背包问题[穷举法]

Posted 2020-06-21 YuRi

/*-------------完整代码@映雪-------------*/

#include <iostream>
using namespace std;
typedef struct goods
{
    double *value; //价值
    double *weight; //重量 
    int num;//物品数量 
    int limitw; //限制重量
}GOODS;
int binadd(char select1[],int n) //二进制运算 
{
    int i,carry=0;
    select1[0] += 1;
    for (i = 0; i < n; i++)
    {
        select1[i] += carry; //加上进位 
        carry = select1[i] /2;//计算进位         
        select1[i] %= 2; //保留0或1; 
        if (carry==0)
            return 0;
    }
    return carry;
}
void backpack(GOODS *g,char select[])
{
   int i,flag;
   char *select1;
   double maxvalue = 0,tw,tv;
   if(!(select1 = (char *)malloc(g->num)))//保存最后加入背包的物品序号 
   {
       printf("内存分配失败\n");
       exit(0);   
   }
   for (i = 0; i < g->num; i++)//将数组清空 
       select1[i] = 0;    
   while(binadd(select1, g->num) == 0) //进行一次二进制加法运算 
   {
       tw = 0;
       tv = 0;
       flag = 1;
       printf("\n");
       for (i = 0; i < g->num; i++) //根据选中状态进行试算 
       {
           if (select1[i] == 1) //若选中该物品
           {
               tw += g->weight[i]; //累加选中物品的重量 
               tv += g->value[i];//累加选中物品的价值 
               if (tw > g->limitw) //若重量超过限制 
               {
                   flag = 0;
                   break; //退出本次方案的试算 
               }
           } 
       }
       if(flag && maxvalue < tv) //若方案选中物品重量未超过限制,并且本方案累加价值大于已有方案的最大价值
       {
           maxvalue = tv;
           for(i = 0; i < g->num; i++) //保存方案 
               select[i] = select1[i];
       } 
   }   
}

int main()
{
   double sumweight,maxvalue; //用来保存阶段最优价值 
   char *select;
   GOODS g;
   int i; //item数组用来保存最后放入背包物品的序号 
   printf("背包最大重量:");
   scanf("%d",&g.limitw);
   printf("可选物品数量:"); 
   scanf("%d",&g.num);
   if(!(g.value = (double *)malloc(sizeof(double)*g.num)))//分配内存保存物品价值 
   {
       printf("内存分配失败\n");
       exit(0); 
   }
   if(!(g.weight = (double *)malloc(sizeof(double)*g.num)))//分配内存保存物品的重量 
   {
       printf("内存分配失败\n");
       exit(0);   
   }
   if(!(select = (char *)malloc(sizeof(char)*g.num)))
    {   printf("内存分配失败\n");
       exit(0);   
   }
   for (i = 0; i < g.num; i++)
   {
      printf("输入第%d号物品的重量和价值:",i + 1);
      scanf("%lf%lf",&g.weight[i],&g.value[i]);
   }
   printf("\n背包最大能装的重量为:%d\n\n",g.limitw);
   for (i = 0; i < g.num; i++)
      printf("第%d号物品重:%.2f,价值:%.2f\n", i + 1, g.weight[i], g.value[i]);
   backpack(&g,select);
   sumweight=0;
   maxvalue=0; 
   printf("\n可将以下物品装入背包,使背包装的物品价值最大:\n");
   for (i = 0; i < g.num; ++i)
      if (select[i])
      {
         printf("第%d号物品,重量:%.2f,价值:%.2f\n", i + 1, g.weight[i], g.value[i]);
         sumweight+=g.weight[i];
         maxvalue+=g.value[i];
      }     
   printf("\n总重量为: %.2f,总价值为:%.2f\n", sumweight, maxvalue );
   return 0;
}

完整代码