3個揹包：0-1揹包 完全揹包 多重揹包

參考：https://www.cnblogs.com/A-S-KirigiriKyoko/p/6036368.html

0-1揹包

#include<iostream>
#include<algorithm>
#include<string>
#include<math.h>
#include<stdlib.h>
#include <iostream>
#include <vector>
#include <queue>

using namespace std;
int main() {
	int i,j,n,t,v;
	cin>>t>>n;
	int time[1000],value[1000];
	int f[100][100]={0};
	for(i=1;i<=n;i++){
		cin>>time[i]>>value[i];
	}
	for(i=1;i<=n;i++){
		for(j=0;j<time[i];j++){
			f[i][j]=f[i-1][j];
//			cout<<f[i][j]<<" ";
		}
		for(j=time[i];j<=t;j++){
			f[i][j]=max(f[i-1][j],f[i-1][j-time[i]]+value[i]);
//			cout<<f[i][j]<<" ";
		}
//		cout<<endl;
	}
	cout<<f[n][t];
    return 0;
}

/* 

70 3
71 100
69 1
1 2

*/

2.完全揹包

#include<iostream>
#include<algorithm>
#include<string>
#include<math.h>
#include<stdlib.h>
#include <iostream>
#include <vector>
#include <queue>

using namespace std;
int main() {
	int i,j,n,t,k;
	cin>>t>>n;
	int time[1000],value[1000];
	int f[200][200]={0};
	for(i=1;i<=n;i++){
		cin>>time[i]>>value[i];
	}
	for(i=1;i<=n;i++){
		for(j=0;j<=t;j++){
			for(k=0;k<=j/time[i];k++){
				f[i][j]=max(f[i][j],f[i-1][j-k*time[i]]+k*value[i]);
				
			}
			cout<<f[i][j]<<" ";
		}
		cout<<endl;
	}
	cout<<f[n][t];
    return 0;
}

/* 

70 3
71 100
69 1
1 2

*/

3.多重揹包

#include<iostream>
#include<algorithm>
#include<string>
#include<math.h>
#include<stdlib.h>
#include <iostream>
#include <vector>
#include <queue>

using namespace std;
int main() {
	int i,j,n,t,k;
	cin>>t>>n;
	int time[1000],value[1000],number[1000];
	int f[200][200]={0};
	for(i=1;i<=n;i++){
		cin>>time[i]>>value[i]>>number[i];
	}
	
	for(i=1;i<=n;i++){
		for(j=1;j<=t;j++){
			for(k=1;k<=number[i];k++){
				if ((j-k*time[i])<0) break;
				f[i][j]=max(f[i-1][j],f[i-1][j-k*time[i]]+k*value[i]);	
			}
			cout<<f[i][j]<<" ";
		}
		cout<<endl<<endl;
	}
	cout<<f[n][t];
    return 0;
}

/* 

140 3
71 100 20
69 1 20
1 2 20

*/