洛谷P1587 [NOI2016]循环之美

传送门

 

不会，先坑着

https://kelin.blog.luogu.org/solution-p1587

//minamoto
#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;
const int N=7e5+5,E=2e6+5;
typedef int arr[N];typedef long long ll;
struct Am{int nx,x,w;}e1[E];
struct Ans{int nx,n,m,k;ll w;}e2[E];
int n,m,k,M,c1,c2,K[2005],f1[E],f2[E];arr vis,p,mu,sum;
int Sm(int x){
    if(x<=M) return sum[x];
    int u=(x+2017)%E;
    for(int i=f1[u];i;i=e1[i].nx)
    if(e1[i].x==x) return e1[i].w;
    e1[++c1]=(Am){f1[u],x,1},f1[u]=c1;
    int &w=e1[c1].w,i=2,j=sqrt(x);
    for(;i<=j;++i) w-=Sm(x/i);
    for(;i<=x;i=j+1)
    j=x/(x/i),w-=(j-i+1)*Sm(x/i);
    return w;
}
ll sol(int n,int m,int k){
    if(!n||!m) return 0;
    int u=(2017ll*n+m+k)%E;
    for(int i=f2[u];i;i=e2[i].nx)
    if(e2[i].n==n&&e2[i].m==m&&e2[i].k==k) return e2[i].w;
    e2[++c2]=(Ans){f2[u],n,m,k,0},f2[u]=c2;ll &w=e2[c2].w;
    if(k==1){
        if(n>m) swap(n,m);
        int i=1,j=sqrt(n),s,t=0,x,y;
        for(;i<=j;++i,t=s) s=Sm(i),w+=1ll*(n/i)*(m/i)*(s-t);
        for(;i<=n;i=j+1,t=s)x=n/i,y=m/i,j=min(n/x,m/y),s=Sm(j),w+=1ll*x*y*(s-t);
        u=(2017ll*m+n+k)%E;e2[++c2]=(Ans){f2[u],m,n,k,w},f2[u]=c2;
    }
    else for(int i=1;i<=K[0]&&K[i]<=k;++i)
    if(k%K[i]==0&&mu[K[i]])
    w+=sol(m/K[i],n,K[i])*mu[K[i]];
    return w;
}
int main(){
//    freopen("testdata.in","r",stdin);
    scanf("%d%d%d",&n,&m,&k);
    M=min(N-5,max(k,min(n,m))),sum[1]=mu[1]=1;
    for(int i=2;i<=M;++i){
        if(!vis[i]) p[++p[0]]=i,mu[i]=-1;
        for(int j=1,x;j<=p[0]&&(x=i*p[j])<=M;++j){
            vis[x]=1;
            if(i%p[j]==0) break;
            mu[x]=-mu[i];
        }
        sum[i]=sum[i-1]+mu[i];
    }
    for(int i=1;i<=k;++i)
    if(k%i==0) K[++K[0]]=i;
    printf("%lld\n",sol(n,m,k));
    return 0;
}