How to stop the stack from overflowing when generating permutations in python

Question

I'm trying to generate permutations in python without using itertools . This is my code thus far:

def generatePermutations(minVal, maxVal, arrayLength, depth = -1, array = []):
    if(depth == -1): # set all values to minVal initially
        for i in range(arrayLength):
            array.append(minVal)
        depth += 1
        generatePermutations(minVal, maxVal, arrayLength, depth, array) # recurse

    elif depth < arrayLength:
        a.append(array[:]) # a is a list declared above the function

        current = 0
        while current <= depth:
            if array[current] < maxVal:
                array[current] += 1
                break
            else:
                if current < depth:
                    array[current] = minVal
                else:
                    depth += 1
                    array[current] = minVal
                    if depth < arrayLength:
                        array[depth] += 1
                    break
            current += 1

        generatePermutations(minVal, maxVal, arrayLength, depth, array)

The function works for a small enough set of numbers. For example, generatePermutations(1,2,2) populates list a with the following:

[1, 1]
[2, 1]
[1, 2]
[2, 2]

But, when I try to create permutations of an array of length 9 ( generatePermutations(1,9,9) ), then I run into a stack overflow error long before the function is finished. Is there any way of preventing this?

Answer 1

I did a little testing, and I found that the way your function is set up, it calls itself for every single permutation . As in, the recursion depth is the same as the number of permutations generated so far. When you try to do generatePermutations(1,9,9) , Python tries to recurse to 9!=362880 levels deep, which is far too deep (it's limited to 1000 ).

Instead, refactor your code so that you iterate over each element in a , appending the current digit, and do this in a loop for each digit. This way, the recursion will only have to go 9 levels deep.