矩阵连乘最优解---动态规划

 

代码如下：

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <map>
#define N 1000005
using namespace std;
int p[1005],s[1005][1005],dp[1005][1005];

void print(int i,int j)
{
    if(i==j)
    {
        cout<<"A"<<i;
        return ;
    }

    int k=s[i][j];
    if(i==k)        cout<<"A"<<i;
    else if(i<k-1)
    {
        cout<<"(";
        print(i,k);
        cout<<")";
    }
    else if(i==k-1) cout<<"(A"<<i<<"A"<<k<<")";

    if(k+1==j)         cout<<"A"<<k+1;
    else if(k+1<j-1)
    {
        cout<<"(";
        print(k+1,j);
        cout<<")";
    }
    else if(k+1==j-1)  cout<<"(A"<<k+1<<"A"<<j<<")";
}

int main()
{
    int n;
    printf("input matrix number:");
    scanf("%d",&n);
    for(int i=0; i<=n; i++)
        scanf("%d",&p[i]);
    memset(dp,0,sizeof(dp));
    for(int len=1; len<n; len++)
    {
        for(int i=1; i+len<=n; i++)
        {
            dp[i][i+len]=dp[i+1][i+len]+p[i-1]*p[i]*p[i+len];
            s[i][i+len]=i;
            for(int k=i+1; k<i+len; k++)
            {
                int t=dp[i][k]+dp[k+1][i+len]+p[i-1]*p[k]*p[i+len];
                if(dp[i][i+len]>t)
                {
                    dp[i][i+len]=t;
                    s[i][i+len]=k;
                }
            }
        }
    }
    for(int i=1; i<=n; i++)
    {
        for(int j=1; j<=n; j++)
        {
            if(j<i) printf("      ");
            else    printf("%6d",dp[i][j]);
        }
        cout<<endl;
    }

    cout<<"answer: ";
    cout<<"(";
    print(1,n);
    cout<<")"<<endl;
    return 0;
}

 运行截图：