多项式除法及求模的计算复杂度

void polynomial_division(int n, int m, long long *A, long long *B, long long *D, long long *R)
{
    static long long A0[MaxN], B0[MaxN];

    int p = 1, t = n - m + 1;
    while(p < t << 1) p <<= 1;

    fill(A0, A0 + p, 0);
    reverse_copy(B, B + m, A0);
    polynomial_inverse(t, A0, B0);
    fill(B0 + t, B0 + p, 0);
    transform(p, B0);

    reverse_copy(A, A + n, A0);
    fill(A0 + t, A0 + p, 0);
    transform(p, A0);

    for(int i = 0; i != p; ++i)
        A0[i] = A0[i] * B0[i] % mod_v;
    inverse_transform(p, A0);
    reverse(A0, A0 + t);
    copy(A0, A0 + t, D);

    for(p = 1; p < n; p <<= 1);
    fill(A0 + t, A0 + p, 0);
    transform(p, A0);
    copy(B, B + m, B0);
    fill(B0 + m, B0 + p, 0);
    transform(p, B0);
    for(int i = 0; i != p; ++i)
        A0[i] = A0[i] * B0[i] % mod_v;
    inverse_transform(p, A0);
    for(int i = 0; i != m; ++i)
        R[i] = (A[i] - A0[i]) % mod_v;
    fill(R + m, R + p, 0);
}

http://blog.miskcoo.com/2015/05/polynomial-division

应用
多项式的扩展欧几里德算法
多项式的乘法逆元
多项式的多点求值