背包问题
思路:
w[i]代表物品重量,j代表可容乃最大重量,v(i,j)代表吧物品为i,重量为w[i]的物品装入可容纳j的容器中,p[i]代表物品i的价值
if(w[i] < j ) v(i,j)=v(i-1,j);
else v[i][j]=max(v[ v[i-1][j], (v[i-1][j-w[i]]+p[i]))
代码:
# include <iostream>
# include <vector>
using namespace std;
int main()
{
int n,m;
cout<<"请输入两个正整数n,m(n代表最大物品数量,m代表最大容量)\n";
cin>>n>>m;
vector<int> w(n+1);//重量
vector<int> p(n+1);//价值
vector<int> w1(n+1);
vector< vector<int> > v(n+1, vector<int>(m+1, 0));
cout<<"请连续输入"<<n<<"个物品的物品重量:\n";//2,2,6,5,4
for(int i = 1;i <= n; i++)
cin>>w[i];//重量
cout<<"请连续输入"<<n<<"个物品的物品价值:\n";////6,3,5,4,6
for(int i = 1;i <= n; i++)
cin>>p[i];
for(int i = 1;i <= n; i++)
for(int j = 1;j <= m; j++)
{
if(j < w[i]) v[i][j] = v[i-1][j];
else{
v[i][j] = v[i-1][j]>(v[i-1][j-w[i]]+p[i])? v[i-1][j]: (v[i-1][j-w[i]]+p[i]);
}
}
cout<<"详细过程如下:"<<endl;
for(int i = 1;i <= n; i++){
for(int j = 1;j <= m; j++)
cout<< v[i][j] << "\t";
cout<<endl;
}
int c = m;
for(int i = n;i >= 1; i--)
{
if(v[i][c] > v[i-1][c]){
w1[i] = 1;
c = c-w[i];
}
else w1[i] = 0;
}
cout<<"最大价值为:"<<v[n][m]<<endl;
cout<<"1代表选中,0代表没选中:\n";
for(int i = 1;i <= n ;i++)
cout<<w1[i]<<" ";
cout<<endl;
return 0;
}