C # Implementation of the winning algorithm,

C # Implementation of the winning algorithm,

Algorithm name Alias Method

public class AliasMethod {        /* The probability and alias tables. */        private int[] _alias;        private double[] _probability;        public AliasMethod(List<Double> probabilities) {            /* Allocate space for the probability and alias tables. */            _probability = new double[probabilities.Count];            _alias = new int[probabilities.Count];            /* Compute the average probability and cache it for later use. */            double average = 1.0 / probabilities.Count;            /* Create two stacks to act as worklists as we populate the tables. */            var small = new Stack<int>();            var large = new Stack<int>();            /* Populate the stacks with the input probabilities. */            for (int i = 0; i < probabilities.Count; ++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[i] >= average)                    large.Push(i);                else                    small.Push(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.Count > 0 && large.Count > 0) {                /* Get the index of the small and the large probabilities. */                int less = small.Pop();                int more = large.Pop();                /* 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[less] * probabilities.Count;                _alias[less] = more;                /* Decrease the probability of the larger one by the appropriate                 * amount.                 */                probabilities[more] = (probabilities[more] + probabilities[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[more] >= average)                    large.Push(more);                else                    small.Push(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.Count > 0)                _probability[small.Pop()] = 1.0;            while (large.Count > 0)                _probability[large.Pop()] = 1.0;        }        /**         * Samples a value from the underlying distribution.         *         * @return A random value sampled from the underlying distribution.         */        public int next() {            long tick = DateTime.Now.Ticks;            var seed = ((int)(tick & 0xffffffffL) | (int)(tick >> 32));            unchecked {                seed = (seed + Guid.NewGuid().GetHashCode() + new Random().Next(0, 100));            }            var random = new Random(seed);            int column = random.Next(_probability.Length);            /* Generate a biased coin toss to determine which option to pick. */            bool coinToss = random.NextDouble() < _probability[column];            return coinToss ? column : _alias[column];        }    }

Test

Dictionary <String, Double> map = new Dictionary <String, Double> (); map. add ("1 gold coin", 0.2); map. add ("2 gold coins", 0.15); map. add ("3 gold coins", 0.1); map. add ("4 gold coins", 0.05); map. add ("not winning", 0.5); List <Double> list = new List <Double> (map. values); List <String> gifts = new List <String> (map. keys); AliasMethod method = new AliasMethod (list); Dictionary <String, int> resultMap = new Dictionary <String, int> (); for (int I = 0; I <10; I ++) {int index = method. next (); string key = gifts [index]; Console. writeLine (index + ":" + key );}

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