shardcalc.py

import sys

def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n - 1)

def choose(n, m):
    return factorial(n) / (factorial(m) * factorial(n - m))

def overlap(n, m, o):
    return (choose(m, o) * choose(n - m, m - o)) / choose(n, m)

def usage():
    print "shard.py n m"
    print
    print " n: The total number of elements"
    print " m: The number of elements per shard"
    print


if __name__ == "__main__":

    if len(sys.argv) != 3:
        usage()

    try:
        n = int(sys.argv[1])
        m = int(sys.argv[2]) 
    except:
        usage()

    if m > n:
        usage()

    print "n = ", n
    print "m = ", m
    print

    for i in range(0, m + 1):
        print 'overlap: %-4d %0.20f' % (i, overlap(float(n), float(m), float(i)) * 100)