01背包问题

#include <iostream>  
#include <cstring>  
using namespace std;  
const int N=15;  
int main()  
{  
    int v[N]={0,8,10,6,3,7,2};  
    int w[N]={0,4,6,2,2,5,1};  
    int m[N][N];  
    int n=6,c=12;  
    memset(m,0,sizeof(m));  
    for(int i=1;i<=n;i++)  
    {  
        for(int j=1;j<=c;j++)  
        {  
            if(j>=w[i])  
                m[i][j]=max(m[i-1][j],m[i-1][j-w[i]]+v[i]);  
            else  
                m[i][j]=m[i-1][j];  
        }  
    }  
    for(int i=1;i<=n;i++)  
    {  
        for(int j=1;j<=c;j++)  
        {  
            cout<<m[i][j]<<' ';  
        }  
        cout<<endl;  
    }  
    return 0;  
}  

这一段代码很简单的把01背包问题最后的最大值答案求出，下面这个函数用来从后往前求最优解

void traceback()
{
    for (int i = n; i>1; i--)
    {
        if (m[i][c] == m[i - 1][c])
            x[i] = 0;
        else
        {
            x[i] = 1;
            c -= w[i];
        }
    }
    x[1] = (m[1][c]>0) ? 1 : 0;
}

完整代码如下:

#include <iostream>  
#include<windows.h>
using namespace std;
const int N = 15;
int v[N] = { 0,8,10,6,3,7,2 };
int w[N] = { 0,4,6,2,2,5,1 };
int x[N];
int m[N][N];
int n = 6, c = 12;
void traceback()
{
    for (int i = n; i>1; i--)
    {
        if (m[i][c] == m[i - 1][c])
            x[i] = 0;
        else
        {
            x[i] = 1;
            c -= w[i];
        }
    }
    x[1] = (m[1][c]>0) ? 1 : 0;
}

int main()
{
    
    memset(m, 0, sizeof(m));
    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= c; j++)
        {
            if (j >= w[i])
                m[i][j] = max(m[i - 1][j], m[i - 1][j - w[i]] + v[i]);
            else
                m[i][j] = m[i - 1][j];
        }
    }

    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= c; j++)
        {
            cout << m[i][j] << ' ';
        }
        cout << endl;
    }
    traceback();
    for (int i = 1; i <= n; i++)
        cout << x[i]<<" ";
    return 0;

}