# This piece of code is more mathy than normal; it shows that there's a
# correspondance between the positive integers and the positive fractions.
# For example:
###
# >>> two2one(0,0)
# 0
# >>> two2one(1,0)
# 1
# >>> two2one(3,4)
# 32
# >>> one2two(31)
# (4, 3)
# >>> one2two(32)
# (3, 4)
###
# and it's related to the math proof that the rationals are countable.
# It can also be used to take the "cross-product" of two infinite sequences,
# so it's not quite "useless", but it is weird. *grin* Hope you like it.
###
def two2one(x, y):
"""Maps a positive (x,y) to an element in the naturals."""
diag = x + y
bottom = diag * (diag + 1) / 2
return bottom + y
def one2two(k):
"""Inverts the two2one map --- given a natural number, return its
corresponding (x,y) pair."""
diag = int((sqrt(1 + 8*k) - 1) / 2)
offset = k - diag * (diag + 1) / 2
return (diag - offset, offset)
class xcross_inf:
def __init__(self, X, Y):
self.X, self.Y = X, Y
def __getitem__(self, key):
i, j = one2two(key)
return (self.X[i], self.Y[j])
class Evens:
def __getitem__(self, key):
return key * 2
class Odds:
def __getitem__(self, key):
return key * 2 + 1
def test2():
seq = xcross_inf(Evens(), Odds())
for i in range(20): print seq[i]
###
