拉格朗日插值模板

已知 $n$ 个点，快速确定一个 $n-1$ 次多项式。

求 $f(x)$ 。

$$f(x)=\sum _{i=1}^n{y}_i\prod _{j\ne i}{\displaystyle \frac{x-x_j}{x_i-x_j}}$$

查看代码

#include <cstdio>
#include <utility>
using namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int N = 2e3 + 10, mod = 998244353;
PII p[N];
int n, k;
LL binpow(LL b, int k)
{
    LL res = 1;
    while (k)
    {
        if (k & 1)
            res = res * b % mod;
        b = b * b % mod;
        k >>= 1;
    }
    return res;
}
int main()
{
    scanf("%d%d", &n, &k);
    for (int i = 1; i <= n; i++)
        scanf("%d%d", &p[i].first, &p[i].second);
    LL res = 0;
    for (int i = 1; i <= n; i++)
    {
        LL s = p[i].second;
        for (int j = 1; j <= n; j++)
            if (i != j)
                s = s * (k - p[j].first) % mod * binpow(p[i].first - p[j].first, mod - 2) % mod;
        res = (res + s) % mod;
    }
    printf("%lld", (res % mod + mod) % mod);
    return 0;
}