高效随机数算法Java实现

前言

事情起源于一位网友分享了一个有趣的面试题:

生成由六位数字组成的ID,要求随机数字,不排重,不可自增,且数字不重复。ID总数为几十万。

初次解答

我一开始想到的办法是

  1. 生成一个足够大的ID池(其实就是需要多少就生成多少)
  2. 对ID池中的数字进行随机排序
  3. 依次消费ID池中的数字

可惜这个方法十分浪费空间,且性能很差。

初遇梅森旋转算法

后面咨询了网友后得知了一个高效的随机数算法:梅森旋转(Mersenne Twister/MT)。通过搜索资料得知:

梅森旋转算法(Mersenne twister)是一个伪随机数发生算法。由松本真和西村拓士在1997年开发,基于有限二进制字段上的矩阵线性递归。可以快速产生高质量的伪随机数,修正了古典随机数发生算法的很多缺陷。

最为广泛使用Mersenne Twister的一种变体是MT19937,可以产生32位整数序列。

PS:此算法依然无法完美解决面试题,但是也算学到了新知识

MT19937算法实现

后面通过Google,找到了一个高效的MT19937的Java版本代码。原代码链接为http://www.math.sci.hiroshima...

import java.util.Random;

/**
 * MT19937的Java实现
 */
public class MTRandom extends Random {
    
    // Constants used in the original C implementation
    private final static int UPPER_MASK = 0x80000000;
    private final static int LOWER_MASK = 0x7fffffff;

    private final static int N = 624;
    private final static int M = 397;
    private final static int MAGIC[] = { 0x0, 0x9908b0df };
    private final static int MAGIC_FACTOR1 = 1812433253;
    private final static int MAGIC_FACTOR2 = 1664525;
    private final static int MAGIC_FACTOR3 = 1566083941;
    private final static int MAGIC_MASK1   = 0x9d2c5680;
    private final static int MAGIC_MASK2   = 0xefc60000;
    private final static int MAGIC_SEED    = 19650218;
    private final static long DEFAULT_SEED = 5489L;

    // Internal state
    private transient int[] mt;
    private transient int mti;
    private transient boolean compat = false;

    // Temporary buffer used during setSeed(long)
    private transient int[] ibuf;

    /**
     * The default constructor for an instance of MTRandom.  This invokes
     * the no-argument constructor for java.util.Random which will result
     * in the class being initialised with a seed value obtained by calling
     * System.currentTimeMillis().
     */
    public MTRandom() { }

    /**
     * This version of the constructor can be used to implement identical
     * behaviour to the original C code version of this algorithm including
     * exactly replicating the case where the seed value had not been set
     * prior to calling genrand_int32.
     * 

* If the compatibility flag is set to true, then the algorithm will be * seeded with the same default value as was used in the original C * code. Furthermore the setSeed() method, which must take a 64 bit * long value, will be limited to using only the lower 32 bits of the * seed to facilitate seamless migration of existing C code into Java * where identical behaviour is required. *

* Whilst useful for ensuring backwards compatibility, it is advised * that this feature not be used unless specifically required, due to * the reduction in strength of the seed value. * * @param compatible Compatibility flag for replicating original * behaviour. */ public MTRandom(boolean compatible) { super(0L); compat = compatible; setSeed(compat?DEFAULT_SEED:System.currentTimeMillis()); } /** * This version of the constructor simply initialises the class with * the given 64 bit seed value. For a better random number sequence * this seed value should contain as much entropy as possible. * * @param seed The seed value with which to initialise this class. */ public MTRandom(long seed) { super(seed); } /** * This version of the constructor initialises the class with the * given byte array. All the data will be used to initialise this * instance. * * @param buf The non-empty byte array of seed information. * @throws NullPointerException if the buffer is null. * @throws IllegalArgumentException if the buffer has zero length. */ public MTRandom(byte[] buf) { super(0L); setSeed(buf); } /** * This version of the constructor initialises the class with the * given integer array. All the data will be used to initialise * this instance. * * @param buf The non-empty integer array of seed information. * @throws NullPointerException if the buffer is null. * @throws IllegalArgumentException if the buffer has zero length. */ public MTRandom(int[] buf) { super(0L); setSeed(buf); } // Initializes mt[N] with a simple integer seed. This method is // required as part of the Mersenne Twister algorithm but need // not be made public. private final void setSeed(int seed) { // Annoying runtime check for initialisation of internal data // caused by java.util.Random invoking setSeed() during init. // This is unavoidable because no fields in our instance will // have been initialised at this point, not even if the code // were placed at the declaration of the member variable. if (mt == null) mt = new int[N]; // ---- Begin Mersenne Twister Algorithm ---- mt[0] = seed; for (mti = 1; mti < N; mti++) { mt[mti] = (MAGIC_FACTOR1 * (mt[mti-1] ^ (mt[mti-1] >>> 30)) + mti); } // ---- End Mersenne Twister Algorithm ---- } /** * This method resets the state of this instance using the 64 * bits of seed data provided. Note that if the same seed data * is passed to two different instances of MTRandom (both of * which share the same compatibility state) then the sequence * of numbers generated by both instances will be identical. *

* If this instance was initialised in 'compatibility' mode then * this method will only use the lower 32 bits of any seed value * passed in and will match the behaviour of the original C code * exactly with respect to state initialisation. * * @param seed The 64 bit value used to initialise the random * number generator state. */ public final synchronized void setSeed(long seed) { if (compat) { setSeed((int)seed); } else { // Annoying runtime check for initialisation of internal data // caused by java.util.Random invoking setSeed() during init. // This is unavoidable because no fields in our instance will // have been initialised at this point, not even if the code // were placed at the declaration of the member variable. if (ibuf == null) ibuf = new int[2]; ibuf[0] = (int)seed; ibuf[1] = (int)(seed >>> 32); setSeed(ibuf); } } /** * This method resets the state of this instance using the byte * array of seed data provided. Note that calling this method * is equivalent to calling "setSeed(pack(buf))" and in particular * will result in a new integer array being generated during the * call. If you wish to retain this seed data to allow the pseudo * random sequence to be restarted then it would be more efficient * to use the "pack()" method to convert it into an integer array * first and then use that to re-seed the instance. The behaviour * of the class will be the same in both cases but it will be more * efficient. * * @param buf The non-empty byte array of seed information. * @throws NullPointerException if the buffer is null. * @throws IllegalArgumentException if the buffer has zero length. */ public final void setSeed(byte[] buf) { setSeed(pack(buf)); } /** * This method resets the state of this instance using the integer * array of seed data provided. This is the canonical way of * resetting the pseudo random number sequence. * * @param buf The non-empty integer array of seed information. * @throws NullPointerException if the buffer is null. * @throws IllegalArgumentException if the buffer has zero length. */ public final synchronized void setSeed(int[] buf) { int length = buf.length; if (length == 0) throw new IllegalArgumentException("Seed buffer may not be empty"); // ---- Begin Mersenne Twister Algorithm ---- int i = 1, j = 0, k = (N > length ? N : length); setSeed(MAGIC_SEED); for (; k > 0; k--) { mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >>> 30)) * MAGIC_FACTOR2)) + buf[j] + j; i++; j++; if (i >= N) { mt[0] = mt[N-1]; i = 1; } if (j >= length) j = 0; } for (k = N-1; k > 0; k--) { mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >>> 30)) * MAGIC_FACTOR3)) - i; i++; if (i >= N) { mt[0] = mt[N-1]; i = 1; } } mt[0] = UPPER_MASK; // MSB is 1; assuring non-zero initial array // ---- End Mersenne Twister Algorithm ---- } /** * This method forms the basis for generating a pseudo random number * sequence from this class. If given a value of 32, this method * behaves identically to the genrand_int32 function in the original * C code and ensures that using the standard nextInt() function * (inherited from Random) we are able to replicate behaviour exactly. *

* Note that where the number of bits requested is not equal to 32 * then bits will simply be masked out from the top of the returned * integer value. That is to say that: *

     * mt.setSeed(12345);
     * int foo = mt.nextInt(16) + (mt.nextInt(16) << 16);
* will not give the same result as *
     * mt.setSeed(12345);
     * int foo = mt.nextInt(32);
* * @param bits The number of significant bits desired in the output. * @return The next value in the pseudo random sequence with the * specified number of bits in the lower part of the integer. */ protected final synchronized int next(int bits) { // ---- Begin Mersenne Twister Algorithm ---- int y, kk; if (mti >= N) { // generate N words at one time // In the original C implementation, mti is checked here // to determine if initialisation has occurred; if not // it initialises this instance with DEFAULT_SEED (5489). // This is no longer necessary as initialisation of the // Java instance must result in initialisation occurring // Use the constructor MTRandom(true) to enable backwards // compatible behaviour. for (kk = 0; kk < N-M; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK); mt[kk] = mt[kk+M] ^ (y >>> 1) ^ MAGIC[y & 0x1]; } for (;kk < N-1; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK); mt[kk] = mt[kk+(M-N)] ^ (y >>> 1) ^ MAGIC[y & 0x1]; } y = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N-1] = mt[M-1] ^ (y >>> 1) ^ MAGIC[y & 0x1]; mti = 0; } y = mt[mti++]; // Tempering y ^= (y >>> 11); y ^= (y << 7) & MAGIC_MASK1; y ^= (y << 15) & MAGIC_MASK2; y ^= (y >>> 18); // ---- End Mersenne Twister Algorithm ---- return (y >>> (32-bits)); } // This is a fairly obscure little code section to pack a // byte[] into an int[] in little endian ordering. /** * This simply utility method can be used in cases where a byte * array of seed data is to be used to repeatedly re-seed the * random number sequence. By packing the byte array into an * integer array first, using this method, and then invoking * setSeed() with that; it removes the need to re-pack the byte * array each time setSeed() is called. *

* If the length of the byte array is not a multiple of 4 then * it is implicitly padded with zeros as necessary. For example: *

    byte[] { 0x01, 0x02, 0x03, 0x04, 0x05, 0x06 }
* becomes *
    int[]  { 0x04030201, 0x00000605 }
*

* Note that this method will not complain if the given byte array * is empty and will produce an empty integer array, but the * setSeed() method will throw an exception if the empty integer * array is passed to it. * * @param buf The non-null byte array to be packed. * @return A non-null integer array of the packed bytes. * @throws NullPointerException if the given byte array is null. */ public static int[] pack(byte[] buf) { int k, blen = buf.length, ilen = ((buf.length+3) >>> 2); int[] ibuf = new int[ilen]; for (int n = 0; n < ilen; n++) { int m = (n+1) << 2; if (m > blen) m = blen; for (k = buf[--m]&0xff; (m & 0x3) != 0; k = (k << 8) | buf[--m]&0xff); ibuf[n] = k; } return ibuf; } }

测试

测试代码

        // MT19937的Java实现
        MTRandom mtRandom=new MTRandom();
        Map map=new HashMap<>();
        //循环次数
        int times=1000000;
        long startTime=System.currentTimeMillis();
        for(int i=0;i

测试结果

times:1000000
num:999886
proportion:0.999886
time:374

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