用回溯法求01背包问题，怎样使用C++模板啊，迫切求指点！

Posted 2023-03-30

#include<iostream>
#include<algorithm>
using namespace std;

template<class Typew,class Typep>
class Knap

friend Typep Knapsack(Typep *,Typew *,Typew,int);

private:
Typep Bound(int i);
void Backtrack(int i);
Typew c;
int n;
Typew *w;
Typep *p;
Typew cw;
Typep cp;
Typep bestp;
;

template<class Typew,class Typep>
void Knap<Typew,Typep>::Backtrack(int i)

if(i>n)

bestp=cp;
return;

if(cw+w[i]<=c)

cw+=w[i];
cp+=p[i];
Backtrack(i+1);
cw-=w[i];
cp-=p[i];

if(Bound(i+1)>bestp)
Backtrack(i+1);


template<class Typew,class Typep>
Typep Knap<Typew,Typep>::Bound(int i)

Typew cleft=c-cw;
Typep b=cp;

while(i<=n && w[i]<=cleft)

cleft-=w[i];
b+=p[i];
i++;

if(i<=n)
b+=p[i]*cleft/w[i];
return b;


class Object

friend int Knapsack(int *,int *,int,int);
public:
int operator<=(Object a)const

return d>=a.d;


private:
int ID;
float d;
;

template<class Typew,class Typep>
Typep Knapsack(Typep p[],Typew w[],Typew c,int n)

Typew W=0;
Typep P=0;
Object *Q=new Object[n];
for(int i=1;i<=n;i++)

Q[i-1].ID=i;
Q[i-1].d=1.0*p[i]/w[i];
P+=p[i];
W+=w[i];


if(W<=c)
return P;

sort(Q,Q+n);
Knap<Typew,Typep>K;
K.p=new Typep[n+1];
K.w=new Typew[n+1];
for(int j=1;j<=n;j++)

K.p[i]=p[Q[i-1].ID];
K.w[i]=w[Q[i-1].ID];


K.cp=0;
K.cw=0;
K.c=c;
K.n=n;
K.bestp=0;

K.Backtrack(1);
delete[]Q;
delete[]K.w;
delete[]K.p;
return K.bestp;


int main()

int n=3;
int w[3]=16,15,15;
int p[3]=45,25,25;
int c=30;
int bestprice=Knapsack(p,w,c,n);
cout<<"最优价值："<<bestprice<<endl;

return 0;

参考技术A #include<iostream>
using namespace std;

class Knap

friend int Knapsack(int p[],int w[],int c,int n );
public:
//输出当前最优解
void print()

for(int m=1;m<=n;m++)

cout<<bestx[m]<<" ";

cout<<endl;
;
private:
int Bound(int i); //计算右子树的上界
void Backtrack(int i);
int c;//背包容量
int n; //物品数
int *w;//物品重量数组
int *p;//物品价值数组
int cw;//当前重量
int cp;//当前价值
int bestp;//当前最优值
int *bestx;//当前最优解
int *x;//当前解
;

int Knap::Bound(int i)

//计算上界
int cleft=c-cw;//剩余容量
int b=cp;
//以物品单位重量价值递减序装入物品
while(i<=n&&w[i]<=cleft)

cleft-=w[i];
b+=p[i];
i++;

//剩余物品取部分来装满背包
if(i<=n)
b+=p[i]/w[i]*cleft;
return b;


void Knap::Backtrack(int i)

if(i>n)//到达叶结点

if(bestp<cp)

for(int j=1;j<=n;j++)
bestx[j]=x[j];//更新当前最优解
bestp=cp;

return;

if(cw+w[i]<=c) //搜索左子树

x[i]=1;//装入
cw+=w[i];
cp+=p[i];
Backtrack(i+1);
cw-=w[i];
cp-=p[i];

if(Bound(i+1)>bestp)//搜索右子树

x[i]=0;//不装入
Backtrack(i+1);



class Object

friend int Knapsack(int p[],int w[],int c,int n);
public:
int operator<=(Object a)const

return (d>=a.d);

private:
int ID;
float d;//单位重量价值
;

int Knapsack(int p[],int w[],int c,int n)

//为Knap::Backtrack初始化
int W=0;
int P=0;
int i=1;
Object *Q=new Object[n];
for(i=1;i<=n;i++)

Q[i-1].ID=i;
Q[i-1].d=1.0*p[i]/w[i];//计算单位重量价值
P+=p[i];
W+=w[i];

if(W<=c)
return P;//装入所有物品
//依物品单位重量排序
float f;
for( i=0;i<n;i++)
for(int j=i;j<n;j++)

if(Q[i].d<Q[j].d)

f=Q[i].d;
Q[i].d=Q[j].d;
Q[j].d=f;



Knap K;
K.p = new int[n+1];
K.w = new int[n+1];
K.x = new int[n+1];
K.bestx = new int[n+1];
K.x[0]=0;
K.bestx[0]=0;
for( i=1;i<=n;i++)

K.p[i]=p[Q[i-1].ID];
K.w[i]=w[Q[i-1].ID];

K.cp=0;
K.cw=0;
K.c=c;
K.n=n;
K.bestp=0;
//回溯搜索
K.Backtrack(1);
K.print();
delete [] Q;
delete [] K.w;
delete [] K.p;
return K.bestp;

void main()

int *p;
int *w;
int c=7;
int n=4;
int i=0;
p=new int[n+1];
w=new int[n+1];
p[0]=0;
w[0]=0;
p[1]=9;w[1]=3;
p[2]=10;w[2]=5;
p[3]=7;w[3]=2;
p[4]=4;w[4]=1;
cout<<Knapsack(p,w,c,n)<<endl;
system("pause");
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