01 backpack problems [Dynamic Planning]

Problem:

Assume that there are n items, each item has weight, and each item is also valuable. To put these items in a backpack, the carrying capacity of this backpack is limited, how can we maximize the total value of items in a backpack?

Symbol:

N: number of items

W: carrying weight of a backpack

W [I]: Weight of item I (1 <I <= N)

V [I]: Value of item I (1 <I <= N)

C [I, j]: the optimal weight limit of the backpack to item I is J (1 <I <= N, 1 <j <= W)

Analysis:

1. Optimal Solution Structure: For item I, there are only two conditions: Put or not put. Assuming that item I is placed in a part of the optimal solution, then we can remove item I, C [I-1, J-W [I] at this time should also be the optimal solution
2. Recursively defines the value of the optimal solution:
4. Calculate the optimal value based on the bottom-up mode: double loop, I from 1 to n loop, J from 1 to W Loop
5. An optimal solution is constructed from the calculated results: top-down, I loops from N to 1, if C [I, j]> C [I-1, J], put item I into the backpack; otherwise, the opposite is true.

Code (C ++ ):

#ifndef ___1package__package__#define ___1package__package__#include <iostream>#include <string>#include <vector>using namespace std;class Package{public:    void init(string dataSource);    void print();private:    void compute();    int m_nN;  // The number of object    int m_nW;  // The max weight of package    vector<int> m_vecWeight;  // The weight of object    vector<int> m_vecValue;   // The value of object    vector<vector<int> > m_vecMatrix;  // The results matrix    };#endif /* defined(___1package__package__) */

////  package.cpp//  01package#include "package.h"#include <fstream>void Package::init(string dataSource){    // read data from datasource    ifstream file;    file.open(dataSource);    if (file.is_open()){        string buffer;        file>>m_nW;        file>>m_nN;        m_vecWeight.clear();        m_vecWeight.push_back(0);        m_vecValue.clear();        m_vecValue.push_back(0);        int w, v;        for (int i=0; i<m_nN; ++i) {            file>>w>>v;            m_vecWeight.push_back(w);            m_vecValue.push_back(v);        }        while(!file.eof()){            file>>buffer;            cout<<buffer<<endl;        }    }    file.close();        m_vecMatrix.clear();    // set first row and first column to zero    for (int i=0; i<=m_nN; ++i) {        m_vecMatrix.push_back(vector<int>(m_nW+1, 0));    }    }void Package::print(){    compute();    cout<<"\n=====The Results======\n"<<"The max value: "<<m_vecMatrix[m_nN][m_nW]<<endl;}void Package::compute(){    for (int i=1; i<=m_nN; ++i) {        for (int j=1; j<=m_nW; ++j) {            int cur_weight = m_vecWeight[i];            if (cur_weight>j) {                m_vecMatrix[i][j] = m_vecMatrix[i-1][j];            } else{                m_vecMatrix[i][j] = max<int>(m_vecMatrix[i-1][j-cur_weight]+m_vecValue[i], m_vecMatrix[i-1][j]);            }        }    }}

The input test data can refer to: http://zhidao.baidu.com/question/77646243.html