高效隨機數演算法Java實現
前言
事情起源於一位網友分享了一個有趣的面試題:
生成由六位數字組成的ID,要求隨機數字,不排重,不可自增,且數字不重複。ID總數為幾十萬。
初次解答
我一開始想到的辦法是
- 生成一個足夠大的ID池(其實就是需要多少就生成多少)
- 對ID池中的數字進行隨機排序
- 依次消費ID池中的數字
可惜這個方法十分浪費空間,且效能很差。
初遇梅森旋轉演算法
後面諮詢了網友後得知了一個高效的隨機數演算法:梅森旋轉(Mersenne Twister/MT) 。通過搜尋資料得知:
最為廣泛使用Mersenne Twister的一種變體是MT19937,可以產生32位整數序列。
PS:此演算法依然無法完美解決面試題,但是也算學到了新知識
MT19937演算法實現
後面通過Google,找到了一個高效的MT19937 的Java版本程式碼。原始碼連結為http://www.math.sci.hiroshima...
import java.util.Random; /** * MT19937的Java實現 */ 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; } }
測試
測試程式碼
// MT19937的Java實現 MTRandom mtRandom=new MTRandom(); Map<Integer,Integer> map=new HashMap<>(); //迴圈次數 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); } //列印迴圈次數 System.out.println("times:"+times); //列印Map的個數 System.out.println("num:"+map.size()); //列印非重複比率 System.out.println("proportion:"+map.size()/(double)times); //花費的時間(單位為毫秒) System.out.println("time:"+(System.currentTimeMillis()-startTime));
測試結果
times:1000000 num:999886 proportion:0.999886 time:374