小白进阶之贪心算法-活动选择问题

来源：互联网发布：粒子群算法的工具箱编辑：程序博客网时间：2024/06/06 02:20

问题描述：给定活动集合，包括活动i的开始时间si和结束时间fi，求最大兼容活动子集。

i1234567891011si130535688212fi4567991011121416

问题的解法有三个：动态规划，递归的贪心算法和迭代的贪心算法

下面给出源码：

activitySelector.h

#include<stdio.h>#include<stdlib.h>struct res{int key;struct res *next;};void DActivitySelector(int *s,int *f,int **c,int **r,int n);//动态规划的活动选择算法void printResult(int **c,int **r,int i,int j);//打印动态规划算法的结果void recursiveActivitySelector(int *s,int *f,int k,int n,struct res *head);//递归的贪心算法void printRescursiveResult(struct res *head);//打印递归的贪心算法的结果void greedyActivitySelector(int *s,int *f,int n,struct res *head);//迭代的贪心算法void printGreedyResult(struct res *head);//打印迭代的贪心算法的结果

activitySelector.cpp

#include"activitySelector.h"void DActivitySelector(int *s,int *f,int **c,int **r,int n){int i,j;for(i=0;i<n;i++){for(j=0;j<n;j++){c[i][j]=0;r[i][j]=0;}c[i][i]=1;}int l;for(l=3;l<=n;l++){for(i=0;i<n-l+1;i++){j=i+l-1;for(int k=i+1;k<j;k++){if(s[k]>=f[i]&&f[k]<=s[j]){int q=c[i][k]+c[k][j]+1;if(c[i][j]<q){c[i][j]=q;r[i][j]=k;}}}}}}void printResult(int **c,int **r,int i,int j){if(c[i][j]==0)return ;else{int k=r[i][j];if(c[i][i]!=0){printf("a[%d]",i+1);c[i][i]=0;}printResult(c,r,i,k);printf("a[%d]",k+1);c[k][k]=0;printResult(c,r,k,j);if(c[j][j]!=0){printf("a[%d]",j+1);c[j][j]=0;}}}void recursiveActivitySelector(int *s,int *f,int k,int n,struct res *head){int m=k+1;while(m<=n&&s[m]<f[k])m=m+1;//寻找ak结束之后第一个结束的任务if(m<=n){struct res *p;p=(struct res *)malloc(sizeof(struct res));p->key=m;p->next=NULL;head->next=p;recursiveActivitySelector(s,f,m,n,p);}else{head->next=NULL;}}void printRescursiveResult(struct res *head){struct res *p;p=head->next;while(p!=NULL){printf("a[%d]",p->key);p=p->next;}}void greedyActivitySelector(int *s,int *f,int n,struct res *head){head->key=0;int k=0;struct res *p;p=head;for(int m=1;m<n;m++){if(s[m]>=f[k]){struct res *q;q=(struct res *)malloc(sizeof(struct res));q->key=m;q->next=NULL;p->next=q;p=p->next;k=m;}}}void printGreedyResult(struct res *head){struct res *p;p=head;while(p!=NULL){printf("a[%d]",p->key+1);p=p->next;}}

main.cpp

#include"activitySelector.h"int main(){int n=11;int s1[11]={1,3,0,5,3,5,6,8,8,2,12},f1[11]={4,5,6,7,9,9,10,11,12,14,16};int **c,**r;c=(int **)malloc(sizeof(int *)*11);r=(int **)malloc(sizeof(int *)*11);int i;for(i=0;i<11;i++){c[i]=(int *)malloc(sizeof(int)*11);r[i]=(int *)malloc(sizeof(int)*11);}DActivitySelector(s1,f1,c,r,11);printResult(c,r,0,10);//printf("\n");int s2[12]={0,1,3,0,5,3,5,6,8,8,2,12},f2[12]={0,4,5,6,7,9,9,10,11,12,14,16};struct res *head;head=(struct res *)malloc(sizeof(struct res));head->key=0;head->next=NULL;recursiveActivitySelector(s2,f2,0,12,head);printRescursiveResult(head);//printf("\n");struct res *head1;head1=(struct res *)malloc(sizeof(struct res));head1->key=0;head1->next=NULL;greedyActivitySelector(s1,f1,11,head1);//迭代的贪心算法printGreedyResult(head1);//打印迭代的贪心算法的结果system("pause");return 0;}

0 0