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.
     * <p>
     * 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.
     * <p>
     * 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.
     * <p>
     * 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.
     * <p>
     * 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:
     * <pre>
     * mt.setSeed(12345);
     * int foo = mt.nextInt(16) + (mt.nextInt(16) << 16);</pre>
     * will not give the same result as
     * <pre>
     * mt.setSeed(12345);
     * int foo = mt.nextInt(32);</pre>
     *
     * @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.
     * <p>
     * If the length of the byte array is not a multiple of 4 then
     * it is implicitly padded with zeros as necessary.  For example:
     * <pre>    byte[] { 0x01, 0x02, 0x03, 0x04, 0x05, 0x06 }</pre>
     * becomes
     * <pre>    int[]  { 0x04030201, 0x00000605 }</pre>
     * <p>
     * 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<Integer,Integer> map=new HashMap<>();
        //循环次数
        int times=1000000;
        long startTime=System.currentTimeMillis();
        for(int i=0;i<times;i++){
            //使用Map去重
            map.put(mtRandom.next(32),0);
        }
        //打印循环次数
        System.out.println("times:"+times);
        //打印Map的个数
        System.out.println("num:"+map.size());
        //打印非重复比率
        System.out.println("proportion:"+map.size()/(double)times);
        //花费的时间(单位为毫秒)
        System.out.println("time:"+(System.currentTimeMillis()-startTime));

测试结果

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