并行计算第k小的数

串行计算第k小的数的算法有很多，比如用堆，用一个长度为k的队列。这里说一下如何并行计算这个问题。原理很简单，将数列分为两半，在两半部分分别查找前k个数，然后合并，得到整个数列的前k个数。由此即可得到第k小的数。

用java实现的代码如下所示。

package org;import java.lang.reflect.Array;import java.util.Arrays;import java.util.Random;public class Main {public static void main(String[] args) {// TODO Auto-generated method stubSystem.out.println("Hello, world!");//int[] arr3 = {1000, 0, 6, 5, 4, 3, 2, 1, 7, 156, 44, 23, 123, 11, 50, 454, 234, 99, 32, 45};Integer[]arr3=new Integer[1000];Random ran=new Random();for(int k=0; k<arr3.length; ++k)arr3[k]=ran.nextInt();QuickSelect<Integer>quick=new QuickSelect<Integer>(arr3);for (int k = 1; k < 50; ++k) {int sel = quick.select(k);//System.out.printf("%d-th number is %d\n", k, sel);Arrays.sort(arr3);int sel2=arr3[k-1];if(sel!=sel2)System.out.printf("Error: %d-th, sel=%d, sel2=%d\n", k, sel, sel2);for(int j=0; j<arr3.length; ++j)arr3[j]=ran.nextInt();//System.out.printf("%d-th number is %d\n", k, arr3[k - 1]);}}}class QuickSelect<T extends Comparable<T>> implements Runnable{private T[] arr;private int kTh;private int start;private int end;private int limitLen;private T[]result;public QuickSelect(T[] arr){this.arr=arr;start=0;end=arr.length;}public T select(int kTh){this.kTh=kTh;limitLen=(int) Math.round(Math.sqrt(kTh*arr.length));Thread thread=new Thread(this);thread.start();try {thread.join();} catch (InterruptedException e) {e.printStackTrace();}return result[kTh-1];}private QuickSelect(T[]arr, int start, int end, int kTh, int limitLen){this.arr=arr;this.start=start;this.end=end;this.kTh=kTh;this.limitLen=limitLen;}public void run() {System.out.printf("k=%d, start=%d, end=%d\n", kTh, start, end);int len=end-start;if(len<=kTh){result=Arrays.copyOfRange(arr, start, end);Arrays.sort(result);}else if(len<=limitLen){result=Arrays.copyOfRange(arr, start, start+kTh);Arrays.sort(result);//insertfor(int j=start+kTh; j<end; ++j){int i=result.length-1;if(arr[j].compareTo(result[i])<0){result[i]=arr[j];while(i>0&&result[i].compareTo(result[i-1])<0){T tmp=result[i];result[i]=result[i-1];result[i-1]=tmp;--i;}}}}else{QuickSelect<T> runleft=new QuickSelect<T>(arr, start, start+len/2, kTh, limitLen);QuickSelect<T> runright=new QuickSelect<T>(arr, start+len/2, end, kTh, limitLen);Thread leftThread=new Thread(runleft);Thread rightThread=new Thread(runright);leftThread.start();rightThread.start();try {leftThread.join();rightThread.join();result=merge(runleft.result, runright.result);} catch (InterruptedException e) {e.printStackTrace();}}}private T[]merge(T[]left, T[]right){int len;if(left.length+right.length<=kTh){len=left.length+right.length;}elselen=kTh;@SuppressWarnings("unchecked")T[]r=(T[])Array.newInstance(arr[0].getClass(), len);int p=0, q=0;for(int j=0; j<len; ++j){if(left[p].compareTo(right[q])<0){r[j]=left[p];++p;}else{r[j]=right[q];++q;}}return r;}}