多項式板子 新

upd於2.19:拉格朗日反演、多項式倍增快速冪

(好像是還差乙個多項式取模...)算了不寫了

注意本板子使用過程中：每個函式傳的len一定要保證是2的倍數，並且傳遞的陣列需要保證他有多於2*len的空間

每個函式傳進來的指標保證[0,len)有值，[len,2*len)有定義

注意new出來的記憶體一定要清零，不然肯定會炸

#include #include using namespace std;

const int p = 998244353;
int qpow(int x, int y)
return res;
}void ntt(int *a, int len, int flag)
} if (flag == -1)
delete r;
}void poly_inv(int *a, int len)
int len1 = len / 2;
int *f0 = new int[len * 2];
for (int i = 0; i < len1; i++) f0[i] = a[i];
for (int i = len1; i < len * 2; i++) f0[i] = 0;
poly_inv(f0, len1);
for (int i = len1; i < len * 2; i++) f0[i] = 0;
ntt(f0, len * 2, 1), ntt(a, len * 2, 1);
for (int i = 0; i < len * 2; i++) a[i] = ((2 * f0[i] % p - a[i] * (long long)f0[i] % p * f0[i] % p) % p + p) % p;
ntt(a, len * 2, -1);
for (int i = len; i < len * 2; i++) a[i] = 0;
delete f0;
}void poly_derivation(int *a, int len)
void poly_intergal(int *a, int len)
void poly_ln(int *a, int len)
//這裡本來應該打二次剩餘的，但是因為那道題只有常數項為1的情況，就寫了暴力列舉了
int mod_sqrt(int x)
void poly_sqrt(int *a, int len)
int len1 = len / 2;
int *f0 = new int[len * 2];
for (int i = 0; i < len1; i++) f0[i] = a[i];
for (int i = len1; i < len * 2; i++) f0[i] = 0;
poly_sqrt(f0, len1);
for (int i = len1; i < len * 2; i++) f0[i] = 0;
int *tmp = new int[len * 2];
for (int i = 0; i < len * 2; i++) tmp[i] = f0[i] * 2 % p;
poly_inv(tmp, len);
ntt(f0, len * 2, 1);
for (int i = 0; i < len * 2; i++) f0[i] = f0[i] * (long long)f0[i] % p;
ntt(f0, len * 2, -1);
for (int i = 0; i < len; i++) f0[i] = (f0[i] + a[i]) % p;
ntt(f0, len * 2, 1);
for (int i = len; i < 2 * len; i++) tmp[i] = 0;
ntt(tmp, len * 2, 1);
for (int i = 0; i < len * 2; i++) a[i] = tmp[i] * (long long)f0[i] % p;
ntt(a, len * 2, -1);
for (int i = len; i < len * 2; i++) a[i] = 0;
delete tmp;
delete f0;
}void poly_exp(int *a, int len)
int len1 = len / 2;
int *f0 = new int[len * 2];
for (int i = 0; i < len1; i++) f0[i] = a[i];
for (int i = len1; i < len * 2; i++) f0[i] = 0;
poly_exp(f0, len1);
for (int i = len1; i < len * 2; i++) f0[i] = 0;
int *lnf0 = new int[len * 2];
for (int i = 0; i < len * 2; i++) lnf0[i] = f0[i];
poly_ln(lnf0, len);
a[0]++;
for (int i = 0; i < len; i++)
ntt(a, len * 2, 1);
ntt(f0, len * 2, 1);
for (int i = 0; i < len * 2; i++) a[i] = a[i] * (long long)f0[i] % p;
ntt(a, len * 2, -1);
for (int i = len; i < len * 2; i++) a[i] = 0;
}void poly_qpow(int *a, int len, int n)
for (int i = 0; i < len * 2; i++) tmp[i] = tmp[i] * (long long)tmp[i] % p;
ntt(tmp, len * 2, -1);
for (int i = len; i < len * 2; i++) tmp[i] = 0;
n >>= 1;
} delete tmp;
}int lagrange_inversion(int *aa, int len, int n)
int a[1000000], n, len = 1;
int main()

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