Fast power-related matrix

Fast Power matrix may be O (n) linear recursive optimization to O (log n), is a very good optimization

Did a lot of questions, feel better, I learned a lot.

However, doing P2151 [SDOI2009] HH go for a walk  when the people are autistic up. Autistic after a morning + noon, afternoon finally want to understand.

After AC, write a blog about the matter recorded rapid matrix powers.

1. Handwritten matrix structure, package various functions.

    1 struct Mar{
    2     int a[maxm][maxm],n;
    3     Mar (int _n=0) {n=_n;memset(a,0,sizeof a);}//不传参数默认为0
    4     Mar operator ~ () {for(int i=0;i<n;i++) a[i][i]=1;}//单位矩阵
    5     Mar operator * (const Mar &b) const {
    6         Mar c(n);
    7         for(int i=0;i<n;i++) for(int j=0;j<n;j++) for(int k=0;k<n;k++)
    8             c.a[i][j]=(c.a[i][j]+a[i][k]%mod*b.a[k][j]%mod)%mod;
    9         return c;
   10     }
   11     Mar operator ^ (int b){//快速幂
   12         Mar c(n),x=*this;~c;//  "*this" 有意思
   13         while(b){
   14             if(b&1) c=c*x;
   15             x=x*x;
   16             b>>=1;
   17         }
   18         return c;
   19     }
   20 };

2. Mar ans (15) indicates a length and width of the opening n matrix; Mar ans () denotes a length and width for the opening 0 of the matrix.
3. Matrix multiplication is not commutative, to distinguish between left and right multiplication multiply;
4. P2151 [SDOI2009] HH to walk  a little bit different, the relationship between the points is replaced Unicom Unicom side relationship, without the side edge unidirectional stored twice. I finally found a moment of multiplication principle:       Figure represents A * B = C

　　　　　　It looks like the feeling of three views. Color line represents the length is equal, the blue line can be multiplied conditions.

　　　　　　C in the i-th row, j-th column is equal to the value of the i-th row out of A, B of the j-th column out, put together sequentially multiplied (that is, the blue line and the like).

　　　　　　Gone. .