1、给定 n 种物品和一个背包，物品 i 的重量是 w[i], 其价值是 p[i], 背包的容量为 C。设物品已按单位重量价值递减的次序排序。每种物品不可以装入背包多次，但可以装入部分的物品 i。背包问题是选择装入背包中的物品，在不超过背包容量的前提下使背包的得总价值最大。用贪心法设计与实现一个算法，求解背包问题。
#include <iostream>
#include <stdio.h>
#include <string.h>
using namespace std;
typedef struct
{
char name[5];
float value;
float weight;
float rate;
}Thing;
typedef struct
{
Thing thing[3];
float value;
float weight;
float rate;
}Bag;
void sort(Thing thing1,Thing thing2)
{
Thing temp;
if(thing1.rate>thing2.rate)
{
temp = thing1;
thing1 = thing2;
thing2 = temp;
}
}
int main()
{
Thing thing[3];
thing[0].value = 9;thing[1].value = 10;thing[2].value = 12;
thing[0].weight = 3;thing[1].weight = 5;thing[2].weight = 8;
thing[0].rate = thing[0].value/thing[0].weight;
thing[1].rate = thing[1].value/thing[1].weight;
thing[2].rate = thing[2].value/thing[2].weight;
strcpy(thing[0].name,"book");
strcpy(thing[1].name,"note");
strcpy(thing[2].name,"pen");
for(int i = 0;i<3;i++)
{
for(int j = 0;j<2;j++)
{
sort (thing[j],thing[j+1]);
}
}
cout<<"目前总共有以下物品："<<endl;
for(int i = 0 ;i<3;i++)
{
cout<<thing[i].name<<" "<<thing[i].value<<" "<<thing[i].weight<<"kg "<<thing[i].rate<<endl;
}
Bag bag;
bag.weight = 14;
int i = 0;
bag.rate = 0;
bag.value = 0;
while(bag.weight>0)
{
if(bag.weight-thing[i].weight >=0)
{
bag.weight -= thing[i].weight;
bag.thing[i].weight = thing[i].weight;
bag.value +=thing[i].value;
bag.rate += (bag.weight/14)/100;
bag.thing[i] = thing[i];
bag.thing[i].weight = thing[i].weight;
thing[i].weight = 0;
}
else
{
bag.thing[i].weight = bag.weight;
thing[i].weight -= bag.weight;
bag.value +=thing[i].rate*bag.weight;
bag.rate = 1;
strcpy(bag.thing[i].name,thing[i].name);
bag.weight = 14;
break;
}
if(i == 2)bag.weight = 14 - bag.weight;
i++;
}
cout<<"背包外有以下物品："<<endl;
for(int i = 0 ;i<3;i++)
{
cout<<thing[i].name<<" "<<thing[i].weight<<"kg "<<endl;
}
cout<<"背包的总重量为："<<bag.weight<<"kg"<<endl;
cout<<"背包的承重比例为："<<bag.rate<<endl;
cout<<"背包的总价值为："<<bag.value<<endl;
cout<<"背包内有以下物品："<<endl;
for(int i = 0 ;i<3;i++)
{
if(strcmp(bag.thing[i].name,thing[i].name)==0)
{
cout<<bag.thing[i].name<<" "<<bag.thing[i].weight<<"kg "<<endl;
}
else break;
}
}