bzoj 1025 DP

这道题根据群论的基础知识，我们可以转化成将n拆分成若干数，求这些数

的lcm的方案数

先筛下素数表prime

那么我们可以用DP来解决这个问题，用W[I,J]代表I这个数，拆成若干个数，

其中质因数最大的不超过prime[j]的方案数

那么我们可以得到转移W[I,J]:=W[I,J-1]+ΣW[I-prime[j]^k,j-1] （I>=prime[j]）

 

/**************************************************************

    Problem: 1025

    User: BLADEVIL

    Language: Pascal

    Result: Accepted

    Time:44 ms

    Memory:8220 kb

****************************************************************/

 

//By BLADEVIL

var

    prime                       :array[0..1010] of longint;

    mindiv                      :array[0..1010] of longint;

    i, j                        :longint;

    n                           :longint;

    w                           :array[0..1010,0..1010] of int64;

    cur                         :longint;

     

begin

    read(n);

    for i:=2 to n do

    begin

        if mindiv[i]=0 then

        begin

            inc(prime[0]);

            prime[prime[0]]:=i;

            mindiv[i]:=i;

        end;

        for j:=1 to prime[0] do

        begin

            if prime[j]*i>n then break;

            mindiv[prime[j]*i]:=prime[j];

            if i mod prime[j]=0 then break;

        end;

    end;

     

    for i:=0 to n do w[i,0]:=1;

    for i:=1 to prime[0] do w[0,i]:=1;

     

    for j:=1 to prime[0] do

        for i:=1 to n do

        begin

            w[i,j]:=w[i,j-1];

            cur:=prime[j];

            while i-cur>=0 do

            begin

                w[i,j]:=w[i,j]+w[i-cur,j-1];

                cur:=cur*prime[j];

            end;

        end;

    writeln(w[n,prime[0]]);

end.