/**/
/************************************************************************
* 0/1背包问题求解 (visual studio 2005)
* 给定一个载重量为m,及n个物品,其重量为wi,价值为vi,1<=i<=n
* 要求:把物品装入背包,并使包内物品价值最大
************************************************************************/
#include
<
>
#include
<
>
#include
<
string
.h
>
#define
FILENAMELENGTH 100
class
CBeibao
...
{
public:
int m_nNumber; //物品数量
int m_nMaxWeight; //最大载重量
int *m_pWeight; //每个物品的重量
int *m_pValue; //每个物品的价值
int *m_pCount; //每个物品被选中的次数
int m_nMaxValue; //最大价值
public:
CBeibao(const char *filename);
~CBeibao();
int GetMaxValue();
int GetMaxValue(int n,int m,int *w,int *v,int *c);
void Display(int nMaxValue);
void Display(int nMaxValue,const char *filename);
}
;
//
读入数据
CBeibao::CBeibao(
const
char
*
filename)
...
{
FILE *fp=fopen(filename,"r");
if(fp==NULL)
...{
printf("can not open file!");
return; //exit(0);
}
//读入物品数量和最大载重量
fscanf(fp,"%d%d",&m_nNumber,&m_nMaxWeight);
m_pWeight=new int[m_nNumber+1];
m_pValue=new int[m_nNumber+1];
m_pWeight[0]=0;
//读入每个物品的重量
for(int i=1;i<=m_nNumber;i++)
fscanf(fp,"%d",m_pWeight+i);
m_pValue[0]=0;
//读入每个物品的价值
for(int i=1;i<=m_nNumber;i++)
fscanf(fp,"%d",m_pValue+i);
//初始化每个物品被选中次数为0
m_pCount=new int[m_nNumber+1];
for(int i=0;i<=m_nNumber;i++)
m_pCount[i]=0;
fclose(fp);
}
CBeibao::
~
CBeibao()
...
{
delete[] m_pWeight;
m_pWeight=NULL;
delete[] m_pValue;
m_pValue=NULL;
delete[] m_pCount;
m_pCount=NULL;
}
/**/
/************************************************************************
* 动态规划求出满足最大载重量的最大价值
* 参数说明：n:物品个数
* m:背包载重量
* w:重量数组
* v:价值数组
* c:是否被选中数组
* 返回值：最大价值
************************************************************************/
int
CBeibao::GetMaxValue(
int
n,
int
m,
int
*
w,
int
*
v,
int
*
c)
...
{
int row=n+1;
int col=m+1;
int i,j; //循环变量:前i个物品能够装入载重量为j的背包中
//value[i][j]表示前i个物品能装入载重量为j的背包中物品的最大价值
int **value=new int*[row];
for(i=0;i<row;i++)
value[i]=new int[col];
//初始化第0行
for(j=0;j<col;j++)
value[0][j]=0;
//初始化第0列
for(i=0;i<row;i++)
value[i][0]=0;
//计算
for(i=1;i<row;i++)
...{
for(j=1;j<col;j++)
...{
//w[i]>j,第i个物品不装入背包
value[i][j]=value[i-1][j];
//w[i]<=j,且第i个物品装入背包后的价值>value[i-1][j],则记录当前最大价值
int temp=value[i-1][j-w[i]]+v[i];
if(w[i]<=j && temp>value[i][j])
value[i][j]=temp;
}
}
//逆推求装入的物品
j=m;
for(i=row-1;i>0;i--)
...{
if(value[i][j]>value[i-1][j])
...{
c[i]=1;
j-=w[i];
}
}
//记录最大价值
int nMaxVlaue=value[row-1][col-1];
//释放该二维数组
for(i=0;i<row;i++)
...{
delete [col]value[i];
value[i]=NULL;
}
delete[] value;
value=NULL;
return nMaxVlaue;
}
int
CBeibao::GetMaxValue()
...
{
int nValue=GetMaxValue(m_nNumber,m_nMaxWeight,m_pWeight,m_pValue,m_pCount);
m_nMaxValue=nValue;
return nValue;
}
//
显示结果
void
CBeibao::Display(
int
nMaxValue)
...
{
printf(" %d ",nMaxValue);
for(int i=1;i<=m_nNumber;i++)
...{
if(m_pCount[i])
printf(" %d %d ",i,m_pCount[i]);
}
printf(" ");
}
void
CBeibao::Display(
int
nMaxValue,
const
char
*
filename)
...
{
FILE *fp=fopen(filename,"w");
if(fp==NULL)
...{
printf("can not write file!");
return; //exit(0);
}
fprintf(fp,"%d ",nMaxValue);
for(int i=1;i<=m_nNumber;i++)
...{
if(m_pCount[i])
fprintf(fp,"%d %d ",i,m_pCount[i]);
}
fclose(fp);
}
//
显示菜单
void
show_menu()
...
{
printf("--------------------------------------------- ");
printf("input command to test the program ");
printf(" i or I : input filename to test ");
printf(" q or Q : quit ");
printf("--------------------------------------------- ");
printf("$ input command >");
}
void
main()
...
{
char sinput[10];
char sfilename[FILENAMELENGTH];
show_menu();
scanf("%s",sinput);
while(stricmp(sinput,"q")!=0)
...{
if(stricmp(sinput,"i")==0)
...{
printf(" please input a filename:");
scanf("%s",sfilename);
//获取满足最大载重量的最大价值
CBeibao beibao(sfilename);
int nMaxValue=();
if(nMaxValue)
...{
(nMaxValue);
int nlen=strlen(sfilename);
strcpy(sfilename+nlen-4,"_result.txt");
(nMaxValue,sfilename);
}
else
printf(" error! please check the input data! ");
}
//输入命令
printf("$ input command >");
scanf("%s",sinput);
}
}