Python Integer Partitioning with given k partitions

Question

I\'m trying to find or develop Integer Partitioning code for Python.

FYI, Integer Partitioning is representing a given integer n as a sum of integers smaller than n.

Answer 1

First I want to thanks everyone for their contribution. I arrived here needing an algorithm for generating integer partitions with the following details :

Generate partitions of a number into EXACTLY k parts but also having MINIMUM and MAXIMUM constraints.

Therefore, I modified the code of "Snakes and Coffee" to accommodate these new requirements:

def partition_min_max(n,k,l, m):
'''n is the integer to partition, k is the length of partitions, 
l is the min partition element size, m is the max partition element size '''
if k < 1:
    raise StopIteration
if k == 1:
    if n <= m and n>=l :
        yield (n,)
    raise StopIteration
for i in range(l,m+1):
    for result in partition_min_max(n-i,k-1,i,m):                
        yield result+(i,)


>>> x = list(partition_min_max(20 ,3, 3, 10 ))
>>> print(x)
>>> [(10, 7, 3), (9, 8, 3), (10, 6, 4), (9, 7, 4), (8, 8, 4), (10, 5, 5), (9, 6, 5), (8, 7, 5), (8, 6, 6), (7, 7, 6)]