Project Euler 78 - Coin Partition

Question

Problem statement:

Let p(n) represent the number of different ways in which n coins can be separated into piles. For example, five coins can be separated into piles in exactly seven different ways, so p(5)=7

Find the least value of n for which p(n) is divisible by one million.

So that's a code i got using recursion to solve this problem. I know that's not the optimal aproach, but should give me the right answer... But for some reason I don't understand it gives me back that n = 2301 has a p(n) = 17022871133751703055227888846952967314604032000000, which is divisible by 1,000,000 and is the least n to do that. So why this is not the correct answer? I checked the for n<20 and it matches. So what's wrong with my code?

import numpy as np
import sys

sys.setrecursionlimit(3000)

table = np.zeros((10000,10000))

def partition(sum, largestNumber):
    if (largestNumber == 0):
        return 0

    if (sum == 0):
        return 1

    if (sum < 0):
        return 0

    if (table[sum,largestNumber] != 0):
        return table[sum,largestNumber]

    table[sum,largestNumber] = partition(sum,largestNumber-1) + partition(sum-largestNumber,largestNumber)
    return table[sum,largestNumber]



def main():
    result = 0
    sum = 0
    largestNumber = 0
    while (result == 0 or result%1000000 != 0):
        sum += 1
        largestNumber += 1
        result = int(partition(sum,largestNumber))
        print("n = {}, resultado = {}".format(sum,result))

    return 0

if __name__ == '__main__':
    main()

score 2 · Accepted Answer · answered Mar 15 '19 at 15:32

2

I believe the NumPy data type used in your np.zeroes declaration is a restricted rather than unlimited number. The number of partitions of 2301 is in fact 17022871133751761754598643267756804218108498650480 and not 17022871133751703055227888846952967314604032000000, which you can see if you run your (correct) program with a regular table declaration like

table = [10000 * [0] for i in xrange(10000)]

and then call on the table appropriately.

answered Mar 15 '19 at 15:32

גלעד ברקן

23,602
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@JoãoVitorDegrandi if you use a regular two dimensional table, I think accessing the table would need to be written like `table[i][j]` and not `table[i, j]`. Yes, I believe you can switch `xrange` to `range` for Python3. I'm not a Python expert :) – גלעד ברקן Mar 18 '19 at 15:50
What's the difference between what you did and what I did? The problem is with numpy? – João Vitor Degrandi Mar 18 '19 at 15:54
and what can I do to make it go to infinity? Cause i looked online and the answer is around 55,000... around 6000 it gives stackoverflow – João Vitor Degrandi Mar 18 '19 at 16:08
1

@JoãoVitorDegrandi that might be a good subject for another question :) – גלעד ברקן Mar 18 '19 at 16:55

Project Euler 78 - Coin Partition

1 Answers1