算法设计与分析——回溯法—

算法设计与分析——回溯法——01背包问题


//0-1背包问题 回溯法求解
#include<bits/stdc++.h>
#include <iostream>using namespace std; template<class Typew,class Typep>
class Knap
{public:Typep Bound(int i);void Backtrack(int i);Typew c;	//背包容量int n;		//物品数Typew *w;	//物品重量数组Typep *p;	//物品价值数组Typew cw;	//当前重量Typep cp;	//当前价值Typep bestp;//当前最后价值};template<class Typew,class Typep>Typep Knapsack(Typep p[],Typew w[],Typew c,int n);template <class Type>inline void Swap(Type &a,Type &b);template<class Type>void BubbleSort(Type a[],int n);
int main()
{int n;int c = 7;//背包容量	cout<<"请输入物品数目:";	//物品数cin>>n;int p[n+1];// p[] = {0,9,10,7,4};//物品价值 下标从1开始p[0]=0;int w[n+1];//int w[] = {0,3,5,2,1};//物品重量 下标从1开始w[0]=0;cout<<"输入物品的价值序列：";for(int i=1;i<=n;i++){cin>>p[i];} cout<<"输入物品的重量序列：";for(int i=1;i<=n;i++){cin>>w[i];}cout<<"背包容量为："<<c<<endl;cout<<"物品重量和价值分别为："<<endl;for(int i=1; i<=n; i++){cout<<"("<<w[i]<<","<<p[i]<<") ";}cout<<endl;cout<<"背包能装下的最大价值为："<<Knapsack(p,w,c,n)<<endl;return 0;
}
template<class Typew,class Typep>
void Knap<Typew,Typep>::Backtrack(int i)
{if(i>n)//到达叶子节点{bestp = cp;return;}if(cw + w[i] <= c)//进入左子树{cw += w[i];cp += p[i];Backtrack(i+1);cw -= w[i];cp -= p[i];}if(Bound(i+1)>bestp)//进入右子树{Backtrack(i+1);}
}
template<class Typew, class Typep>
Typep Knap<Typew, Typep>::Bound(int i)// 计算上界
{Typew cleft = c - cw;  // 剩余容量Typep 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++;}// 装满背包if (i <= n){b += p[i]/w[i] * cleft;}return b;
}
class Object
{template<class Typew,class Typep>friend Typep Knapsack(Typep[],Typew [],Typew,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)
{//为Knap::Backtrack初始化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)//装入所有物品{return P;}//依物品单位重量价值排序BubbleSort(Q,n);Knap<Typew,Typep> K;K.p = new Typep[n+1];K.w = new Typew[n+1];for(int 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);delete []Q;delete []K.w;delete []K.p;return K.bestp;
}template<class Type>
void BubbleSort(Type a[],int n)
{//记录一次遍历中是否有元素的交换   bool exchange;  for(int i=0; i<n-1;i++)  {  exchange = false ;  for(int j=i+1; j<=n-1; j++)  {  if(a[j]<=a[j-1])  {  Swap(a[j],a[j-1]); exchange = true;  }   }   //如果这次遍历没有元素的交换,那么排序结束   if(false == exchange)  {break ;  }}
}
template <class Type>
inline void Swap(Type &a,Type &b)
{Type temp = a;a = b;b = temp;
}