P4781 模板拉格朗日插值

Posted 2021-02-03 sdutning

P4781 【模板】拉格朗日插值

证明 ：https://wenku.baidu.com/view/0f88088a172ded630b1cb6b4.html

http://www.ebola.pro/article/notes/Lagrange

#include<bits/stdc++.h>
using namespace std;
#define mod 998244353
#define ll long long
#define maxn 2345
ll n,k,x[maxn],y[maxn],z,m,ans;
ll qpow(ll a,ll b)
{
    ll re=1;
    while(b)
    {
        if(b%2)re=(re*a)%mod;
        a=(a*a)%mod;
        b>>=1;
    }
    return re;
}
int main()
{
    scanf("%lld%lld",&n,&k);
    for(int i=1; i<=n; i++)
        scanf("%lld%lld",&x[i],&y[i]);
    for(int i=1; i<=n; i++)
    {
        z=y[i],m=1;
        for(int j=1; j<=n; j++)
        {
            if(i==j)continue;
            z=(z*(k-x[j])%mod+mod)%mod;
            m=(m*(x[i]-x[j])%mod+mod)%mod;
        }
        ans=(ans+z*qpow(m,mod-2)%mod+mod)%mod;
    }
    printf("%lld
",ans);
    return 0;
}