【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;

}