4 |
"""return log2(p(k balls thrown to n bins, all end up alone)) |
"""return log2(p(k balls thrown to n bins, all end up alone)) |
5 |
""" |
""" |
6 |
return ( |
return ( |
7 |
(n+.5) * log(n) |
(n-k+.5) * (log(n) - log(n-k)) |
|
- (n-k+.5) * log(n-k) |
|
8 |
- k |
- k |
|
- k * log(n) |
|
9 |
) / log(2) |
) / log(2) |
10 |
|
|
11 |
print log2birthdayprob(41, 31) |
print log2birthdayprob(41, 31) |
13 |
print log2birthdayprob(41, 11) |
print log2birthdayprob(41, 11) |
14 |
print log2birthdayprob(41, 2) |
print log2birthdayprob(41, 2) |
15 |
print log2birthdayprob(2L**56, 2L**23) |
print log2birthdayprob(2L**56, 2L**23) |
16 |
|
|
17 |
|
for k in [20, 23]: |
18 |
|
for n in [56, 60]: |
19 |
|
print n,k,log2birthdayprob(2L**n,2L**k) |
20 |
|
|