2326: [HNOI2011]数学作业

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[1..3,1..3]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:=1 to 3 do
          for j:=1 to 3 do
            d[i,j]:=0;
        for i:=1 to 3 do
          for j:=1 to 3 do
            for k:=1 to 3 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:=1 to 3 do
          a[i,i]:=1;
        b[2,1]:=1;
        b[2,2]:=1;
        b[3,2]:=1;
        b[3,3]:=1;
        k:=1;
        while n>=k do
          begin
            b[1,1]:=(k*10)mod m;
            c:=b;
            s:=min(n,k*10-1)-k+1;
            while s>0 do
              begin
                if s and 1=1 then cheng(a,c);
                cheng(c,c);
                s:=s>>1;
              end;
            k:=k*10;
          end;
        write((a[2,1]+a[3,1])mod m);
end;
 
begin
        main;
end.