动态规划01背包

#include <iostream>
#include <cstdlib>
#include<cstring>
using namespace std;

int max(int a, int b)
{
    return (a >= b)? a : b;
}

int min(int a, int b)
{
    return (a < b)? a : b;
}

void knapsack(int v[], int w[], int c, int n, int m[][20])
{
    //memset(m, 90, sizeof(m) );
    for(int j = 1; j <= c; j  ++)
        m[1][j] = 0;

    int jMax = min(w[n] - 1, c);
    for(int j = 0;  j <= jMax; j ++)
        m[n][j] = 0;
    for(int j = w[n];  j <= c; j ++)
        m[n][j] = v[n];

    //优化版：节省不必要的运算，第一行只需m[1][c]即可
    /*
    for(int i = n - 1; i > 1; -- i){
        jMax = min(w[i] - 1, c);
        for(int j = 0; j <= jMax; ++j)
            m[i][j] = m[i + 1][j];
        for(int j = w[i]; j <= c;  ++j)
            m[i][j] = max(m[i + 1][j], m[i + 1][j - w[i]] + v[i]);
    }
    m[1][c] = m[2][c];
    if(c >= w[1])
        m[1][c] = max(m[1][c], m[2][c - w[1]] + v[1]);
        */

    //配合可见表格版
    for(int i = n - 1; i > 0; -- i){
        jMax = min(w[i] - 1, c);
        for(int j = 0; j <= jMax; ++j)
            m[i][j] = m[i + 1][j];
        for(int j = w[i]; j <= c;  ++j)
            m[i][j] = max(m[i + 1][j], m[i + 1][j - w[i]] + v[i]);
    }

    for(int j = 0; j <= c; ++j){
        m[0][j] = 0;
    }//为了配合课件的表格
    for(int i = 0; i <= n; ++ i){
        for(int j = 0; j <= c; j ++){
            cout<<m[i][j]<<"  ";
        }
        cout<<endl;
    }
    cout<<endl;
}


void traceback(int m[][20], int w[], int c, int n, int x[])
{
    for(int i = 1; i < n; ++ i)
        if(m[i][c] == m[i + 1][c])
            x[i] = 0;
        else{
            x[i] = 1; 
            c -= w[i];
        }
        x[n] = (m[n][c]) ? 1 : 0;
}

int main()
{
    int n, c, w[20], v[102], m[20][20], x[20];
    cout<<"n, c:"<<endl;
    cin>>n>>c;
    cout<<"Weight"<<endl;
    for(int i = 1; i <= n; ++i){
        cin>>w[i];
    }
    cout<<"Value"<<endl;
    for(int i = 1; i <= n; ++i){
        cin>>v[i];
    }

    knapsack(v, w, c, n, m);
    traceback(m, w, c, n, x);

    for(int i = 1; i <= n; ++i)
        cout<<x[i]<<" ";
    cout<<endl;
    cout<<m[1][c]<<endl;
    system("pause");
}