ACM程序&算法

   算法设计 动态规划 矩阵连乘问题

////////////////////////////////////////////////////////////////

//TITLE: 矩阵连乘问题

//EDITOR:小桥流水

//DADE： 2008.11.16

//TOOL:  Microsoft Visual Studio 2008

////////////////////////////////////////////////////////////////

 

#include<iostream>

usingnamespacestd;

 

//计算最优值

voidMatrixChain(int *p,intn,int **m,int **s)

{

   for (inti = 1;i <= n;i++)

   {

       m[i][i] = 0;

   }

   for (intr = 2;r <= n;r++)

   {

       for (inti = 1;i <=n-r+1;i++)

       {

           intj = i+r-1;

           m[i][j] =m[i+1][j] +p[i-1]*p[i]*p[j];

           s[i][j] =i;

           for(intk = i+1;k <j;k++)

           {

               intt = m[i][k] +m[k+1][j] +p[i-1]*p[k]*p[j];

               if (t <m[i][j])

               {

                   m[i][j] =t;

                   s[i][j] =k;

               }

           }

       }

   }

}

 

//构造最优解

voidTraceback(inti,intj,int **s)

{

   if (i ==j)

       return ;

   Traceback(i,s[i][j],s);

   Traceback(s[i][j]+1,j,s);

   cout<<"Multiply A"<<i<<","<<s[i][j];

   cout<<"and A"<<s[i][j]+1<<","<<j<<endl;

}

 

intmain()

{

   intN,*P,**M,**S;

   cout<<"输入矩阵的个数N: ";

   cin>>N;

   P = new int [N+1]; //为矩阵的维数分配空间

   M = new int *[N+1];//为二维数组M动态分配空间

   for (inti = 0;i <= N;i++)

   {

       M[i] =new int [N+1];

   }

   S = new int *[N+1]; //为记录最优断开位置的二

   //维数组S动态分配空间

   for (inti = 0;i <= N;i++)

   {

       S[i] =new int [N+1];

   }

 

   for (inti = 0;i <= N;i++)

   {

       cin>>P[i];

   }

 

   MatrixChain(P,N,M,S);

   Traceback(1,N,S);

 

   //释放动态分配的空间

   delete []P;

   for (inti = 0;i <=N;i++)

   {

       deleteM[i];

       M[i] =NULL;

   }

   delete []M;

   M = NULL;

   for (inti = 0;i <=N;i++)

   {

       deleteS[i];

       S[i] =NULL;

   }

   delete []S;

   S = NULL;

 

   return 0;

}