2326: [HNOI2011]数学作业 - BZOJ

首先是DP，分段DP（按位数讨论）

然后每一段构造出它对应的矩阵，用矩阵快速幂加速

 type
         matrix=array[..,..]of int64;
 var
         n,m:int64;
         a,b,c,d:matrix;

 function min(x,y:int64):int64;
 begin
         if x<y then exit(x);
         exit(y);
 end;

 procedure cheng(var a,b:matrix);
 var
         i,j,k:longint;
 begin
         for i:= to  do
           for j:= to  do
             d[i,j]:=;
         for i:= to  do
           for j:= to  do
             for k:= to  do
               d[i,j]:=(d[i,j]+a[i,k]*b[k,j])mod m;
         a:=d;
 end;

 procedure main;
 var
         k,s:int64;
         i:longint;
 begin
         read(n,m);
         for i:= to  do
           a[i,i]:=;
         b[,]:=;
         b[,]:=;
         b[,]:=;
         b[,]:=;
         k:=;
         while n>=k do
           begin
             b[,]:=(k*)mod m;
             c:=b;
             s:=min(n,k*-)-k+;
             while s> do
               begin
                 if s and = then cheng(a,c);
                 cheng(c,c);
                 s:=s>>;
               end;
             k:=k*;
           end;
         write((a[,]+a[,])mod m);
 end;

 begin
         main;
 end.