partitions.py

def EnumPartitions(m, n):
    P = {(0, 0) : 1}
    for i in range(1, m + 1):
        P[(i, 0)] = 0
    for i in range(1, m + 1):
        for j in range(1, min(i, n) + 1):
            if i < 2 * j:
                P[(i, j)] = P[(i - 1, j - 1)]
            else:
                P[(i, j)] = P[(i - 1, j - 1)] + P[(i - j, j)]
    return P

def PartitionLexUnrank(m, n, r):
    P = EnumPartitions(m, n)
    a = [0] * n
    while m > 0:
        if r < P[(m - 1, n - 1)]:
            a[n - 1] = a[n - 1] + 1
            m = m - 1
            n = n - 1
        else:
            for i in range(0, n):
                a[i] = a[i] + 1
            r = r - P[(m - 1, n - 1)]
            m = m - n
    return a

def getPartitions(num, parts):
    l = EnumPartitions(num, parts)[num, parts]
    return [PartitionLexUnrank(num, parts, rank) for rank in range(0, l)]