abc335F - Hop Sugoroku

发布时间 2024-01-12 10:59:32作者: gan_coder

abc335F - Hop Sugoroku

首先容易想到\(O(n^2)\)的dp
考虑优化,对于一个i,只会对满足\(i+a[i]*x=j\)的j有贡献。
也就是j%a[i]=i%a[i]
那么我们可以延迟转移,用cnt[a[i]][i%a[i]],来记录贡献,
然后我们数组不可能开那么大,所以以根号为分界,小于根号的就用cnt记录,大于根号的就可以直接算,因为不会超过\(\sqrt{n}\)
时间复杂度\(O(n\sqrt{n})\)

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<map>
#include<queue>
#include<bitset>
#include<cmath>
#define fo(i,a,b) for (ll (i)=(a);(i)<=(b);(i)++)
#define fd(i,b,a) for (ll (i)=(b);(i)>=(a);(i)--)
#define mk(x,y) make_pair((x),(y))
#define A puts("Yes")
#define B puts("No")
using namespace std;
typedef double db;
typedef long long ll;
const int N=1e6+5;
const ll inf = 1ll << 60;
const ll mo = 998244353;
const ll mo1=1e9+7;
const ll mo2=1e9+9;
const ll P=131;
const ll Q=13331;
ll n,f[N],cnt[1005][1005],a[N],sq,x;
void add(ll &x,ll y){
	x=(x+y)%mo;
}
int main()
{
//	freopen("data.in","r",stdin);
	
	scanf("%lld",&n);
	fo(i,1,n) scanf("%lld",&a[i]);
	
	sq=sqrt(n)+3;
	f[1]=1;
	fo(i,1,n) {
		fo(j,1,sq) add(f[i], cnt[j][i%j]);
		
		if (a[i]>sq) {
			fo(j,1,n) {
				x=a[i]*j+i;
				if (x>n) break;
				add(f[x], f[i]);
			}
		}
		else {
			add(cnt[a[i]][i%a[i]], f[i]);
		}
	}
	ll ans=0;
	fo(i,1,n) add(ans, f[i]);
	printf("%lld",ans);
	
	
	return 0;
}