正题

题目链接:https://www.luogu.com.cn/problem/P4781

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题目大意

给出$n$个点确定一个多项式$y=f(x)$，求$f(k)$的值

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解题思路

拉格朗日插值：
$$f(k)=\sum _{i=1}^n{y}_i\prod _{i\ne j}\frac{k-x_j}{x_i-x_j}$$

时间复杂度$O(n^2)$

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$code$

#include<cstdio>
#include<cstring>
#include<algorithm>
#define ll long long
using namespace std;
const ll N=2e3+10,XJQ=998244353;
ll n,k,x[N],y[N],ans;
ll power(ll x,ll b){x%=XJQ;ll ans=1;while(b){if(b&1)ans=ans*x%XJQ;x=x*x%XJQ;b>>=1;}return ans;
}
int main()
{scanf("%lld%lld",&n,&k);for(ll i=1;i<=n;i++)scanf("%lld%lld",&x[i],&y[i]);for(ll i=1;i<=n;i++){for(ll j=1;j<=n;j++)if(i!=j)(y[i]*=(k-x[j]+XJQ)%XJQ*power(x[i]-x[j]+XJQ,XJQ-2)%XJQ)%=XJQ;(ans+=y[i])%=XJQ;		}printf("%lld",ans);
}