算法导论16.1 活动选择问题

这篇文章主要讲述一个经典问题：活动选择问题。并给出该问题的贪心算法实现和动态规划实现。

对于该问题的描述，在算法导论第16章给出了详细的讲解，这里就不做解释说明了，下面给出贪心算法的Java语言实现：

package chapter1.homework1;import java.util.*;public class ActivitySelector {private int activitiesNum=0;//活动总数private Activity[] activities=null;//记录所有活动，包括虚拟活动public static void main(String[] args) {// TODO Auto-generated method stubActivitySelector sample=new ActivitySelector();sample.getInputInfo();System.out.println("活动选择结果：");sample.greedyActivitySelector();}public void greedyActivitySelector(){int i=0;for(int m=1;m<=this.activitiesNum;m++){if(this.activities[m].start>=this.activities[i].end){System.out.println("id="+this.activities[m].id+" start="+this.activities[m].start+" end="+this.activities[m].end);i=m;}}}public void getInputInfo(){System.out.println("请输入活动的总数");Scanner in=new Scanner(System.in);this.activitiesNum=in.nextInt();System.out.println("请依次输入活动的序号，活动的起始时间和活动的截止时间");activities=new Activity[this.activitiesNum+1];int id,start,end;activities[0]=new Activity(0,0,0);for(int i=1;i<this.activitiesNum+1;i++){id=in.nextInt();start=in.nextInt();end=in.nextInt();activities[i]=new Activity(id,start,end);}}public class Activity{private int id;private int start;private int end;public int getId() {return id;}public int getStart() {return start;}public int getEnd() {return end;}public Activity(int id,int start,int end){this.id=id;this.start=start;this.end=end;}}}

上述代码是按照算法导论书中GREEDY-ACTIVITY-SELECTOR(s,f)伪代码实现的，大家可以参考下，运行结果如下所示：

请输入活动的总数11请依次输入活动的序号，活动的起始时间和活动的截止时间1 1 42 3 53 0 64 5 75 3 86 5 97 6 108 8 119 8 1210 2 1311 12 14活动选择情况如下：id=1 start=1 end=4id=4 start=5 end=7id=8 start=8 end=11id=11 start=12 end=14

在课后练习题16.1-1中，要求给出活动选择问题的动态规划算法，下面就给出动态规划的算法。

在动态规划算法中，我们要利用到书中公式16.3，并且要定义数组c[i][j]来保存在活动ai之后，活动aj之前的最大活动子集的数目。

算法实现如下所示：

package chapter1.homework1;import java.util.Scanner;public class ActivitySelectorDP {private int activitiesNum=0;//活动总数private Activity[] activities=null;//记录所有活动，包括虚拟活动private int c[][]=null;//定义数组存储public static void main(String[] args) {// TODO Auto-generated method stubActivitySelectorDP sample=new ActivitySelectorDP();sample.getInputInfo();sample.dynamicProgramming();System.out.println("活动选择情况如下：");sample.printSelectedActivity(0, sample.activitiesNum+1);}public void getInputInfo(){System.out.println("请输入活动的总数");Scanner in=new Scanner(System.in);this.activitiesNum=in.nextInt();System.out.println("请依次输入活动的序号，活动的起始时间和活动的截止时间");activities=new Activity[this.activitiesNum+2];int id,start,end;activities[0]=new Activity(0,0,0);for(int i=1;i<this.activitiesNum+1;i++){id=in.nextInt();start=in.nextInt();end=in.nextInt();activities[i]=new Activity(id,start,end);}activities[this.activitiesNum+1]=new Activity(this.activitiesNum+1,Integer.MAX_VALUE,Integer.MAX_VALUE);}public void dynamicProgramming(){this.c=new int[this.activitiesNum+2][this.activitiesNum+2];for(int i=0;i<=this.activitiesNum;i++){c[i][i+1]=0;}for(int step=2;step<=this.activitiesNum+1;step++){for(int i=0;i<=this.activitiesNum;i++){int j=i+step;if(j<this.activitiesNum+2){if(this.activities[i].end<=this.activities[j].start){int max=0;for(int k=i+1;k<j;k++){if(this.activities[k].start>=this.activities[i].end&&this.activities[k].end<=this.activities[j].start){int temp=c[i][k]+c[k][j]+1;if(temp>max)max=temp;}}if(max>c[i][j]){c[i][j]=max;}}}}}}public void printSelectedActivity(int start,int end){if(end-start==1){return;}for(int k=start+1;k<end;k++){if(this.activities[k].start>=this.activities[start].end&&this.activities[k].end<=this.activities[end].start){if(c[start][k]+c[k][end]+1==c[start][end]){printSelectedActivity(start,k);System.out.println("id="+k+" start="+this.activities[k].start+" end="+this.activities[k].end);printSelectedActivity(k,end);break;}}}}public class Activity{private int id;private int start;private int end;public int getId() {return id;}public int getStart() {return start;}public int getEnd() {return end;}public Activity(int id,int start,int end){this.id=id;this.start=start;this.end=end;}}}

程序运行结果如下所示：

请输入活动的总数11请依次输入活动的序号，活动的起始时间和活动的截止时间1 1 42 3 53 0 64 5 75 3 86 5 97 6 108 8 119 8 1210 2 1311 12 14活动选择情况如下：id=1 start=1 end=4id=4 start=5 end=7id=8 start=8 end=11id=11 start=12 end=14