利用动态规划解决0-1背包问题

#include<iostream>
#include<stack>
#include<vector>

using namespace std;

stack<int> KnapSack(int c,vector<int> w,vector<int> v,int &max_m)
{
    vector<vector <int> > m(w.size(),vector<int>(c+1));
    stack<int> res;
    int i,j;

    max_m=0;
    for(j=0;j<c+1;j++) //对于m[n][j]，
        if(j<w[w.size()-1])
            m[w.size()-1][j]=0;  //当j<w[n]时，物品n不能放入背包中，此时背包的价值为0。
        else
            m[w.size()-1][j]=v[v.size()-1];  //当j>=w[n]时，物品n可以放入背包，此时背包的价值为v[n]

    for(i=w.size()-2;i>=0;i--) //对于m[i][j]，
    {
        for(j=0;j<c+1;j++)
            if(j<w[i])          //当j<w[i]时，物品i不能放入背包中，此时背包的价值为m[i+1][j]。
                m[i][j]=m[i+1][j];
            else                //当j>=w[i]时，物品n可以放入背包
            {
                int m1=m[i+1][j];  //当物品i不放入背包时，能达到的最大价值为m[i+1][j]
                int m2=m[i+1][j-w[i]]+v[i];  //当物品i放入背包后，对于物品i+1到n，能达到的最大价值为m[i+1][j-w[i]]+v[i]
                m[i][j]=m1>m2?m1:m2;         //两者取其大者
            }
    }
/*    cout << "最优值矩阵:"<<endl;
    for(i=0;i<w.size();i++)
    {
        for(j=0;j<c+1;j++)
            cout<<m[i][j]<<" ";
        cout <<endl;
    }
    cout <<endl;
    */
    j=c;
    for(i=0;i<w.size()-1;i++)
    {
        if(m[i][j]!=m[i+1][j])
        {
            res.push(i+1);
            max_m+=v[i];
            j=j-w[i];
        }
    }
    if(m[w.size()-1][j]!=0)
    {
        res.push(w.size());
        max_m+=v[w.size()-1];
    }

    return res;
}

int main()
{
    vector<int> weight;
    vector<int> value;
    stack<int>  result;
    int max_weight;
    int tmp;
    int result_m=0;

    cout<< "输入背包最大容量"<<endl;
    cin >> max_weight;
    cout <<"输入物品重量,以0结束"<<endl;

    while(1)
    {
        cin>>tmp;
        if(tmp!=0)
            weight.push_back(tmp);
        else
            break;
    }
    cout <<"物品重量: "<<endl;
    for(int i=0;i<weight.size();i++)
        cout <<weight[i]<<" ";
    cout << endl;
    cout <<"输入物品权重,以0结束"<<endl;
    while(1)
    {
        cin>>tmp;
        if(tmp!=0)
            value.push_back(tmp);
        else
            break;
    }

    cout <<"物品权重: "<<endl;
    for(int i=0;i<value.size();i++)
        cout <<value[i]<<" ";
    cout << endl;

    result=KnapSack(max_weight,weight,value,result_m);

    cout <<"放入背包的物品为："<<endl;
    while(!result.empty())
    {
        cout <<result.top()<<" ";
        result.pop();
    }
    cout <<endl;
    cout<<"背包最大价值为："<<result_m<<endl;

    return 0;
}