矩阵的快速比较 HDU2807 The Shortest Path

矩阵的快速比较 HDU2807 The Shortest Path

http://acm.hdu.edu.cn/showproblem.php?pid=2807

常规矩阵比较复杂度是O(n^2), 我们可把2维的数组乘以一个一维数组  来比较
通过这道题的测试，效果灰常让人吃惊。。。

常规比较的代码用C++提交超时，但是G++可以过掉，1484MS

#include  < iostream >
using   namespace  std;
#define  N 81
#define  INF 99999999
int  map[N][N], n, m;
struct  node{
     int  Map[N][N];
} rec[N];

struct  nnode{
     int  Map[N];
}recone[N];

void  cmp( int  a,  int  x)
{
     int  i;
     for  (i = 1 ; i <= m; i ++ )        
         if  (recone[x].Map[i]  !=  recone[ 0 ].Map[i])
             return ;
    map[a][x]  =   1 ;
}

void  creat( int  a,  int  b)
{
     int  i, j, k, s;
     for  (i = 1 ; i <= m; i ++ )
    {
        recone[ 0 ].Map[i]  =   0 ;
         for  (j = 1 ; j <= m; j ++ )
        {
            recone[ 0 ].Map[i]  +=  rec[a].Map[i][j]  *  recone[b].Map[j];            
        }
    }
        
     for  (i = 1 ; i <= n; i ++ )
         if  (i  !=  a  &&  i  !=  b)
            cmp(a, i);  // 判断 a 与 i的关系
}

int  main()
{
     int  i, j, k;
     while  (scanf( " %d %d " ,  & n,  & m), n + m)
    {
         for  (i = 1 ; i <= n; i ++ )
             for  (map[i][i] = 0 , j = i + 1 ; j <= n; j ++ )
                map[i][j]  =  map[j][i]  =  INF;  // 初始化矩阵之间关系
            
             for  (k = 1 ; k <= n; k ++ )
            {
                 for  (i = 1 ; i <= m; i ++ )
                {
                    recone[k].Map[i]  =   0 ;
                     for  (j = 1 ; j <= m; j ++ )
                    {
                        scanf( " %d " ,  & rec[k].Map[i][j]);
                        recone[k].Map[i]  +=  rec[k].Map[i][j]  *  j;  //    2->1
                    }
                }
            }  //  接受矩阵信息
            
             for  (i = 1 ; i <= n; i ++ )
                 for  (j = 1 ; j <= n; j ++ )
                     if  (i  !=  j)
                        creat(i, j);  //  处理矩阵 i*j
                    
                     for  (k = 1 ; k <= n; k ++ )
                         for  (i = 1 ; i <= n; i ++ )
                             for  (j = 1 ; j <= n; j ++ )
                                 if  (map[i][k]  +  map[k][j]  <  map[i][j])
                                    map[i][j]  =  map[i][k]  + map[k][j];
                                scanf( " %d " ,  & m);
                                 while  (m -- )
                                {
                                    scanf( " %d %d " ,  & i,  & j);
                                     if  (map[i][j]  !=  INF)
                                        printf( " %d\n " , map[i][j]);
                                     else
                                        printf( " Sorry\n " );
                                }
    }
     return   0 ;
}