P4781 【模板】拉格朗日插值

传送门
在这里插入图片描述

把公式实现一下即可：在这里插入图片描述
当 $x$ 连续的时候可以优化为 $O (N)$ 。

// Problem: P4781 【模板】拉格朗日插值
// Contest: Luogu
// URL: https://www.luogu.com.cn/problem/P4781
// Memory Limit: 125 MB
// Time Limit: 1000 ms
// 
// Powered by CP Editor (https://cpeditor.org)//#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native")
//#pragma GCC optimize(2)
#include<cstdio>
#include<iostream>
#include<string>
#include<cstring>
#include<map>
#include<cmath>
#include<cctype>
#include<vector>
#include<set>
#include<queue>
#include<algorithm>
#include<sstream>
#include<ctime>
#include<cstdlib>
#include<random>
#include<cassert>
#define X first
#define Y second
#define L (u<<1)
#define R (u<<1|1)
#define pb push_back
#define mk make_pair
#define Mid ((tr[u].l+tr[u].r)>>1)
#define Len(u) (tr[u].r-tr[u].l+1)
#define random(a,b) ((a)+rand()%((b)-(a)+1))
#define db puts("---")
using namespace std;//void rd_cre() { freopen("d://dp//data.txt","w",stdout); srand(time(NULL)); }
//void rd_ac() { freopen("d://dp//data.txt","r",stdin); freopen("d://dp//AC.txt","w",stdout); }
//void rd_wa() { freopen("d://dp//data.txt","r",stdin); freopen("d://dp//WA.txt","w",stdout); }typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int,int> PII;const int N=1000010,mod=998244353,INF=0x3f3f3f3f;
const double eps=1e-6;LL n,k;
pair<LL,LL> p[N];LL qmi(LL a,LL b) {LL ans=1;a%=mod; a+=mod; a%=mod;while(b) {if(b&1) ans=ans*a%mod;a=a*a%mod;b>>=1;}return ans%mod;
}int main()
{
//	ios::sync_with_stdio(false);
//	cin.tie(0);scanf("%lld%lld",&n,&k);for(int i=1;i<=n;i++) scanf("%lld%lld",&p[i].X,&p[i].Y);LL ans=0;for(int i=1;i<=n;i++) {LL now1=p[i].Y,now2=1;for(int j=1;j<=n;j++) {if(i==j) continue;now1*=((k-p[j].X+mod)%mod); now1%=mod;now2*=p[i].X-p[j].X; now2%=mod;}now2=qmi(now2,mod-2);ans+=now1*now2%mod; ans%=mod;}printf("%lld\n",ans%mod);return 0;
}
/**/