P3708 koishi的数学题(取模转化减法)

发布时间 2023-10-24 16:26:11作者: gan_coder

\(\displaystyle f(x) = \sum_{i=1}^n x \bmod i\)

对于一个i,枚举k
对于[xk, x(k+1) ),中的数,贡献的形式都为a[i]-i*k
直接差分维护即可

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
#include<map>
#include<vector>
#define A puts("YES")
#define B puts("NO")
#define fo(i,a,b) for (ll (i)=(a);(i)<=(b);(i)++)
#define fd(i,b,a) for (int (i)=(b);(i)>=(a);(i)--)
#define mk(x,y) make_pair((x),(y))
using namespace std;
typedef double db;
typedef long long ll;
const int N=1e6+5;
const ll mo=998244353;
ll n,c[N];
int main()
{
//	freopen("data.in","r",stdin);	
	
	scanf("%lld",&n);
	fo(i,1,n) {
		fo(j,1,n/i){
			c[i*j]+=i*j;
			c[min(i*(j+1),(ll)N-1)]-=i*j;
		}
	}
	
	ll ans=0;
	fo(i,1,n) {
		ans+=c[i];
		printf("%lld ",n*i-ans);
	}
	
    return 0;
}