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
- 生成一个足够大的ID池（其实就是需要多少就生成多少）
- 对ID池中的数字进行随机排序
- 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-u.ac.jp/~m-mat/MT/VERSIONS/JAVA/MTRandom.java
import java.util.Random;
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;
public MTRandom() { }
public MTRandom(boolean compatible) {
super(0L);
compat = compatible;
setSeed(compat?DEFAULT_SEED:System.currentTimeMillis());
}
public MTRandom(long seed) {
super(seed);
}
public MTRandom(byte[] buf) {
super(0L);
setSeed(buf);
}
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 ----
}
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);
}
}
public final void setSeed(byte[] buf) {
setSeed(pack(buf));
}
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 ----
}
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.
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
以上就是本文的全部内容，希望对大家的学习有所帮助，也希望大家多多支持考高分网。
