bzoj 2301 莫比乌斯反演

Posted 2020-10-06 ( m Lweleth)

求$(i,j)=k$的一系列模板题之一。

但是这里i,j是有下界的，注意用容斥去掉重复组，其他都一样了。

 

 

/** @Date    : 2017-09-09 19:21:18
  * @FileName: bzoj 2301 莫比乌斯反演 多组 范围内 GCD=k.cpp
  * @Platform: Windows
  * @Author  : Lweleth ([email protected])
  * @Link    : https://github.com/
  * @Version : $Id$
  */
#include <bits/stdc++.h>
#define LL long long
#define PII pair<int ,int>
#define MP(x, y) make_pair((x),(y))
#define fi first
#define se second
#define PB(x) push_back((x))
#define MMG(x) memset((x), -1,sizeof(x))
#define MMF(x) memset((x),0,sizeof(x))
#define MMI(x) memset((x), INF, sizeof(x))
using namespace std;

const int INF = 0x3f3f3f3f;
const int N = 5e4+20;
const double eps = 1e-8;

int pri[N];
int mu[N];
int c = 0;
int vis[N];
LL sum[N];

void prime()
{
	MMF(vis);
	mu[1] = 1;
	for(int i = 2; i < N; i++)
	{
		if(!vis[i])
			pri[c++] = i, mu[i] = -1;
		for(int j = 0; j < c && i * pri[j] < N; j++)
		{
			vis[i * pri[j]] = 1;
			if(i % pri[j] == 0)
			{
				mu[i * pri[j]] = 0;
				break;
			}
			else mu[i * pri[j]] = -mu[i];
		}
	}
	sum[0] = 0;
	for(int i = 1; i < N; i++)
		sum[i] += sum[i - 1] + mu[i];
}

LL getsum(LL n, LL m)
{
	LL ans = 0;
	if(n > m) swap(n, m);
	for(int i = 1, last; i <= n; i = last + 1)
	{
		last = min(n/(n/i), m/(m/i));
		ans += (LL)(n / i) * (m / i) * (sum[last] - sum[i - 1]);
	}
	return ans;
}

int main()
{
	int T;
	prime();
	cin >> T;
	while(T--)
	{
		LL a, b, c, d, k;
		scanf("%lld%lld%lld%lld%lld", &a, &b, &c, &d, &k);
		a = (a - 1) / k;
		b = b / k;
		c = (c - 1) / k;
		d = d / k;
		LL ans = getsum(a, c) + getsum(b, d) - getsum(a, d) - getsum(b, c);//容斥
		printf("%lld\n", ans);
	}
    return 0;
}