out. – vroomfondel Jul 05 '13 at 07:02

Update a key by calling a recursive function, updating other keys during same sequence

3 Answers3