Question

Edit: to clarify, the problem is with the second algorithm.

I have a bit of C++ code that samples cards from a 52 card deck, which works just fine:

void sample_allcards(int table[5], int holes[], int players) {
    int temp[5 + 2 * players];
    bool try_again;
    int c, n, i;

    for (i = 0; i < 5 + 2 * players; i++) {
        try_again = true;
        while (try_again == true) {
            try_again = false;
            c = fast_rand52();
            // reject collisions
            for (n = 0; n < i + 1; n++) {
                try_again = (temp[n] == c) || try_again;
            }
            temp[i] = c;
        }
    }
    copy_cards(table, temp, 5);
    copy_cards(holes, temp + 5, 2 * players);
}

I am implementing code to sample the hole cards according to a known distribution (stored as a 2d table). My code for this looks like:

void sample_allcards_weighted(double weights[][HOLE_CARDS], int table[5], int holes[], int players) {
    // weights are distribution over hole cards
    int temp[5 + 2 * players];
    int n, i;

    // table cards
    for (i = 0; i < 5; i++) {
        bool try_again = true;
        while (try_again == true) {
            try_again = false;
            int c = fast_rand52();
            // reject collisions
            for (n = 0; n < i + 1; n++) {
                try_again = (temp[n] == c) || try_again;
            }
            temp[i] = c;
        }
    }

    for (int player = 0; player < players; player++) {
        // hole cards according to distribution
        i = 5 + 2 * player;
        bool try_again = true;
        while (try_again == true) {
            try_again = false;
            // weighted-sample c1 and c2 at once
            // h is a number < 1325
            int h = weighted_randi(&weights[player][0], HOLE_CARDS);
            // i2h uses h and sets temp[i] to the 2 cards implied by h
            i2h(&temp[i], h);
            // reject collisions
            for (n = 0; n < i; n++) {
                try_again = (temp[n] == temp[i]) || (temp[n] == temp[i+1]) || try_again;
            }
        }
    }

    copy_cards(table, temp, 5);
    copy_cards(holes, temp + 5, 2 * players);
}

My problem? The weighted sampling algorithm is a factor of 10 slower. Speed is very important for my application.

Is there a way to improve the speed of my algorithm to something more reasonable? Am I doing something wrong in my implementation?

Thanks.

edit: I was asked about this function, which I should have posted, since it is key

inline int weighted_randi(double *w, int num_choices) {
double r = fast_randd();
double threshold = 0;
int n;

for (n = 0; n < num_choices; n++) {
    threshold += *w;
    if (r <= threshold) return n;
    w++;
}
// shouldn't get this far
cerr << n << "\t" << threshold << "\t" << r << endl;
assert(n < num_choices);
return -1;

}

…and i2h() is basically just an array lookup.

Answer 1

Your reject collisions are turning an O(n) algorithm into (I think) an O(n^2) operation.

There are two ways to select cards from a deck: shuffle and pop, or pick sets until the elements of the set are unique; you are doing the latter which requires a considerable amount of backtracking.

I didn’t look at the details of the code, just a quick scan.