问题:
假设有n个物品,每个物品都是有重量的,同时每个物品也是有价值的,要求把这些物品放到一个背包中,这个背包的载重量是有限制的,怎么使得背包里面的物品总价值最大?
符号表示:
N:物品个数
W:背包载重量
w[i]:物品i的重量(1<i<=N)
v[i]:物品i的价值(1<i<=N)
c[i, j]:到物品i为止,背包重量限制为j的最优解(1<i<=N, 1<j<=W)
分析:
#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]); } } } }
原文:http://blog.csdn.net/liu1064782986/article/details/33739917