01背包问题回溯法和动态规划

题目要求：

输入背包的容量v和物品的数量n；接下来n 行每行输入两个数字,第一个是物品质量，第二个是物品价值；

输出背包容纳物品的最大价值。

下面直接贴代码：

回溯法

#include<iostream>//之前必须知道背包容量和n个物品 
#include<algorithm>
using namespace std;
class Property
{
    public: 
    int weight,profit;
    double average;
    friend bool operator<(Property a,Property b)
    {
        return a.average>b.average;
    }
};
class Pack
{
    public:
        Pack(int Q,int n)//构造函数，初始化 
        {
            capcity=Q;
            number=n;
            property=new Property[n+1];
            bestp=cw=cp=0;
        }
        ~Pack()
        {
            delete []property;
        }
        void inputproperty()
        {
            for(int i=0;i<number;i++)
            {
                cin>>property[i].weight>>property[i].profit;
                property[i].average=1.0*property[i].profit/property[i].weight;
            }
            sort(property,property+number);
        }
        int command()
        {
            int totalweight=0;
            int totalvalue=0;
            for(int i=0;i<number;i++)
            {
            totalweight+=property[i].weight;
            totalvalue+=property[i].profit;
            }
            if(totalweight<capcity)return totalvalue;
            backtrack(0);
            return bestp;
        }
        bool bound(int i)
        {
            int currentp=cp;
            int currentw=capcity-cw;
            while(currentw>=property[i].weight&&i<number)
            {
                currentw-=property[i].weight;
                currentp+=property[i].profit;
                i++;
            }
            if(i<number)
            currentp+=1.0*property[i].profit*currentw/property[i].weight;
            return currentp>bestp;
        }
        void backtrack(int i)
        {
            if(i>number-1)
            {
                if(bestp<cp)
                bestp=cp;
                return;
            }
            if(cw+property[i].weight<=capcity)//此处必须用<=比较符号，不然会错 
            {
                cw+=property[i].weight;
                cp+=property[i].profit;
                backtrack(i+1);
                cw-=property[i].weight;
                cp-=property[i].profit;
            }
            if(bound(i+1));
            backtrack(i+1);
        }
    private:
    int capcity,number;    
    Property *property;
    int cw,cp,bestp; 
};
int main()
{
    int n,m;
    while(cin>>n>>m)
    {
        Pack object(n,m);
        object.inputproperty();
        cout<<object.command()<<endl;
    }
    return 0;
}

输入：

20 5
4 7
5 8
2 10
5 10
8 16

输出：
44

动态规划法

#include<iostream>
#include<cstring>
using namespace std;
int main()
{
    int Capcity,weight;
    int *w,*p;
    int profit[200][200];
    while(cin>>Capcity>>weight)
    {
        memset(profit,0,sizeof(profit));
        w=new int[weight+1];
        p=new int[weight+1];
        for(int i=1;i<=weight;i++)
        cin>>w[i]>>p[i];//输入重量和价值 
        for(int i=1;i<=weight;i++)
        {
            for(int j=1;j<=Capcity;j++)
            {
                if(w[i]>j)profit[i][j]=profit[i-1][j];
                else if(profit[i-1][j]<profit[i-1][j-w[i]]+p[i])
                profit[i][j]=profit[i-1][j-w[i]]+p[i];
                else profit[i][j]=profit[i-1][j];
            }
        }
        for(int i=1;i<=weight;i++)
        {
        for(int j=1;j<=Capcity;j++)
        {
            cout<<profit[i][j]<<" ";
        }
        cout<<endl;    
        }
    }
    return 0;
}