Most efficient way of randomly choosing a set of distinct integers

Question

I\'m looking for the most efficient algorithm to randomly choose a set of n distinct integers, where all the integers are in some range [0..maxValue].

Constraints:<

Answer 1

UPDATE: I am wrong. The output of this is not uniformly distributed. Details on why are here.

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I think this algorithm below is optimum. I.e. you cannot get better performance than this.

For choosing n numbers out of m numbers, the best offered algorithm so far is presented below. Its worst run time complexity is O(n), and needs only a single array to store the original numbers. It partially shuffles the first n elements from the original array, and then you pick those first n shuffled numbers as your solution.

This is also a fully working C program. What you find is:

• Function getrand: This is just a PRNG that returns a number from 0 up to upto.
• Function randselect: This is the function that randmoly chooses n unique numbers out of m many numbers. This is what this question is about.
• Function main: This is only to demonstrate a use for other functions, so that you could compile it into a program and have fun.

#include 
#include 

int getrand(int upto) {
    long int r;
    do {
        r = rand();
    } while (r > upto);
    return r;
}

void randselect(int *all, int end, int select) {
    int upto = RAND_MAX - (RAND_MAX % end);
    int binwidth = upto / end;

    int c;
    for (c = 0; c < select; c++) {
        /* randomly choose some bin */
        int bin = getrand(upto)/binwidth;

        /* swap c with bin */
        int tmp = all[c];
        all[c] = all[bin];
        all[bin] = tmp;
    }
}

int main() {
    int end = 1000;
    int select = 5;

    /* initialize all numbers up to end */
    int *all = malloc(end * sizeof(int));
    int c;
    for (c = 0; c < end; c++) {
        all[c] = c;
    }

    /* select select unique numbers randomly */
    srand(0);
    randselect(all, end, select);
    for (c = 0; c < select; c++) printf("%d ", all[c]);
    putchar('\n');

    return 0;
}

Here is the output of an example code where I randomly output 4 permutations out of a pool of 8 numbers for 100,000,000 many times. Then I use those many permutations to compute the probability of having each unique permutation occur. I then sort them by this probability. You notice that the numbers are fairly close, which I think means that it is uniformly distributed. The theoretical probability should be 1/1680 = 0.000595238095238095. Note how the empirical test is close to the theoretical one.