How would you pick a uniform random element in linked list with unknown length?

问题

How would you pick a uniform random element in linked list with unknown length in one pass or if not two passes?

回答1:

Use reservoir sampling http://en.wikipedia.org/wiki/Reservoir_sampling . You need only one pass of the data.

For picking one element:

1. Pick first element (probability 1)
2. Later, for kth element pick it with probability 1/k (i.e. replace the existing selection with kth element)

I will let you prove that this results in uniform selection of elements.

来源：https://stackoverflow.com/questions/9401375/how-would-you-pick-a-uniform-random-element-in-linked-list-with-unknown-length