Unfortunately, this cannot be done efficiently (better than O(n)) in any of the Standard Library set containers.
This is odd, since it is very easy to add a randomized pick function to hash sets as well as binary sets. In a not to sparse hash set, you can try random entries, until you get a hit. For a binary tree, you can choose randomly between the left or right subtree, with a maximum of O(log2) steps. I've implemented a demo of the later below:
import random
class Node:
def __init__(self, object):
self.object = object
self.value = hash(object)
self.size = 1
self.a = self.b = None
class RandomSet:
def __init__(self):
self.top = None
def add(self, object):
""" Add any hashable object to the set.
Notice: In this simple implementation you shouldn't add two
identical items. """
new = Node(object)
if not self.top: self.top = new
else: self._recursiveAdd(self.top, new)
def _recursiveAdd(self, top, new):
top.size += 1
if new.value < top.value:
if not top.a: top.a = new
else: self._recursiveAdd(top.a, new)
else:
if not top.b: top.b = new
else: self._recursiveAdd(top.b, new)
def pickRandom(self):
""" Pick a random item in O(log2) time.
Does a maximum of O(log2) calls to random as well. """
return self._recursivePickRandom(self.top)
def _recursivePickRandom(self, top):
r = random.randrange(top.size)
if r == 0: return top.object
elif top.a and r <= top.a.size: return self._recursivePickRandom(top.a)
return self._recursivePickRandom(top.b)
if __name__ == '__main__':
s = RandomSet()
for i in [5,3,7,1,4,6,9,2,8,0]:
s.add(i)
dists = [0]*10
for i in xrange(10000):
dists[s.pickRandom()] += 1
print dists
I got [995, 975, 971, 995, 1057, 1004, 966, 1052, 984, 1001] as output, so the distribution seams good.
I've struggled with the same problem for myself, and I haven't yet decided weather the performance gain of this more efficient pick is worth the overhead of using a python based collection. I could of course refine it and translate it to C, but that is too much work for me today :)
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