0-1背包问题

#include "cstdio"
#include "queue"
#define MAX 20
#define INF 999
using namespace std;

int n;  //物品数量
float w[MAX];  //物品重量数组
float c;  //背包容量
float nowc;  //当前背包内物品重量
float nowp;  //当前背包内物品价值
int x[MAX];  //解向量
float bestp = 0;

struct Item
{
float weight;  //重量
float value;   //价值
float vDw;   //单位重量价值
};

int cmp(const void *item1, const void *item2)  //按单位重量价值降序
{
if((*(Item *)item1).vDw < (*(Item *)item2).vDw)
return 1;
else
return 0;
}

Item item[MAX];

struct Node
{
float upvalue;  //价值上界
int level;  //结点所在层
float cp;   //当前价值
float cw;  //当前重量

//按价值上界建立优先队列，价值上界大的结点先出队列
bool operator < (const Node &nod) const
{
if(upvalue > nod.upvalue)
return 1;
else
return 0;
}
};

priority_queue<Node> pq;

void EnQueue(float upv, float cp, float cw, int le)
{
Node node;
node.upvalue = upv;
node.level = le;
node.cp = cp;
node.cw = cw;
pq.push(node);
}

//计算结点所相应价值的上界
float bound(int i)
{
float cleft = c - nowc;  //背包剩余容量
float nowv = nowp;  //当前背包内物品价值
int j;
//以物品单位重量价值递减序装剩余容量
while(i<n && item[i].weight<=cleft)  //如果该物品还装得进去
{
cleft -= item[i].weight;  //剩余容量减少
nowv += item[i].value;     //当前背包内物品价值增加
i++;
}
if(i<n)  //将背包填满
nowv += (item[i].value / item[i].weight * cleft);
return nowv;
}

float maxKnapsack()
{
Node node;  //扩展结点
nowc = 0;  //当前背包内物品重量
nowp = 0;  //当前背包内所装物品价值
int i = 0;  //当前结点所在层
float up = bound(0);  //计算上界
while(i!=n)
{
if(nowc + item[i].weight <= c)//如果当前物品还装得进去，搜索左子树
{
if(nowp+item[i].value > bestp) //更改最优价值
bestp = nowp+item[i].value;
EnQueue(up, nowp+item[i].value, nowc+item[i].weight, i+1);//入队列
x[i] = 1;
}
up = bound(i+1);  //计算上界
if(up >= bestp) //如果上界不小于当前最优价值，可能产生最优价值，搜索右子树
{
EnQueue(up, nowp, nowc, i+1);//入队列
x[i] = 0;
}
node = pq.top();  //取下一个扩展结点
pq.pop();
nowc = node.cw;
nowp = node.cp;
i = node.level;
}
return bestp;
}

float knapsack(float weight[], float value[], int n1, int c1)
{
n = n1;
c = c1;
int i;
for(i=0; i<n; i++)
{
item[i].weight = weight[i];
item[i].value = value[i];
item[i].vDw = value[i]/weight[i];
}
qsort(item, n, sizeof(Item), cmp);
return maxKnapsack();
}

int main()
{
float c1 = 30;
int n1 = 3;
float weight[] = {16, 15, 15};
float value[] = {45, 25, 25};
float sum = knapsack(weight, value, n1, c1);
printf("背包容量为：%.1f\n", c);
printf("物品为(重量，价值)：\n");
int i;
for(i=0; i<n; i++)
printf("(%.1f, %.1f)\t", item[i].weight, item[i].value);
printf("\n");
printf("背包内所装物品的最大价值为：%.1f\n", sum);
printf("最优解为：\n");
for(i=0; i<n; i++)
printf("%d ", x[i]);
printf("\n");
return 0;
}