n个矩阵连乘问题

 #include<iostream>

using namespace std;

 

int m[100][100];

int r[101];

 

int matrix(int i, int j)

{

int u,k,t;

if(m[i][j]>=0)

return m[i][j];

if(i==j)

return 0;

if(i==(j-1))

{

m[i][j]=r[i]*r[i+1]*r[i+2];

return m[i][j];

}

u=matrix(i,i)+matrix(i+1,j)+r[i]*r[i+1]*r[j+1];

for(k=i+1;k<j;k++)

{

t=matrix(i,k)+matrix(k+1,j)+r[i]*r[k+1]*r[j+1];

if(t<u)

u=t;

}

m[i][j] = u;

return u;

}

 

int main()

{

int n;

cout<<"请输入矩阵数目："<<endl;

cin>>n;

int i,j;

cout<<"请输入"<<n+1<<"个矩阵系数"<<endl;

for(i=1;i<=n+1;i++)

cin>>r[i];

for(i=1;i<=n+1;i++)

for(j=1;j<=n+1;j++)

m[i][j]=-1;

cout<<"最少乘法运算次数为："<<matrix(1,n)<<endl;

return 0;

}