Java
- 最近接到个小程序活动的需求，用户参与活动有不同中奖概率不同金额的算法，找到这个方法，挺好用收藏一下。
private int lotteryMethod() {
// 每种情况对应的中奖概率
List<Double> values = Arrays.asList(new Double[]{0.6, 0.2, 0.1, 0.06, 0.04});
AliasMethod method = new AliasMethod(values);
// 随机获取一种情况
int index = method.next();
// 中奖金额
int amount = 0;
switch (index) {
case 0:
amount = 30;
break;
case 1:
amount = 80;
break;
case 2:
amount = 100;
break;
case 3:
amount = 200;
break;
case 4:
amount = 250;
break;
default:
amount = 0;
}
return amount;
}
public final class AliasMethod {
/* The random number generator used to sample from the distribution. */
private final Random random;
/* The probability and alias tables. */
private final int[] alias;
private final double[] probability;
/**
* Constructs a new AliasMethod to sample from a discrete distribution and
* hand back outcomes based on the probability distribution.
* <p>
* Given as input a list of probabilities corresponding to outcomes 0, 1,
* ..., n - 1, this constructor creates the probability and alias tables
* needed to efficiently sample from this distribution.
*
* @param probabilities The list of probabilities.
*/
public AliasMethod(List<Double> probabilities) {
this(probabilities, new Random());
}
/**
* Constructs a new AliasMethod to sample from a discrete distribution and
* hand back outcomes based on the probability distribution.
* <p>
* Given as input a list of probabilities corresponding to outcomes 0, 1,
* ..., n - 1, along with the random number generator that should be used
* as the underlying generator, this constructor creates the probability
* and alias tables needed to efficiently sample from this distribution.
*
* @param probabilities The list of probabilities.
* @param random The random number generator
*/
public AliasMethod(List<Double> probabilities, Random random) {
/* Begin by doing basic structural checks on the inputs. */
if (probabilities == null || random == null) {
throw new NullPointerException();
}
if (probabilities.size() == 0) {
throw new IllegalArgumentException("Probability vector must be nonempty.");
}
/* Allocate space for the probability and alias tables. */
probability = new double[probabilities.size()];
alias = new int[probabilities.size()];
/* Store the underlying generator. */
this.random = random;
/* Compute the average probability and cache it for later use. */
final double average = 1.0 / probabilities.size();
/* Make a copy of the probabilities list, since we will be making
* changes to it.
*/
probabilities = new ArrayList<Double>(probabilities);
/* Create two stacks to act as worklists as we populate the tables. */
Deque<Integer> small = new ArrayDeque<Integer>();
Deque<Integer> large = new ArrayDeque<Integer>();
/* Populate the stacks with the input probabilities. */
for (int i = 0; i < probabilities.size(); ++i) {
/* If the probability is below the average probability, then we add
* it to the small list; otherwise we add it to the large list.
*/
if (probabilities.get(i) >= average) {
large.add(i);
} else {
small.add(i);
}
}
/* As a note: in the mathematical specification of the algorithm, we
* will always exhaust the small list before the big list. However,
* due to floating point inaccuracies, this is not necessarily true.
* Consequently, this inner loop (which tries to pair small and large
* elements) will have to check that both lists aren't empty.
*/
while (!small.isEmpty() && !large.isEmpty()) {
/* Get the index of the small and the large probabilities. */
int less = small.removeLast();
int more = large.removeLast();
/* These probabilities have not yet been scaled up to be such that
* 1/n is given weight 1.0. We do this here instead.
*/
probability[less] = probabilities.get(less) * probabilities.size();
alias[less] = more;
/* Decrease the probability of the larger one by the appropriate
* amount.
*/
probabilities.set(more, (probabilities.get(more) + probabilities.get(less)) - average);
/* If the new probability is less than the average, add it into the
* small list; otherwise add it to the large list.
*/
if (probabilities.get(more) >= 1.0 / probabilities.size()) {
large.add(more);
} else {
small.add(more);
}
}
/* At this point, everything is in one list, which means that the
* remaining probabilities should all be 1/n. Based on this, set them
* appropriately. Due to numerical issues, we can't be sure which
* stack will hold the entries, so we empty both.
*/
while (!small.isEmpty()) {
probability[small.removeLast()] = 1.0;
}
while (!large.isEmpty()) {
probability[large.removeLast()] = 1.0;
}
}
/**
* Samples a value from the underlying distribution.
*
* @return A random value sampled from the underlying distribution.
*/
public int next() {
/* Generate a fair die roll to determine which column to inspect. */
int column = random.nextInt(probability.length);
/* Generate a biased coin toss to determine which option to pick. */
boolean coinToss = random.nextDouble() < probability[column];
/* Based on the outcome, return either the column or its alias. */
return coinToss ? column : alias[column];
}
}
