背包问题

1.  01背包

为题描述：s件物品， 背包容量为  m  ，给出每件物品的cost，与 value 求在背包容量内最大的价值是多少？

 
void pack_01(int weight,int value)
{
    for(int i=背包容量;i>=weight;i--)
        dp[i]=max(dp[i],dp[i-weight]+value);
}

int DP()
{
    for(int i=0;i<物品件数;i++)
        pack_01(weight[i],value[i]);
    return dp[背包容量];
}

2.完全背包

物品件数为正无穷的背包

scanf("%d",&n);
for(i=0; i<n; i++)
{
    scanf("%d%d",&p,&w);
    for(j=w; j<=m; j++) //与01背包相比倒过来
    {
        dp[j]=max(dp[j],dp[j-w]+p);    // dp[i] 表示i容量的背包最多装的价值。
    }
}

3.多重背包

int v[10],dp[MM];
int sum;
void pack01(int weight,int val)
{
    int i;
    for(i=sum; i>=weight; i--)
        dp[i]=max(dp[i],dp[i-weight]+val);
}
void packcomplete(int weight,int val)
{
    int i;
    for(i=weight; i<=sum; i++)
        dp[i]=max(dp[i],dp[i-weight]+val);
}
void packmul(int weight,int val,int coutt)
{
    if(weight*coutt>=sum)  
    {
        packcomplete(weight,val);
        return ;
    }
    int k=1,tot=0;;
    while(k<coutt)   //二进制优化
    {
        pack01(k*weight,k*val);
        coutt-=k;
        k=k*2;
    }
    pack01(coutt*weight,coutt*val);
}
void DP()
{
    int i;
    for(i=0; i<=sum; i++)
        dp[i]=-INF;
    dp[0]=0;
    for(i=1; i<=6; i++)
    {
        packmul(i,i,v[i]);
    }
}

杭电题目  题目链接>点这里打开<

AC代码

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

using namespace std;
const int INF=10000000;
const int MM=60005;

int v[10],dp[MM];
int sum;
void pack01(int weight,int val)
{
    int i;
    for(i=sum; i>=weight; i--)
        dp[i]=max(dp[i],dp[i-weight]+val);
}
void packcomplete(int weight,int val)
{
    int i;
    for(i=weight; i<=sum; i++)
        dp[i]=max(dp[i],dp[i-weight]+val);
}
void packmul(int weight,int val,int coutt)
{
    if(weight*coutt>=sum)
    {
        packcomplete(weight,val);
        return ;
    }
    int k=1,tot=0;;
    while(k<coutt)
    {
        pack01(k*weight,k*val);
        coutt-=k;
        k=k*2;
    }
    pack01(coutt*weight,coutt*val);
}
void DP()
{
    int i;
    for(i=0; i<=sum; i++)
        dp[i]=-INF;
    dp[0]=0;
    for(i=1; i<=6; i++)
    {
        packmul(i,i,v[i]);
    }
}
int main()
{
    int ncase=0;
    while(1)
    {
        int i;
        ncase++;
        sum=0;
        for(i=1; i<=6; i++)
        {
            cin>>v[i];
            sum+=i*v[i];
        }
        if(!sum) break;   //如果全是0  程序结束
        printf("Collection #%d:
",ncase);
        if(sum%2==1)  //总和为奇数个数则不可能评分
        {
            printf("Can't be divided.

");
            continue;
        }
        sum=sum/2;  //背包容量减半
        DP();
        if(dp[sum]>=0)
            printf("Can be divided.

");
        else
            printf("Can't be divided.

");
    }
    return 0;
}