xfclose(stdout);
exit(0);
}
-
-/** @brief Weighted track record */
-struct weighted_track {
- /** @brief Next track in the list */
- struct weighted_track *next;
- /** @brief Track name */
- const char *track;
- /** @brief Weight for this track (always positive) */
- unsigned long weight;
-};
-
-/** @brief List of tracks with nonzero weight */
-static struct weighted_track *tracks;
-
/** @brief Sum of all weights */
static unsigned long long total_weight;
+/** @brief The winning track */
+static const char *winning = 0;
+
/** @brief Count of tracks */
static long ntracks;
return 90000;
}
-/** @brief Called for each track */
-static int collect_tracks_callback(const char *track,
- struct kvp *data,
- struct kvp *prefs,
- void attribute((unused)) *u,
- DB_TXN attribute((unused)) *tid) {
- unsigned long weight = compute_weight(track, data, prefs);
-
- if(weight) {
- struct weighted_track *const t = xmalloc(sizeof *t);
-
- /* Clamp weight so that we can fit in billions of tracks when we do
- * arithmetic in long long */
- if(weight > 0x7fffffff)
- weight = 0x7fffffff;
- t->next = tracks;
- t->track = track;
- t->weight = weight;
- tracks = t;
- total_weight += weight;
- ++ntracks;
- }
- return 0;
-}
-
/** @brief Pick a random integer uniformly from [0, limit) */
static void random_bytes(unsigned char *buf, size_t n) {
static int fd = -1;
return r - slop;
}
-/** @brief Pick a track at random and write it to stdout */
-static void pick_track(void) {
- long long w;
- struct weighted_track *t;
+/** @brief Called for each track */
+static int collect_tracks_callback(const char *track,
+ struct kvp *data,
+ struct kvp *prefs,
+ void attribute((unused)) *u,
+ DB_TXN attribute((unused)) *tid) {
+ unsigned long weight = compute_weight(track, data, prefs);
- w = pick_weight(total_weight);
- t = tracks;
- while(t && w >= t->weight) {
- w -= t->weight;
- t = t->next;
+ /* Decide whether this is the winning track.
+ *
+ * Suppose that we have n things, and thing i, for 0 <= i < n, has weight
+ * w_i. Let c_i = w_0 + ... + w_{i-1} be the cumulative weight of the
+ * things previous to thing i, and let W = c_n = w_0 + ... + w_{i-1} be the
+ * total weight. We can clearly choose a random thing with the correct
+ * weightings by picking a random number r in [0, W) and chooeing thing i
+ * where c_i <= r < c_i + w_i. But this involves having an enormous list
+ * and taking two passes over it (which has bad locality and is ugly).
+ *
+ * Here's another way. Initialize v = -1. Examine the things in order;
+ * for thing i, choose a random number r_i in [0, c_i + w_i). If r_i < w_i
+ * then set v <- i.
+ *
+ * Claim. For all 0 <= i < n, the above algorithm chooses thing i with
+ * probability w_i/W.
+ *
+ * Proof. Induction on n. The claim is clear for n = 1. Suppose it's
+ * true for n - 1. Let L be the event that we choose thing n - 1. Clearly
+ * Pr[L] = w_{n-1}/W. Condition on not-L: then the probabilty that we
+ * choose thing i, for 0 <= i < n - 1, is w_i/c_{n-1} (induction
+ * hypothesis); undoing the conditioning gives the desired result.
+ */
+ if(weight) {
+ total_weight += weight;
+ if (pick_weight(total_weight) < weight)
+ winning = track;
}
- if(!t)
- fatal(0, "ran out of tracks but %lld weighting left", w);
- xprintf("%s", t->track);
+ ntracks++;
+ return 0;
}
int main(int argc, char **argv) {
//info("ntracks=%ld total_weight=%lld", ntracks, total_weight);
if(!total_weight)
fatal(0, "no tracks match random choice criteria");
+ if(!winning)
+ fatal(0, "internal: failed to pick a track");
/* Pick a track */
- pick_track();
+ xprintf("%s", winning);
xfclose(stdout);
return 0;
}