动态规划 的方法求矩阵乘法的最少计算加括号方式

#include<iostream>
#include<stdio.h>
using namespace std;

void init(int ***,int ***,int **,int);
void destroy(int ***,int ***,int **,int);
void MatrixChain(int ***,int ***,int *,int);
void TraceBack(int **s,int,int);

int main(void)
{
int ** m = NULL;
int ** s = NULL;
int *p = NULL;
int n = 0;

cout<<"请输入矩阵的个数:"<<endl;
cin>>n;

//初始化
init(&m,&s,&p,n);

MatrixChain(&m,&s,p,n);

printf("\n\nmatrix m's information:\n");
for(int i = 0;i < n;i++)
{
for(int j = 0;j < n;j++)
printf("%6d ",m[i][j]);
printf("\n");
}
printf("\n\nmatrix s's information:\n");
for(int i = 0;i < n;i++)
{
for(int j = 0;j < n;j++)
printf("%2d ",s[i][j]);
printf("\n");
}

//构造最优解
TraceBack(s,0,n-1);

//释放资源
destroy(&m,&s,&p,n);

return 0;

}

//分配资源(初始化)
void init(int ***m,int ***s,int **p,int  n)
{

//数组初始化

(*p) = new int[n+1];

(*m) = new int*
;
(*s) = new int*
;

for(int i = 0;i < n;i++)
(*m)[i] = new int
;

for(int i = 0;i < n;i++)
(*s)[i] = new int
;

//3õꌻˉ
for(int i = 0;i < n;i++)
{
for(int j = 0;j < n;j++)
{
(*m)[i][j] = 0;
(*s)[i][j] = 0;
}
}

cout<<"请输入维度信息:"<<endl;
for(int i = 0;i <= n;i++)
{
cin>>(*p)[i];
}

}

//构造最优解
void MatrixChain(int ***m,int ***s,int *p,int n)
{
//纵横轴的调试
for(int i = 1;i < n;i++)
{
for(int j = 0;j < n-i;j++)
{
int k = i+j;
(*m)[j][k] = (*m)[j+1][k]+p[j]*p[j+1]*p[k+1];
(*s)[j][k] = j;
for(int q = j+1;q < k;q++)
{
int t = (*m)[j][q]+(*m)[q+1][k] + p[j]*p[q+1]*p[k+1];
if(t < (*m)[j][k])
{
(*m)[j][k] = t;
(*s)[j][k] = q;
}
}
}
}
}

//释放资源
void destroy(int ***m,int ***s,int **p,int  n)
{
delete [] (*p);
(*p) = NULL;

for(int i = 0;i < n;i++)
{
delete [] (*s)[i];
delete [] (*m)[i];
(*s)[i] = NULL;
(*m)[i] = NULL;
}

delete [] (*s);
delete [] (*m);
(*s) = NULL;
(*m) = NULL;
}

//构造最优解

void TraceBack(int ** s,int i,int j)
{
if(i == j) return ;
TraceBack(s,i,s[i][j]);
TraceBack(s,s[i][j]+1,j);
cout<<"Multi A "<<i<<","<<s[i][j];
cout<<" and A "<<(s[i][j]+1)<<","<<j<<endl;
}