The problem of sampling without replacement: given integers n, k such that 0 ≤ k ≤ n, return kdistinct nonnegative integers < n, choosing at random such that every possible result is equally likely. One way to get a precise understanding of the problem is to look at the simplest algorithm for solving it, via these Python or C++ implementations.
Here, I propose an algorithm I call "Cardchoose" for this problem which as far as I know is novel, and which in C++ outperforms all other solutions to either problem for most (n, k) inputs. The only data structure used is the output vector, so no extra memory is needed; it runs in O(k log k) time. I've implemented this and other algorithms in C++ and Python to compare their performance.
In my C++ tests, cardchoose outperforms rejectionsample,
floydf2, and hsel for all values of n and k. quadraticreject is
best where k < 100 or so, and select and iterativechoose perform well
when k/n is large. cardchoose always performs within an acceptable factor of other algorithms.
defsorted_choose(n, k):
"k distinct integers 0 <= x < n, sorted"t=n-k+1d= [None] *kforiinrange(k):
r=random.randrange(t+i)
ifr<t:
d[i] =relse:
d[i] =d[r-t]
d.sort()
foriinrange(k):
d[i] +=ireturnd
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