【动态规划】矩阵连乘分析

 1 //3d1-1 重叠子问题的递归最优解
 2 //A1 30*35 A2 35*15 A3 15*5 A4 5*10 A5 10*20 A6 20*25
 3 //p[0-6]={30,35,15,5,10,20,25}
 4 #include "stdafx.h"
 5 #include <iostream> 
 6 using namespace std; 
 7 
 8 const int L = 7;
 9 
10 int RecurMatrixChain(int i,int j,int **s,int *p);//递归求最优解
11 void Traceback(int i,int j,int **s);//构造最优解
12 
13 int main()
14 {
15     int p[L]={30,35,15,5,10,20,25};
16 
17     int **s = new int *[L];
18     for(int i=0;i<L;i++)  
19     {  
20         s[i] = new int[L];  
21     } 
22 
23     cout<<"矩阵的最少计算次数为："<<RecurMatrixChain(1,6,s,p)<<endl;
24     cout<<"矩阵最优计算次序为："<<endl;
25     Traceback(1,6,s);
26     return 0;
27 }
28 
29 int RecurMatrixChain(int i,int j,int **s,int *p)
30 {
31     if(i==j) return 0;
32     int u = RecurMatrixChain(i,i,s,p)+RecurMatrixChain(i+1,j,s,p)+p[i-1]*p[i]*p[j];
33     s[i][j] = i;
34 
35     for(int k=i+1; k<j; k++)
36     {
37         int t = RecurMatrixChain(i,k,s,p) + RecurMatrixChain(k+1,j,s,p) + p[i-1]*p[k]*p[j];
38         if(t<u)
39         {
40             u=t;
41             s[i][j]=k;
42         }
43     }
44     return u;
45 }
46 
47 void Traceback(int i,int j,int **s)
48 {
49     if(i==j) return;
50     Traceback(i,s[i][j],s);
51     Traceback(s[i][j]+1,j,s);
52     cout<<"Multiply A"<<i<<","<<s[i][j];
53     cout<<" and A"<<(s[i][j]+1)<<","<<j<<endl;
54 }

1 int u = RecurMatrixChain(i,i,s,p)+RecurMatrixChain(i+1,j,s,p)+p[i-1]*p[i]*p[j]; 
2 //为下面执行的找最小代价的算法提供比较初值   
3  s[i][j] = i;//因为比较是<而不是<=，故也要对s[i][j]赋初值