c_cpp 给定Ñ个矩阵:A1,A2,...,AN,其中艾与艾+ 1是可乘的,I = 1,2,...,N-1确定计算矩阵连乘积的计算次序,使得依此次序计算矩阵连乘积需要的数乘次数最少。输入数
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//3d1-1 重叠子问题的递归最优解
//A1 30*35 A2 35*15 A3 15*5 A4 5*10 A5 10*20 A6 20*25
//p[0-6]={30,35,15,5,10,20,25}
#include "stdafx.h"
#include <iostream>
using namespace std;
const int L = 7;
int RecurMatrixChain(int i,int j,int **s,int *p);//递归求最优解
void Traceback(int i,int j,int **s);//构造最优解
int main()
{
int p[L]={30,35,15,5,10,20,25};
int **s = new int *[L];
for(int i=0;i<L;i++)
{
s[i] = new int[L];
}
cout<<"矩阵的最少计算次数为:"<<RecurMatrixChain(1,6,s,p)<<endl;
cout<<"矩阵最优计算次序为:"<<endl;
Traceback(1,6,s);
return 0;
}
int RecurMatrixChain(int i,int j,int **s,int *p)
{
if(i==j) return 0;
int u = RecurMatrixChain(i,i,s,p)+RecurMatrixChain(i+1,j,s,p)+p[i-1]*p[i]*p[j];
s[i][j] = i;
for(int k=i+1; k<j; k++)
{
int t = RecurMatrixChain(i,k,s,p) + RecurMatrixChain(k+1,j,s,p) + p[i-1]*p[k]*p[j];
if(t<u)
{
u=t;
s[i][j]=k;
}
}
return u;
}
void Traceback(int i,int j,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;
}
//3d1-2 矩阵连乘 备忘录递归实现
//A1 30*35 A2 35*15 A3 15*5 A4 5*10 A5 10*20 A6 20*25
//p[0-6]={30,35,15,5,10,20,25}
#include "stdafx.h"
#include <iostream>
using namespace std;
const int L = 7;
int LookupChain(int i,int j,int **m,int **s,int *p);
int MemoizedMatrixChain(int n,int **m,int **s,int *p);
void Traceback(int i,int j,int **s);//构造最优解
int main()
{
int p[L]={30,35,15,5,10,20,25};
int **s = new int *[L];
int **m = new int *[L];
for(int i=0;i<L;i++)
{
s[i] = new int[L];
m[i] = new int[L];
}
cout<<"矩阵的最少计算次数为:"<<MemoizedMatrixChain(6,m,s,p)<<endl;
cout<<"矩阵最优计算次序为:"<<endl;
Traceback(1,6,s);
return 0;
}
int MemoizedMatrixChain(int n,int **m,int **s,int *p)
{
for(int i=1; i<=n; i++)
{
for(int j=1; j<=n; j++)
{
m[i][j]=0;
}
}
return LookupChain(1,n,m,s,p);
}
int LookupChain(int i,int j,int **m,int **s,int *p)
{
if(m[i][j]>0)
{
return m[i][j];
}
if(i==j)
{
return 0;
}
int u = LookupChain(i,i,m,s,p) + LookupChain(i+1,j,m,s,p)+p[i-1]*p[i]*p[j];
s[i][j]=i;
for(int k=i+1; k<j; k++)
{
int t = LookupChain(i,k,m,s,p) + LookupChain(k+1,j,m,s,p) + p[i-1]*p[k]*p[j];
if(t<u)
{
u=t;
s[i][j] = k;
}
}
m[i][j] = u;
return u;
}
void Traceback(int i,int j,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;
}
//3d1-2 矩阵连乘 动态规划迭代实现
//A1 30*35 A2 35*15 A3 15*5 A4 5*10 A5 10*20 A6 20*25
//p[0-6]={30,35,15,5,10,20,25}
#include "stdafx.h"
#include <iostream>
using namespace std;
const int L = 7;
int MatrixChain(int n,int **m,int **s,int *p);
void Traceback(int i,int j,int **s);//构造最优解
int main()
{
int p[L]={30,35,15,5,10,20,25};
int **s = new int *[L];
int **m = new int *[L];
for(int i=0;i<L;i++)
{
s[i] = new int[L];
m[i] = new int[L];
}
cout<<"矩阵的最少计算次数为:"<<MatrixChain(6,m,s,p)<<endl;
cout<<"矩阵最优计算次序为:"<<endl;
Traceback(1,6,s);
return 0;
}
int MatrixChain(int n,int **m,int **s,int *p)
{
for(int i=1; i<=n; i++)
{
m[i][i] = 0;
}
for(int r=2; r<=n; r++) //r为当前计算的链长(子问题规模)
{
for(int i=1; i<=n-r+1; i++)//n-r+1为最后一个r链的前边界
{
int j = i+r-1;//计算前边界为r,链长为r的链的后边界
m[i][j] = m[i+1][j] + p[i-1]*p[i]*p[j];//将链ij划分为A(i) * ( A[i+1:j] )
s[i][j] = i;
for(int k=i+1; k<j; k++)
{
//将链ij划分为( A[i:k] )* (A[k+1:j])
int t = 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;
}
}
}
}
return m[1][L-1];
}
void Traceback(int i,int j,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;
}
以上是关于c_cpp 给定Ñ个矩阵:A1,A2,...,AN,其中艾与艾+ 1是可乘的,I = 1,2,...,N-1确定计算矩阵连乘积的计算次序,使得依此次序计算矩阵连乘积需要的数乘次数最少。输入数的主要内容,如果未能解决你的问题,请参考以下文章
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