algorithm - 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. For example, an integer 5 can be expressed as 4 + 1 = 3 + 2 = 3 + 1 + 1 = 2 + 2 + 1 = 2 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1

I've found a number of solutions for this. http://homepages.ed.ac.uk/jkellehe/partitions.php and http://code.activestate.com/recipes/218332-generator-for-integer-partitions/

However, what I really want is to restrict the number of partitions.

Say, # of partition k = 2, a program only need to show 5 = 4 + 1 = 3 + 2,

if k = 3, 5 = 3 + 1 + 1 = 2 + 2 + 1

Answer 1

I've written a generator solution

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

This generates all the partitions of n with length k with each one being in order of least to greatest.

Just a quick note: Via cProfile, it appears that using the generator method is much faster than using falsetru's direct method, using the test function lambda x,y: list(partitionfunc(x,y)). On a test run of n=50,k-5, my code ran in .019 seconds vs the 2.612 seconds of the direct method.