【0-1 背包模板】 poj 3624

先看个未经优化的二维空间dp：

#include <iostream>
#include <cstdio>
#include <cmath>
#include <memory.h>
using namespace std;
const int maxn1=3500;
const int maxn2=1300;
int dp[maxn2][maxn2];
//int dp[maxn2];
int w[maxn1],v[maxn2];
int m,n;
int max(int x,int y)
{
 return x>y?x:y;
}
int main()
{
    freopen("in.txt","r",stdin);
 while(~scanf("%d%d",&n,&m))
 {
  for(int i=1;i<=n;i++)
   cin >> w[i] >> v[i];
 }
 memset(dp,0,sizeof(dp));
 int j;
 for(int i=1;i<=n;i++)
    {
        for(j=1;j<=m;j++)
        {
            if(j>=w[i])
            dp[i][j]=max(dp[i-1][j],dp[i-1][j-w[i]]+v[i]);
            else
            dp[i][j] = dp[i-1][j];
        }
    }
 cout << dp[n][m] << endl;
 return 0;
}

改进：

1。二维优化到一维

2。倒写

#include <iostream>
#include <cstdio>
#include <cmath>
#include <memory.h>
using namespace std;
const int maxn1=3500;
const int maxn2=13000;
int dp[maxn2],w[maxn1],v[maxn2];
int m,n;
int max(int a, int b)
{
    if(a>b) return a ;
    else return b ;
}
int main()
{
    freopen("in.txt","r",stdin);
    freopen("out.txt","w",stdout);
 while(~scanf("%d%d",&n,&m))
 {
        memset(dp,0,sizeof(dp));
  for(int i=1;i<=n;i++)
   cin >> w[i] >> v[i];
        int j;
        for(int i=1;i<=n;i++)
        {
            for(j=m;j>=w[i];j--)
            {
                dp[j]=max(dp[j],dp[j-w[i]]+v[i]);
                cout << j << " j "<< dp[j]<< endl;
            }
            cout <<endl;
        }
        cout << dp[m] << endl;
 }
 return 0;
}

给一组数据便于理解：

6 j 4
5 j 4
4 j 4
3 j 4
2 j 4
1 j 4

6 j 10
5 j 10
4 j 10
3 j 10
2 j 6

6 j 22
5 j 18
4 j 16
3 j 12

6 j 23
5 j 19
4 j 16
3 j 12
2 j 7

23

最后给出模板：

#include <iostream>
#include <cstdio>
#include <cmath>
#include <memory.h>
using namespace std;

const int maxn1=3500;
const int maxn2=13000;
int dp[maxn2],w[maxn1],v[maxn1];
int m,n;

int max(int a, int b)
{
    if(a>b) return a ;
    else return b ;
}

int main()
{
    //freopen("in.txt","r",stdin);
    while(~scanf("%d%d",&n,&m))
    {
        memset(dp,0,sizeof(dp));
        for(int i=1;i<=n;i++)
            cin >> w[i] >> v[i];
        int j;
        for(int i=1;i<=n;i++)
            for(j=m;j>=w[i];j--)
                dp[j]=max(dp[j],dp[j-w[i]]+v[i]);
        cout << dp[m] << endl;
    }
    return 0;
}