Raymond Hettinger <[email protected]> added the comment:
Optimizations 2 and 3 look something like this:
bc75 = [comb(75, r) for r in range(75//2+1)]
bc150 = [comb(150, r) for r in range(150//2+1)]
bc225 = [comb(225, r) for r in range(225//2+1)]
def comb(n, k):
if n < 0 or k < 0: raise ValueError
if k > n: return 0
k = min(k, n-k)
if k > n // 3 and n < 100_000:
return factorial(n) // (factorial(r) * factorial(n-r))
if 75 <= n <= 75 + k:
c, num, den, times = bc75[75-(n-k)], 75+1, 75-(n-k)+1, n-75
elif 150 <= n <= 150 + k:
c, num, den, times = bc150[150-(n-k)], 150+1, 150-(n-k)+1, n-150
elif 225 <= n <= 225 + k:
c, num, den, times = bc225[225-(n-k)], 225+1, 225-(n-k)+1, n-225
else:
c, num, den, times = 1, n-k+1, 1, k
for i in range(times):
c = c * num // den
num += 1
den += 1
return c
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Python tracker <[email protected]>
<https://bugs.python.org/issue37295>
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