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.