算法分析与设计——动态规划矩阵连乘问题C++

#include <iostream>

using namespace std;

#define N 7
int MatrixChain(int *p,int n,int m[][N],int s[][N])
{
    
    
	for(int i=1;i<=n;i++){
    
    
		m[i][i]=0;
		
	}
	for(int r=2;r<=n;r++){
    
    
		for(int i=1;i<=n-r+1;i++){
    
    
			int j=i+r-1;
			m[i][j]=m[i][i]+m[i+1][j]+p[i-1]*p[i]*p[j];
			s[i][j]=i;
			for(int k=i+1;k<j;k++){
    
    
				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;
				} 
			}
		}
	}
}

void Traceback(int i,int j,int s[][N]){
    
    
	if(i==j){
    
    
		cout<<"A"<<i;
		
	}
	else{
    
    
		cout<<"(";
		Traceback(i,s[i][j],s);
		Traceback(s[i][j]+1,j,s);
		cout<<")"; 
	}
}
int main()
{
    
    
	int p[N]={
    
    30,35,15,5,10,20,25};
	int m[N][N],s[N][N];
	MatrixChain(p,N-1,m,s);
	Traceback(1,6,s);
	return 0;
	
    
}