贪心算法or背包问题

贪心方法：总是对当前的问题作最好的选择，也就是局部寻优。最后得到整体最优。

应用：1：该问题可以通过“局部寻优”逐步过渡到“整体最优”。贪心选择性质与“动态规划”的主要差别。

2：最优子结构性质：某个问题的整体最优解包含了“子”问题的最优解。

程序1

#include <iostream.h>
struct goodinfo
{
 float p; //物品效益
 float w; //物品重量
 float X; //物品该放的数量
 int flag; //物品编号
};//物品信息结构体

void Insertionsort(goodinfo goods[],int n)
{
 int j,i;
 for(j=2;j<=n;j++)
 {
  goods[0]=goods[j];
     i=j-1;
  
  while (goods[0].p>goods[i].p)
  {
   goods[i+1]=goods[i];
   i--;
  }
  goods[i+1]=goods[0];
 }
}//按物品效益，重量比值做升序排列

void bag(goodinfo goods[],float M,int n)
{ 
 
 float cu;
 int i,j;
 for(i=1;i<=n;i++)
  goods[i].X=0;
 cu=M;  //背包剩余容量
 for(i=1;i<n;i++)
 {
  if(goods[i].w>cu)//当该物品重量大与剩余容量跳出
   break;
  
   goods[i].X=1;
   cu=cu-goods[i].w;//确定背包新的剩余容量
 }
 if(i<=n)
  goods[i].X=cu/goods[i].w;//该物品所要放的量
/*按物品编号做降序排列*/ 
 for(j=2;j<=n;j++)
 {
  goods[0]=goods[j];
     i=j-1;
  
  while (goods[0].flag<goods[i].flag)
  {
   goods[i+1]=goods[i];
   i--;
  }
  goods[i+1]=goods[0];
 }
///////////////////////////////////////////
 cout<<"最优解为:"<<endl;
 for(i=1;i<=n;i++)
 {
  cout<<"第"<<i<<"件物品要放:";
  cout<<goods[i].X<<endl;
 }
}

void main()
{ 
 cout<<"|--------运用贪心法解背包问题---------|"<<endl;
 cout<<"|---power by zhanjiantao(028054115)---|"<<endl;
 cout<<"|-------------------------------------|"<<endl;
 int j;
 int n;
 float M;
 goodinfo *goods;//定义一个指针
 while(j)
 {
 cout<<"请输入物品的总数量：";
 cin>>n;
 goods=new struct goodinfo [n+1];//
 cout<<"请输入背包的最大容量：";
 cin>>M;
 cout<<endl;
 int i;
 for(i=1;i<=n;i++)
  { goods[i].flag=i;
   cout<<"请输入第"<<i<<"件物品的重量:";
   cin>>goods[i].w;
   cout<<"请输入第"<<i<<"件物品的效益:";
   cin>>goods[i].p;
   goods[i].p=goods[i].p/goods[i].w;//得出物品的效益，重量比
   cout<<endl;
   
  }
 
 Insertionsort(goods,n);
 bag(goods,M,n);
 cout<<"press <1> to run agian"<<endl;
 cout<<"press <0> to exit"<<endl;
 cin>>j;
 }
}

程序2

#include<stdio.h>
#include<stdlib.h>
#define Max 100/*定义栈结构*/
typedef struct list{ int data[Max]; int top;}
Seqstack; /*定义一个用来存储结果的链表*/
typedef struct List{ Seqstack result; struct List * Next;}
Seqlist,*Pointer; 
void Inicial_List(Pointer p)
{ p=(Pointer)malloc(sizeof(Seqlist)); 
p->Next=NULL;} 
Seqstack Push_Stack(int n,Seqstack s)
{ s.top++; 
s.data[s.top]=n;
 return s;}
int Add_Stack(Seqstack s)
{   
Int total=0,i;   
if(s.top>=0)  
 {   for(i=0;i<=s.top;i++) 
total+=s.data[i];  
 }   
else   
{ total=0;   }   
return total;}
Seqstack Pop_Stack(Seqstack s)
{
  printf("%d",s.data[s.top]);
 if(s.top>=0) 
s.top--; 
return s;}/*执行回溯操作的函数*//*参数说明：n->数的总的个数，a[]用来存放数的数组,k查找的总体积*/
Pointer Query_Result(int n,int b[],int k)
{ int i,j;
 Seqstack mystack;
 Seqlist *newnode; 
Pointer r,p=NULL; 
Inicial_List(p); 
r=p; for(i=0;i<n;i++) 
{  mystack.top=-1;  
 j=i; 
 while(j<n) 
 {   
 if(Add_Stack(mystack)+b[j]<k)  
 {    mystack=Push_Stack(b[j],mystack);
     j++;   }
   else if(Add_Stack(mystack)+b[j]==k)   
{    mystack=Push_Stack(b[j],mystack); 
   newnode=(Pointer)malloc(sizeof(Seqlist));   
 newnode->result=mystack;  
  newnode->Next=NULL; 
   r->Next=newnode;   
 r=newnode;  
  mystack=Pop_Stack(mystack);  
  j++;    
} 
  else if(Add_Stack(mystack)+b[j]>k)   
{     
j++;   
}  
} 
 }
 return p;
} 
void Print_List(Pointer p)
{
 int i,j=0;
 p=p->Next; 
printf("welcome the outer
"); 
if(p==NULL)
printf("there no results
"); 
while(p!=NULL) 
{  
 j++;  
printf("the %d result is: ",j); 
 for(i=0;i<=p->result.top;i++) 
 {    printf(" %d",p->result.data[i]); 
 }  
p=p->Next;  
printf("
"); } 
printf("
");}
void Sort_Array(int b[],int n)
{ 
int i,j,temp; 
for(i=0;i<n;i++)
 {  for(j=0;j<n-i;j++)  
{      if(b[j]<b[j+1])    
  {   temp=b[j]; 
  b[j]=b[j+1]; 
  b[j+1]=temp;     
 }
  } 
} 
}
void main()
{ 
int i,n,k,select,a[Max]; 
Pointer head;
 printf("******************************************
"); printf("1 start
2 exit
"); 
 scanf("%d",&select); 
  while(select==1) 
 {   
printf("please input the total products
");  
 scanf("%d",&n);  
 printf("please input the volumn of n products
");
   for(i=0;i<n;i++)  
 {   
 printf("please input the %d integers",i+1);   
 scanf("%d",&a[i]);   
} 
  printf("
");  
 printf("please input the volunm to put
");   
scanf("%d",&k);
   Sort_Array(a,n);   
head=Query_Result(n,a,k);   
Print_List(head);  
 printf("******************************************
"); 
  printf("1 start
2 exit
");   scanf("%d",&select);
  }
 }

程序3

#include<stdio.h>
#include<stdlib.h>
#define Max 100
/*定义栈结构*/
typedef struct list{ int data[Max]; int top;}Seqstack; 
/*定义一个用来存储结果的链表*/
typedef struct List
{ 
Seqstack result; 
struct List * Next;
}
Seqlist,*Pointer; 
void Inicial_List(Pointer p)
{
 p=(Pointer)malloc(sizeof(Seqlist)); 
p->Next=NULL;
}
 Seqstack Push_Stack(int n,Seqstack s)
{ s.top++;
 s.data[s.top]=n; 
return s;
}
int Add_Stack(Seqstack s)
{   int total=0,i;  
 if(s.top>=0) 
  {   
for(i=0;i<=s.top;i++)
 total+=s.data[i]; 
  }  
 else   
{
 total=0;  
 }   
return total;
}
Seqstack Pop_Stack(Seqstack s)
{
  printf("%d",s.data[s.top]); 
if(s.top>=0) 
s.top--; return s;}
/*执行回溯操作的函数*//*参数说明：n->数的总的个数，a[]用来存放数的数组,k查找的总体积*/
Pointer Query_Result(int n,int b[],int k)
{ 
int i,j;
 Seqstack mystack; 
Seqlist *newnode; 
Pointer r,p=NULL; 
Inicial_List(p); 
r=p; 
for(i=0;i<n;i++)
 {  
mystack.top=-1; 
  j=i;  
while(j<n)  
{   
 if(Add_Stack(mystack)+b[j]<k)  
 {  
  mystack=Push_Stack(b[j],mystack);
     j++;  
 }  
 else if(Add_Stack(mystack)+b[j]==k)
   { 
   mystack=Push_Stack(b[j],mystack); 
   newnode=(Pointer)malloc(sizeof(Seqlist));    
newnode->result=mystack; 
   newnode->Next=NULL;
    r->Next=newnode; 
   r=newnode; 
   mystack=Pop_Stack(mystack);  
  j++; 
   }  
 else if(Add_Stack(mystack)+b[j]>k)  
 {   
  j++; 
  }  
} 
 }
 return p;
} 
void Print_List(Pointer p)
{ 
int i,j=0; 
p=p->Next; 
printf("welcome the outer
");
 if(p==NULL)
printf("there no results
"); 
while(p!=NULL)
 {   
j++;
  printf("the %d result is: ",j); 
 for(i=0;i<=p->result.top;i++)  
{    
printf(" %d",p->result.data[i]);
  }  
p=p->Next; 
 printf("
"); 
}
 printf("
");
}
void Sort_Array(int b[],int n)
{
 int i,j,temp; 
for(i=0;i<n;i++) {  for(j=0;j<n-i;j++)  
{     
 if(b[j]<b[j+1])      
{ 
  temp=b[j];  
 b[j]=b[j+1];  
 b[j+1]=temp;    
  }
  }
 }
 }
void main()
{ 
int i,n,k,select,a[Max]; Pointer head;
 printf("******************************************
"); 
printf("1 start
2 exit
");  scanf("%d",&select);  
 while(select==1)  
{ 
  printf("please input the total products
"); 
  scanf("%d",&n); 
  printf("please input the volumn of n products
");  
 for(i=0;i<n;i++)  
 {  
  printf("please input the %d integers",i+1);   
 scanf("%d",&a[i]);   }   printf("
");   
printf("please input the volunm to put
");   
scanf("%d",&k);   Sort_Array(a,n);   
head=Query_Result(n,a,k);  
 Print_List(head); 
  printf("******************************************
");  
 printf("1 start
2 exit
");  
 scanf("%d",&select); 
 } 
}