from irr import Irr
from dyn import Dyn
import math
#factorial, with memoization
fact = Dyn()
fact.addBaseCase(0, 1)
def factRecFn(n, fact):
return n * fact(n - 1)
fact.recFn = factRecFn
#compute the number of permutations in S_n with cycle structure l
def countType(l,n):
ls = {}
x = fact(n)
for a in l:
if a in ls:
ls[a] += 1
else:
ls[a] = 1
x /= a
for a in ls:
x /= fact(ls[a])
return x
#compute the number of partitions with all odd parts of given size with all parts under a given size, with memoization
partOdd = Dyn()
partOdd.addBaseCase((0,0), [[]])
import sys
from irr import Irr
from dyn import Dyn
from char import Char
#compute the number of partitions of given size with all parts under a given size, with memoization
part = Dyn()
part.addBaseCase((0,0), [[]])
def parts(tup, part):
if tup[0] < tup[1]:
return part((tup[0], tup[0]))
l = []
k = 1
while k <= tup[0] and k <= tup[1]:
p = part((tup[0]-k, k))
l += [[k] + a for a in p]
k += 1
return l
part.recFn = parts
#size of the triangle
n = int(sys.argv[1])
#is a rep on S_nn... that is, nn is the nth triangular number
nn = n * (n + 1) >> 1
#build the partition and get it into a tuple format
l = range(1,n+1)
