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Calculate the blast radius of a shuffle shard
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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 " n: The total number of elements" | |
print " m: The number of elements per shard" | |
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 | |
for i in range(0, m + 1): | |
print 'overlap: %-4d %0.20f' % (i, overlap(float(n), float(m), float(i)) * 100) |
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