【BZOJ】2820: YY的GCD（莫比乌斯）_#include <cstdio> #include <cstring> #include <alg-优快云博客

本文链接：https://blog.youkuaiyun.com/idle2fish/article/details/81666096

本文详细介绍了一个基于数论的算法实现，包括预处理素数、莫比乌斯函数以及利用这些函数进行快速计数的方法。通过具体示例展示了如何解决特定类型的组合计数问题。

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先留着，晚上继续写

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#include<string>
#include<vector>
#include<stack>
#include<bitset>
#include<cstdlib>
#include<cmath>
#include<set>
#include<list>
#include<deque>
#include<map>
#include<queue>
using namespace std;
typedef long long ll;
const double PI = acos(-1.0);
const double eps = 1e-6;
const int INF = 1000000000;
const int maxn = 1000000;
const ll mod = 1e9+7;
int T,n,m;
ll f[maxn+5];
int vis[maxn+5],prime[maxn+5],mu[maxn+5];
int tot = 0;
int read(){
    char c=getchar();int x=0,f=1;
    while(c<'0'||c>'9'){if(c=='-')f=-1; c=getchar();}
    while(c>='0'&&c<='9'){x=x*10+c-'0'; c=getchar();}
    return x*f;
}
void init (){
    mu[1]=1;
    memset(vis, 0, sizeof(vis));
    for (int i=2;i<=maxn;i++){
        if (!vis[i]){
            prime[++tot]=i;
            mu[i]=-1;
            f[i] = 1;
        }
        for (int j=1;j<=tot &&prime[j]*i<=maxn;j++){
            vis[i*prime[j]] = 1;
            if (i%prime[j]==0){
                mu[i*prime[j]]=0;
                f[i*prime[j]]=mu[i];
                break;
            }
            else {
                mu[i*prime[j]]=-mu[i];
                f[i*prime[j]]=mu[i]-f[i];
            }
        }
    }
    for (int i=1;i<=maxn;i++){
        f[i]+=f[i-1];
    }
}
int main (){
    init ();
    cin >>T;
    while (T--){
        ll ans = 0;
        scanf ("%d %d",&n,&m);
        if (n>m) swap (n,m);
        int last;
        for (int i=1;i<=m;i=last+1){
            last = min(n/(n/i),m/(m/i));
            ans += (f[last]-f[i-1])*(n/i)*(m/i);
        }
        printf("%lld\n",ans);
    }
    return 0;
}