未完待續……(只是給自己存個板子)
快速傅利葉變換
#include using namespace std; const int maxn = 2e6 + 1e2;
struct cp
; } inline cp operator -(const cp& b) const ; }
inline cp operator *(const cp& b) const ; }
};namespace fft
} inline void fft(cp a, int v)
; for (int r = mid << 1, j = 0; j < lim; j += r)
; for (int k = 0; k < mid; k++, w = w * wn)
}} for (int i = 0; i < lim; i++) (v > 0) ? (a[i].x /= lim, a[i].y /= lim) : (a[i].x *= lim, a[i].y /= lim);
} inline void conv(cp a, cp b, cp c)
}cp a[maxn], b[maxn], c[maxn]; int n, m; int main()
快速數論變換:
#include using namespace std; const int maxn = 5e5 + 1e2, mod = 998244353, g = 3, h = 332748118;
namespace fft
} inline int fpow(int x, int k)
return res;
} inline void fft(int a, int v)
}} int inv = fpow(lim, mod - 2);
for (int i = 0; i < lim; i++) (v > 0) ? (a[i] = a[i] * 1ll * inv % mod) : (a[i] = a[i] * 1ll * lim % mod);
} inline void conv(int a, int b, int c)
}int a[maxn], b[maxn], c[maxn]; int n, m; int main()
快速莫比烏斯/沃爾什變換:
namespace fwt
inline void or(modint f, modint t)
inline void and(modint f, modint t)
inline void xor(modint f, modint t) }
inline void conv(modint a, modint b, modint c)
}
modint 類(亂入):
int ttmp; struct modint
modint()
inline modint &operator =(int o)
inline modint &operator +=(modint b)
inline modint &operator -=(modint b)
inline modint &operator *=(modint b)
inline modint operator ^(int k)
return res;
} inline modint operator /=(modint b)
inline modint operator /=(int b)
inline modint operator +(modint b) const
inline modint operator -(modint b) const
inline modint operator *(modint b) const
inline modint operator /(modint b) const
};
多項式乘法逆:
#include using namespace std; const int maxn = 1e6 + 1e2, mod = 998244353, g = 3, gi = 332748118;
namespace ntt
} inline int qpow(int x, int k)
return res;
} inline void ntt(int a, int type)
}} int inv = qpow(lim, mod - 2);
for (int i = 0; i < lim; i++) (type == 1) ? (a[i] = a[i] * 1ll * inv % mod) : (a[i] = a[i] * 1ll * lim % mod);
} int a[maxn], b[maxn]; inline void conv(int a, int b, int c, int n, int m, int k) }
int t[maxn]; inline void polyinv(int f, int g, int n)
int m = (n + 1) >> 1; polyinv(f, g, m);
ntt::conv(f, g, t, n - 1, m - 1, n);
for (int i = 0; i < n; i++) t[i] = -t[i]; t[0] += 2;
ntt::conv(g, t, g, m - 1, n - 1, n);
}int f[maxn], g[maxn], n;
int main()
多項式開根(接在逆元的後面):
int u[maxn]; inline void polysqrt(int f, int g, int n)
int m = (n + 1) >> 1; polysqrt(f, g, m);
polyinv(g, u, n), ntt::conv(u, f, u, n - 1, n - 1, n);
int inv = ntt::qpow(2, mod - 2);
for (int i = 0; i < n; i++) g[i] = (g[i] + u[i]) * 1ll * inv % mod;
}
子集卷積:
#include using namespace std; const int maxn = 1 << 22, mod = 1e9 + 9;
inline void fwt(int f, int n, int t)
int n, a[21][maxn], b[21][maxn], c[21][maxn], t[maxn];
int main()
for (int i = 0; i <= n; i++) fwt(c[i], n, -1);
for (int i = 0; i < (1 << n); i++) cout << (c[__builtin_popcount(i)][i] + mod) % mod << ' ';
}
ln & exp 指數 / 對數函式
int v[maxn]; inline void polyln(int f, int g, int n)
int w[maxn]; inline void polyexp(int f, int g, int n)
int m = (n + 1) >> 1; polyexp(f, g, m);
polyln(g, w, n); for (int i = 0; i < n; i++) w[i] = (- w[i] + f[i]) % mod; w[0]++;
ntt::conv(w, g, g, n - 1, m - 1, n);
}
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