算法导论 第16章 贪心算法-活动选择问题C++实现

参考：[1]Anker—学习成长笔记《算法导论》读书笔记之第16章 贪心算法—活动选择问题

#include <iostream>
#include <vector>
#define N 11//define 后面不能有分号
using namespace std;

//自底向上的动态规划算法
void dynamic_programming_activity_selector(int* s,int* f,int c[N+2][N+2],int ret[N+2][N+2])
{
for(int i=0;i<=N+1;i++)
for(int j=0;j<=N+1;j++)
{
c[i][j]=0;
ret[i][j]=0;
}
for (int i=0;i<=N+1;i++)
for (int j=i+1;j<=N+1;j++)
for(int k=i+1;k<j;k++)
if (c[i][j]<c[i][k]+c[k][j]+1&&s[k]>=f[i]&&f[k]<=s[j])
{
c[i][j]=c[i][k]+c[k][j]+1;
ret[i][j]=k;
}
//display
cout<<" 矩阵C："<<endl;
for(int i=0;i<=N+1;i++)
{
for(int j=0;j<=N+1;j++)
cout<<c[i][j]<<" ";
cout<<endl;
}
cout<<"最大兼容集大小："<<c[0][N+1]<<endl;
cout<<" 矩阵ret："<<endl;
for(int i=0;i<=N+1;i++)
{
for(int j=0;j<=N+1;j++)
cout<<ret[i][j]<<" ";
cout<<endl;
}
cout<<"最大兼容集之一：";
int last=0;
for (int j=1;j<N+2;j++)
{
if (ret[0][j]!=0&&ret[0][j]!=last)
{
cout<<ret[0][j]<<" ";
last=ret[0][j];
}
}
cout<<endl;
}
//CLRS教师手册中的答案
void print_activity(int c[N+2][N+2],int act[N+2][N+2],int i,int j)
{
if (c[i][j]>0)
{
int k=act[i][j];
cout<<k<<" ";
print_activity(c,act,i,k);
print_activity(c,act,k,j);
}
}
void dynamic_programming_activity_selector_clrs(int* s,int* f, int c[N+2][N+2],int act[N+2][N+2])
{
//int c[N+2][N+2],act[N+2][N+2];
for(int i=0;i<=N+1;i++)
for(int j=0;j<=N+1;j++)
{
c[i][j]=0;
act[i][j]=0;
}
for(int l=2;l<N+2;l++)
for(int i=0;i<N-l+2;i++)
{
int j=i+l;
c[i][j]=0;
int k=j-1;
while (f[i]<f[k])
{
if(f[i]<=s[k]&&f[k]<=s[j]&&c[i][k]+c[k][j]+1>c[i][j])
{
c[i][j]=c[i][k]+c[k][j]+1;
act[i][j]=k;
}
k--;
}
}
cout<<" the CLRS answer is:"<<endl;
cout<<" the maximum set's size is: "<<c[0][N+1]<<endl;
cout<<"one of the maximum set is :"<<endl;
print_activity(c,act,0,N+1);

}
//递归式的贪心算法
void recursive_activity_selection(int* s,int* f,int k,int n,vector<int>& v)
{
int m=k+1;
while(m<=n&&s[m]<f[k])
m+=1;
if(m<=n)
{
v.push_back(m);
recursive_activity_selection(s,f,m,n,v);
}
else return;
}
//迭代式的贪心算法
//从前向后
//选择最先结束且与v兼容的活动
//需要预先将活动按f排序
void greedy_activity_selector(int* s,int* f,vector<int>& v)
{
int k=0;
for(int m=1;m<=N;m++)
if(s[m]>=f[k])
{
v.push_back(m);
k=m;
}
}
//迭代式的贪心算法
//从后往前选择
//选择最晚开始的且与V兼容的活动
//需要预先将活动按s排序
void greedy_activity_selector2(int* s,int* f,vector<int>& v)
{
int k=N+1;
for (int m=N;m>0;m--)
if (f[m]<=s[k])
{
v.push_back(m);
k=m;
}
}
void main()
{
int s[]={-1,1,3,0,5,3,5,6,8,8,2,12,20};
int f[]={-1,4,5,6,7,9,9,10,11,12,14,16,20};
//将所有活动按照s递增排序
int s2[]={-1,0,1,2,3,3,5,5,6,8,8,12,20};
int f2[]={-1,6,4,14,5,9,7,9,10,11,12,16,20};
int c[N+2][N+2],ret[N+2][N+2];
dynamic_programming_activity_selector_clrs(s,f,c,ret);
vector<int> v1,v2,v3;
recursive_activity_selection(s,f,0,N,v1);
dynamic_programming_activity_selector(s,f,c,ret);
greedy_activity_selector(s,f,v2);
greedy_activity_selector2(s2,f2,v3);
cout<<" 递归式贪心算法的输出："<<endl;
for(int i=0;i<v1.size();i++)
cout<<v1[i]<<" ";
cout<<endl;
cout<<" 从前往后迭代式贪心算法的输出："<<endl;
for(int i=0;i<v1.size();i++)
cout<<v2[i]<<" ";
cout<<endl;
cout<<" 从后往前迭代式贪心算法的输出："<<endl;
for(int i=0;i<v1.size();i++)
cout<<v3[i]<<" ";
cout<<endl;
}