如何在 C# 中编写线性同余生成器 (LCG)？或者有没有众所周知的实现？

Question

我想生成一个随机的序列数组，这些序列重复并且每个数字只使用一次。例如，给定 0-9 的范围内有 2 个不同的种子，您可能会得到

Seed 1: 7 3 5 9 0 8 1 2 6 4 | 7 3 5 9 0 8 1 2 6 4 | 7 3 5 9 0 8 1 2 6 4
Seed 2: 2 5 7 1 4 9 6 8 3 0 | 2 5 7 1 4 9 6 8 3 0 | 2 5 7 1 4 9 6 8 3 0

据我了解，线性同余随机数生成器或 LCRNG 或 LCG 可以给我这个http://en.wikipedia.org/wiki/Linear_congruential_generator

知道 C# 中是否存在实现，或者我将如何开始编写一个。

Mersenne Twister 与 LCG 有何不同？

不确定我的所有问题都已得到解答，但这是我最终使用的。因为我将样本大小限制在从最大值到最小值的值范围内，所以我选择了一个不同的素数，只要给出相同的初始种子，它就会保持静态。我这样做是因为我想要相同的序列给定相同的种子和相同的最小/最大界限以实现测试的可重复性。

请批评我在这里所做的任何事情，这只是我一时想到的：

using System;
using System.Collections.Generic;

namespace FULLCYCLE
{
    public class RandomNumber
    {
        private int _value;
        private int _prime;
        private static List<int> primes = new List<int>()
        {
            11,
            23,
            47,
            97,
            797,
            1597,
            6421,
            25717,
            51437,
            102877,
            411527,
            823117,
            1646237,
            3292489,
            6584983,
            13169977,
            26339969,
            52679969,
            105359939,
            210719881,
            421439783,
            842879579,
            1685759167
        };

        public RandomNumber( int seed )
        {
            _prime = primes[seed%primes.Count];
            _value = seed;
        }

        public int Next( int min, int max )
        {
            int maxrate = (max-min+1);
            if (_value > maxrate)
            {
                _value = _value % maxrate;
            }

            _value = (_value + _prime) % maxrate;
            return _value + min;
        }
    }
}

Answer 1

为什么不在您的输入序列上使用现有的Random 类和Knuth shuffle？

Answer 2

关于您的编辑，您的 LCG 作为随机数生成器存在几个问题...

1. 它可以产生明显的图案：

   // generates 3, 4, 5, 6, 7, 8, 9, 0, 1, 2
   var rng = new RandomNumber(42);
   for (int i = 0; i < 10; i++) Console.WriteLine(rng.Next(0, 9));
   

2. 它可以重复自己：

   // generates 579, 579, 579, 579, 579, 579, 579, 579, 579, 579
   var rng = new RandomNumber(123);
   for (int i = 0; i < 10; i++) Console.WriteLine(rng.Next(456, 51892));
   

还有许多其他种子/最小值/最大值组合会产生有问题的结果。

Answer 3

试试下面的代码：

namespace System
{
    /// <summary>
    /// Represents a pseudo-random number generator using the linear congruential method:
    /// X[i+1] = (a • X[i] + c) % m (where i is greater than or equal to 0).
    /// </summary>
    public class LinearCongruentialRandom : Random
    {
        private int _x = 1971111612;
        private int _a = 2147483629;
        private int _c = 2147483587;
        private int _m = 2147483647;

        /// <summary>
        /// Initializes a new instance of <see cref="LinearCongruentialRandom"/> with default values.
        /// </summary>
        public LinearCongruentialRandom()
        {
            = base.Next(0, _m);
        }

        /// <summary>
        /// Initializes a new instance of <see cref="LinearCongruentialRandom"/> with default values.
        /// </summary>
        public LinearCongruentialRandom(int seed)
        {
            if (seed >= _m) throw new ArgumentOutOfRangeException(nameof(seed), seed, null);
            _x = seed;

        }


        /// <summary>
        /// Initializes a new instance of <see cref="LinearCongruentialRandom"/> with the specified parameters.
        /// </summary>
        /// <param name="seed">Initial seed value less than m.</param>
        /// <param name="a">A multiple of p for every prime p that is a divisor of m.</param>
        /// <param name="c">Increment c. The numbers c and m must be relatively prime.</param>
        /// <param name="m">The length of the repetition period m. The numbers c and m must be relatively prime.</param>
        public LinearCongruentialRandom(int seed, int a, int c, int m) : this(seed)
        {
            _a = a;
            _c=c;
            _m=m;
        }

        /// <inheritdoc cref="Random.Next()"/>
        public override int Next()
        {
            return _x = (_a * _x + _c) % _m;
        }
         
        /// <inheritdoc cref="Random.NextBytes(byte[])"/>
        public override void NextBytes(byte[] buffer)
        {
            if (buffer == null)
                throw new ArgumentNullException(nameof(buffer));

            unchecked
            {
                for (int index = 0; index < buffer.Length; ++index)
                    buffer[index] = (byte)Next();
            }
        }
    }
}