钢条切割-动态规划

来源：互联网发布：java阅读器编辑：程序博客网时间：2024/06/02 18:30
#include <iostream>#include <limits>#include <boost/timer/timer.hpp>using namespace std;using namespace boost::timer;int cut_rod(int *p,int n,int *result){if(n==0)return 0;int q =numeric_limits<int>::min();//q初始为最小值for(int i=0;i<n;i++){int val=p[i]+cut_rod(p,n-i-1,result);if(q<val){q=val;result[n]=i+1;}}return q;}void print_cut_rod(int *p, int n,int *result){cout<<cut_rod(p,n,result)<<endl;while (n>0){cout<<result[n]<<"\t";n-=result[n];}}int memo_cut_rod(int *r,int *p,int n,int *result)//备忘录法{if(n==0){//为0时返回return 0;}if(r[n-1]!=numeric_limits<int>::min()){//若该值已经存储，则直接返回，否则进行计算return r[n-1];}int q =numeric_limits<int>::min();//q初始为最小值for(int i=0;i<n;i++){int val=p[i]+memo_cut_rod(r,p,n-i-1,result);if (q<val){q=val;result[n]=i+1;}}r[n-1]=q;//创建备忘录return q;}void print_memo_cut_rod(int *r,int *p,int n,int *result){cout<<memo_cut_rod(r,p,n,result)<<endl;while(n>0){cout<<result[n]<<"\t";n-=result[n];}}int bottom_up_cut_rod(int *cos,int *p,int n,int *result)//自底向上法{int q;for(int i=1;i<=n;++i){q=numeric_limits<int>::min();for(int j=0;j<i;++j){if(q<p[j]+cos[i-j-1]){q=p[j]+cos[i-j-1];result[i]=j+1;}}cos[i]=q;}return cos[n];}void print_bottom_up_cut_rod(int *cos,int *p,int n,int *result)//打印bottom_up_cut_rod的信息{cout<<bottom_up_cut_rod(cos,p,n,result)<<endl;while(n>0){cout<<result[n]<<"\t";n-=result[n];}}int modified_cut_rod(int *cos,int *p,int n,int c,int *result){int q;for(int i=1;i<=n;++i){q=p[i-1];result[i]=i;for(int j=0;j<i-1;++j){int val=p[j]+cos[i-j-1]-c;if(q<val){q=val;result[i]=j+1;}}cos[i]=q; }return cos[n];}void print_modified_cut_rod(int *cos,int *p,int n,int c,int *result){cout<<modified_cut_rod(cos,p,n,c,result)<<endl;/*for(int i=1;i<=n;++i){cout<<result[i]<<"\t";}cout<<endl;*/while (n>0){cout<<result[n]<<"\t";n-=result[n];}cout<<endl;}int main(){int p[30]={1,5,8,9,10,17,18,20,24,30,33,35,38,39,43,47,48,50,54,60,62,63,68,69,73,75,78,80,84,90};//代价数组int n=28;int *cos =new int[n+1];int *result=new int[n+1];memset(cos,0,sizeof(int)*(n+1));memset(result,0,sizeof(int)*(n+1));cpu_timer t4;t4.start();print_modified_cut_rod(cos,p,n,1,result);t4.stop();cout<<t4.format();memset(cos,0,sizeof(int)*(n+1));memset(result,0,sizeof(int)*(n+1));cpu_timer t3;t3.start();print_bottom_up_cut_rod(cos,p,n,result);cout<<endl;t3.stop();cout<<t3.format();memset(result,0,sizeof(int)*(n+1));for(int i=0;i<=n;++i){cos[i]=numeric_limits<int>::min();}cout<<endl;cpu_timer t2;t2.start();print_memo_cut_rod(cos,p,n,result);cout<<endl;t2.stop();cout<<t2.format();memset(result,0,sizeof(int)*(n+1));cpu_timer t1;t1.start();print_cut_rod(p,n,result);cout<<endl;t1.stop();cout<<t1.format();delete [] cos;delete [] result;}
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