#include <algorithm>
#include <atomic>
#include <complex>
#include <vector>
#include <future>
#include <iostream>
#include <random>
#include <string>
#include <cstdlib>
#include <cstring>
namespace hint
{
using UINT_8 = uint8_t;
using UINT_16 = uint16_t;
using UINT_32 = uint32_t;
using UINT_64 = uint64_t;
using INT_32 = int32_t;
using INT_64 = int64_t;
using LONG = long;
using Complex = std::complex<double>;
constexpr double HINT_PI = 3.1415926535897932384626433832795;
constexpr double HINT_2PI = HINT_PI * 2;
template <typename T>
constexpr T min_2pow(T n)
{
T res = 1;
while (res < n)
{
res *= 2;
}
return res;
}
template <typename T>
constexpr T max_2pow(T n)
{
T res = 1;
res <<= (sizeof(T) * 8 - 1);
while (res > n)
{
res /= 2;
}
return res;
}
template <typename T>
constexpr bool is_neg(T x)
{
return x < 0;
}
template <typename T>
constexpr bool is_odd(T x)
{
return static_cast<bool>(x & 1);
}
template <typename T>
constexpr std::pair<T, T> div_mod(T a, T b)
{
return std::make_pair(a / b, a % b);
}
template <typename T>
void ary_copy(T *target, const T *source, size_t len)
{
if (len == 0 || target == source)
{
return;
}
if (len >= INT64_MAX)
{
throw("Ary too long\n");
}
std::memcpy(target, source, len * sizeof(T));
}
template <typename T>
inline T *ary_realloc(T *ptr, size_t len)
{
if (len * sizeof(T) < INT64_MAX)
{
ptr = static_cast<T *>(realloc(ptr, len * sizeof(T)));
}
if (ptr == nullptr)
{
throw("realloc error");
}
return ptr;
}
// 从其他类型数组拷贝到复数组实部
template <typename T>
inline void com_ary_combine_copy(Complex *target, const T &source1, size_t len1, const T &source2, size_t len2)
{
size_t min_len = std::min(len1, len2);
size_t i = 0;
while (i < min_len)
{
target[i] = Complex(source1[i], source2[i]);
i++;
}
while (i < len1)
{
target[i].real(source1[i]);
i++;
}
while (i < len2)
{
target[i].imag(source2[i]);
i++;
}
}
template <typename T>
constexpr size_t hint_log2(T n)
{
T res = 0;
while (n > 1)
{
n /= 2;
res++;
}
return res;
}
// FFT与类FFT变换的命名空间
namespace hint_transform
{
template <typename T>
void binary_inverse_swap(T &ary, size_t len)
{
size_t i = 0;
for (size_t j = 1; j < len - 1; j++)
{
size_t k = len >> 1;
i ^= k;
while (k > i)
{
k >>= 1;
i ^= k;
};
if (j < i)
{
std::swap(ary[i], ary[j]);
}
}
}
class ComplexTable
{
private:
std::vector<Complex> table;
INT_32 max_log_size = 2;
INT_32 cur_log_size = 2;
static constexpr double PI = HINT_PI;
ComplexTable(const ComplexTable &) = delete;
ComplexTable &operator=(const ComplexTable &) = delete;
public:
~ComplexTable() {}
// 初始化可以生成平分圆1<<shift份产生的单位根的表
ComplexTable(UINT_32 max_shift)
{
max_shift = std::max<size_t>(max_shift, 2);
max_log_size = max_shift;
size_t ary_size = 1ull << (max_shift - 1);
table.resize(ary_size);
table[0] = Complex(1);
expend(max_shift);
}
void expend(INT_32 shift)
{
if (shift > max_log_size)
{
throw("FFT length too long for lut\n");
}
for (INT_32 i = cur_log_size + 1; i <= shift; i++)
{
size_t len = 1ull << i, vec_size = len / 4;
table[vec_size] = Complex(1, 0);
for (size_t pos = 0; pos < vec_size / 2; pos++)
{
table[vec_size + pos * 2] = table[vec_size / 2 + pos];
}
for (size_t pos = 1; pos < vec_size / 2; pos += 2)
{
double cos_theta = std::cos(HINT_2PI * pos / len);
double sin_theta = std::sin(HINT_2PI * pos / len);
table[vec_size + pos] = Complex(cos_theta, sin_theta);
table[vec_size * 2 - pos] = Complex(sin_theta, cos_theta);
}
table[vec_size + vec_size / 2] = unit_root(len, len / 8);
}
cur_log_size = std::max(cur_log_size, shift);
}
// 返回单位圆上辐角为theta的点
static Complex unit_root(double theta)
{
return std::polar<double>(1.0, theta);
}
// 返回单位圆上平分m份的第n个
static Complex unit_root(size_t m, size_t n)
{
return unit_root((2.0 * PI * n) / m);
}
// shift表示圆平分为1<<shift份,n表示第几个单位根的共轭
Complex get_complex_conj(UINT_32 shift, size_t n) const
{
size_t rank = 1ull << shift;
const size_t rank_ff = rank - 1, quad_n = n << 2;
// n &= rank_ff;
size_t zone = quad_n >> shift; // 第几象限
if ((quad_n & rank_ff) == 0)
{
static constexpr Complex ONES_CONJ[4] = {Complex(1, 0), Complex(0, -1), Complex(-1, 0), Complex(0, 1)};
return ONES_CONJ[zone];
}
Complex tmp;
if ((zone & 2) == 0)
{
if ((zone & 1) == 0)
{
tmp = table[rank / 4 + n];
tmp.imag(-tmp.imag());
}
else
{
tmp = -table[rank - rank / 4 - n];
}
}
else
{
if ((zone & 1) == 0)
{
tmp = table[n - (rank / 4)];
tmp.real(-tmp.real());
}
else
{
tmp = table[rank + rank / 4 - n];
}
}
return tmp;
}
};
constexpr size_t lut_max_rank = 19;
static ComplexTable TABLE(lut_max_rank); // 初始化fft表
// 2点fft
inline void fft_2point(Complex& sum, Complex& diff)
{
Complex tmp0 = sum;
Complex tmp1 = diff;
sum = tmp0 + tmp1;
diff = tmp0 - tmp1;
}
// 4点fft
inline void fft_4point(Complex* input, size_t rank = 1)
{
Complex tmp0 = input[0];
Complex tmp1 = input[rank];
Complex tmp2 = input[rank * 2];
Complex tmp3 = input[rank * 3];
fft_2point(tmp0, tmp2);
fft_2point(tmp1, tmp3);
tmp3 = Complex(tmp3.imag(), -tmp3.real());
input[0] = tmp0 + tmp1;
input[rank] = tmp2 + tmp3;
input[rank * 2] = tmp0 - tmp1;
input[rank * 3] = tmp2 - tmp3;
}
inline void fft_dit_4point(Complex* input, size_t rank = 1)
{
Complex tmp0 = input[0];
Complex tmp1 = input[rank];
Complex tmp2 = input[rank * 2];
Complex tmp3 = input[rank * 3];
fft_2point(tmp0, tmp1);
fft_2point(tmp2, tmp3);
tmp3 = Complex(tmp3.imag(), -tmp3.real());
input[0] = tmp0 + tmp2;
input[rank] = tmp1 + tmp3;
input[rank * 2] = tmp0 - tmp2;
input[rank * 3] = tmp1 - tmp3;
}
inline void fft_dit_8point(Complex* input, size_t rank = 1)
{
Complex tmp0 = input[0];
Complex tmp1 = input[rank];
Complex tmp2 = input[rank * 2];
Complex tmp3 = input[rank * 3];
Complex tmp4 = input[rank * 4];
Complex tmp5 = input[rank * 5];
Complex tmp6 = input[rank * 6];
Complex tmp7 = input[rank * 7];
fft_2point(tmp0, tmp1);
fft_2point(tmp2, tmp3);
fft_2point(tmp4, tmp5);
fft_2point(tmp6, tmp7);
tmp3 = Complex(tmp3.imag(), -tmp3.real());
tmp7 = Complex(tmp7.imag(), -tmp7.real());
fft_2point(tmp0, tmp2);
fft_2point(tmp1, tmp3);
fft_2point(tmp4, tmp6);
fft_2point(tmp5, tmp7);
static constexpr double cos_1_8 = 0.70710678118654752440084436210485;
tmp5 = cos_1_8 * Complex(tmp5.imag() + tmp5.real(), tmp5.imag() - tmp5.real());
tmp6 = Complex(tmp6.imag(), -tmp6.real());
tmp7 = -cos_1_8 * Complex(tmp7.real() - tmp7.imag(), tmp7.real() + tmp7.imag());
input[0] = tmp0 + tmp4;
input[rank] = tmp1 + tmp5;
input[rank * 2] = tmp2 + tmp6;
input[rank * 3] = tmp3 + tmp7;
input[rank * 4] = tmp0 - tmp4;
input[rank * 5] = tmp1 - tmp5;
input[rank * 6] = tmp2 - tmp6;
input[rank * 7] = tmp3 - tmp7;
}
inline void fft_dit_16point(Complex* input, size_t rank = 1)
{
static constexpr double cos_1_8 = 0.70710678118654752440084436210485;
static constexpr double cos_1_16 = 0.92387953251128675612818318939679;
static constexpr double sin_1_16 = 0.3826834323650897717284599840304;
static constexpr Complex w1(cos_1_16, -sin_1_16), w3(sin_1_16, -cos_1_16);
static constexpr Complex w5(-sin_1_16, -cos_1_16), w7(-cos_1_16, -sin_1_16);
fft_dit_8point(input, rank);
fft_dit_8point(input + rank * 8, rank);
Complex tmp0 = input[0];
Complex tmp1 = input[rank];
Complex tmp2 = input[rank * 8];
Complex tmp3 = input[rank * 9] * w1;
input[0] = tmp0 + tmp2;
input[rank] = tmp1 + tmp3;
input[rank * 8] = tmp0 - tmp2;
input[rank * 9] = tmp1 - tmp3;
tmp0 = input[rank * 2];
tmp1 = input[rank * 3];
tmp2 = input[rank * 10];
tmp3 = input[rank * 11] * w3;
tmp2 = cos_1_8 * Complex(tmp2.imag() + tmp2.real(), tmp2.imag() - tmp2.real());
input[rank * 2] = tmp0 + tmp2;
input[rank * 3] = tmp1 + tmp3;
input[rank * 10] = tmp0 - tmp2;
input[rank * 11] = tmp1 - tmp3;
tmp0 = input[rank * 4];
tmp1 = input[rank * 5];
tmp2 = input[rank * 12];
tmp3 = input[rank * 13] * w5;
tmp2 = Complex(tmp2.imag(), -tmp2.real());
input[rank * 4] = tmp0 + tmp2;
input[rank * 5] = tmp1 + tmp3;
input[rank * 12] = tmp0 - tmp2;
input[rank * 13] = tmp1 - tmp3;
tmp0 = input[rank * 6];
tmp1 = input[rank * 7];
tmp2 = input[rank * 14];
tmp3 = input[rank * 15] * w7;
tmp2 = -cos_1_8 * Complex(tmp2.real() - tmp2.imag(), tmp2.real() + tmp2.imag());
input[rank * 6] = tmp0 + tmp2;
input[rank * 7] = tmp1 + tmp3;
input[rank * 14] = tmp0 - tmp2;
input[rank * 15] = tmp1 - tmp3;
}
inline void fft_dit_32point(Complex* input, size_t rank = 1)
{
static constexpr double cos_1_8 = 0.70710678118654752440084436210485;
static constexpr double cos_1_16 = 0.92387953251128675612818318939679;
static constexpr double sin_1_16 = 0.3826834323650897717284599840304;
static constexpr double cos_1_32 = 0.98078528040323044912618223613424;
static constexpr double sin_1_32 = 0.19509032201612826784828486847702;
static constexpr double cos_3_32 = 0.83146961230254523707878837761791;
static constexpr double sin_3_32 = 0.55557023301960222474283081394853;
static constexpr Complex w1(cos_1_32, -sin_1_32), w2(cos_1_16, -sin_1_16), w3(cos_3_32, -sin_3_32);
static constexpr Complex w5(sin_3_32, -cos_3_32), w6(sin_1_16, -cos_1_16), w7(sin_1_32, -cos_1_32);
static constexpr Complex w9(-sin_1_32, -cos_1_32), w10(-sin_1_16, -cos_1_16), w11(-sin_3_32, -cos_3_32);
static constexpr Complex w13(-cos_3_32, -sin_3_32), w14(-cos_1_16, -sin_1_16), w15(-cos_1_32, -sin_1_32);
fft_dit_16point(input, rank);
fft_dit_16point(input + rank * 16, rank);
Complex tmp0 = input[0];
Complex tmp1 = input[rank];
Complex tmp2 = input[rank * 16];
Complex tmp3 = input[rank * 17] * w1;
input[0] = tmp0 + tmp2;
input[rank] = tmp1 + tmp3;
input[rank * 16] = tmp0 - tmp2;
input[rank * 17] = tmp1 - tmp3;
tmp0 = input[rank * 2];
tmp1 = input[rank * 3];
tmp2 = input[rank * 18] * w2;
tmp3 = input[rank * 19] * w3;
input[rank * 2] = tmp0 + tmp2;
input[rank * 3] = tmp1 + tmp3;
input[rank * 18] = tmp0 - tmp2;
input[rank * 19] = tmp1 - tmp3;
tmp0 = input[rank * 4];
tmp1 = input[rank * 5];
tmp2 = input[rank * 20];
tmp3 = input[rank * 21] * w5;
tmp2 = cos_1_8 * Complex(tmp2.imag() + tmp2.real(), tmp2.imag() - tmp2.real());
input[rank * 4] = tmp0 + tmp2;
input[rank * 5] = tmp1 + tmp3;
input[rank * 20] = tmp0 - tmp2;
input[rank * 21] = tmp1 - tmp3;
tmp0 = input[rank * 6];
tmp1 = input[rank * 7];
tmp2 = input[rank * 22] * w6;
tmp3 = input[rank * 23] * w7;
input[rank * 6] = tmp0 + tmp2;
input[rank * 7] = tmp1 + tmp3;
input[rank * 22] = tmp0 - tmp2;
input[rank * 23] = tmp1 - tmp3;
tmp0 = input[rank * 8];
tmp1 = input[rank * 9];
tmp2 = input[rank * 24];
tmp3 = input[rank * 25] * w9;
tmp2 = Complex(tmp2.imag(), -tmp2.real());
input[rank * 8] = tmp0 + tmp2;
input[rank * 9] = tmp1 + tmp3;
input[rank * 24] = tmp0 - tmp2;
input[rank * 25] = tmp1 - tmp3;
tmp0 = input[rank * 10];
tmp1 = input[rank * 11];
tmp2 = input[rank * 26] * w10;
tmp3 = input[rank * 27] * w11;
input[rank * 10] = tmp0 + tmp2;
input[rank * 11] = tmp1 + tmp3;
input[rank * 26] = tmp0 - tmp2;
input[rank * 27] = tmp1 - tmp3;
tmp0 = input[rank * 12];
tmp1 = input[rank * 13];
tmp2 = input[rank * 28];
tmp3 = input[rank * 29] * w13;
tmp2 = -cos_1_8 * Complex(tmp2.real() - tmp2.imag(), tmp2.real() + tmp2.imag());
input[rank * 12] = tmp0 + tmp2;
input[rank * 13] = tmp1 + tmp3;
input[rank * 28] = tmp0 - tmp2;
input[rank * 29] = tmp1 - tmp3;
tmp0 = input[rank * 14];
tmp1 = input[rank * 15];
tmp2 = input[rank * 30] * w14;
tmp3 = input[rank * 31] * w15;
input[rank * 14] = tmp0 + tmp2;
input[rank * 15] = tmp1 + tmp3;
input[rank * 30] = tmp0 - tmp2;
input[rank * 31] = tmp1 - tmp3;
}
inline void fft_dif_4point(Complex* input, size_t rank = 1)
{
Complex tmp0 = input[0];
Complex tmp1 = input[rank];
Complex tmp2 = input[rank * 2];
Complex tmp3 = input[rank * 3];
fft_2point(tmp0, tmp2);
fft_2point(tmp1, tmp3);
tmp3 = Complex(tmp3.imag(), -tmp3.real());
input[0] = tmp0 + tmp1;
input[rank] = tmp0 - tmp1;
input[rank * 2] = tmp2 + tmp3;
input[rank * 3] = tmp2 - tmp3;
}
inline void fft_dif_8point(Complex* input, size_t rank = 1)
{
Complex tmp0 = input[0];
Complex tmp1 = input[rank];
Complex tmp2 = input[rank * 2];
Complex tmp3 = input[rank * 3];
Complex tmp4 = input[rank * 4];
Complex tmp5 = input[rank * 5];
Complex tmp6 = input[rank * 6];
Complex tmp7 = input[rank * 7];
fft_2point(tmp0, tmp4);
fft_2point(tmp1, tmp5);
fft_2point(tmp2, tmp6);
fft_2point(tmp3, tmp7);
static constexpr double cos_1_8 = 0.70710678118654752440084436210485;
tmp5 = cos_1_8 * Complex(tmp5.imag() + tmp5.real(), tmp5.imag() - tmp5.real());
tmp6 = Complex(tmp6.imag(), -tmp6.real());
tmp7 = -cos_1_8 * Complex(tmp7.real() - tmp7.imag(), tmp7.real() + tmp7.imag());
fft_2point(tmp0, tmp2);
fft_2point(tmp1, tmp3);
fft_2point(tmp4, tmp6);
fft_2point(tmp5, tmp7);
tmp3 = Complex(tmp3.imag(), -tmp3.real());
tmp7 = Complex(tmp7.imag(), -tmp7.real());
input[0] = tmp0 + tmp1;
input[rank] = tmp0 - tmp1;
input[rank * 2] = tmp2 + tmp3;
input[rank * 3] = tmp2 - tmp3;
input[rank * 4] = tmp4 + tmp5;
input[rank * 5] = tmp4 - tmp5;
input[rank * 6] = tmp6 + tmp7;
input[rank * 7] = tmp6 - tmp7;
}
inline void fft_dif_16point(Complex* input, size_t rank = 1)
{
static constexpr double cos_1_8 = 0.70710678118654752440084436210485;
static constexpr double cos_1_16 = 0.92387953251128675612818318939679;
static constexpr double sin_1_16 = 0.3826834323650897717284599840304;
static constexpr Complex w1(cos_1_16, -sin_1_16), w3(sin_1_16, -cos_1_16);
static constexpr Complex w5(-sin_1_16, -cos_1_16), w7(-cos_1_16, -sin_1_16);
Complex tmp0 = input[0];
Complex tmp1 = input[rank];
Complex tmp2 = input[rank * 8];
Complex tmp3 = input[rank * 9];
input[0] = tmp0 + tmp2;
input[rank] = tmp1 + tmp3;
input[rank * 8] = tmp0 - tmp2;
input[rank * 9] = (tmp1 - tmp3) * w1;
tmp0 = input[rank * 2];
tmp1 = input[rank * 3];
tmp2 = input[rank * 10];
tmp3 = input[rank * 11];
fft_2point(tmp0, tmp2);
tmp2 = cos_1_8 * Complex(tmp2.imag() + tmp2.real(), tmp2.imag() - tmp2.real());
input[rank * 2] = tmp0;
input[rank * 3] = tmp1 + tmp3;
input[rank * 10] = tmp2;
input[rank * 11] = (tmp1 - tmp3) * w3;
tmp0 = input[rank * 4];
tmp1 = input[rank * 5];
tmp2 = input[rank * 12];
tmp3 = input[rank * 13];
fft_2point(tmp0, tmp2);
tmp2 = Complex(tmp2.imag(), -tmp2.real());
input[rank * 4] = tmp0;
input[rank * 5] = tmp1 + tmp3;
input[rank * 12] = tmp2;
input[rank * 13] = (tmp1 - tmp3) * w5;
tmp0 = input[rank * 6];
tmp1 = input[rank * 7];
tmp2 = input[rank * 14];
tmp3 = input[rank * 15];
fft_2point(tmp0, tmp2);
tmp2 = -cos_1_8 * Complex(tmp2.real() - tmp2.imag(), tmp2.real() + tmp2.imag());
input[rank * 6] = tmp0;
input[rank * 7] = tmp1 + tmp3;
input[rank * 14] = tmp2;
input[rank * 15] = (tmp1 - tmp3) * w7;
fft_dif_8point(input, rank);
fft_dif_8point(input + rank * 8, rank);
}
inline void fft_dif_32point(Complex* input, size_t rank = 1)
{
static constexpr double cos_1_8 = 0.70710678118654752440084436210485;
static constexpr double cos_1_16 = 0.92387953251128675612818318939679;
static constexpr double sin_1_16 = 0.3826834323650897717284599840304;
static constexpr double cos_1_32 = 0.98078528040323044912618223613424;
static constexpr double sin_1_32 = 0.19509032201612826784828486847702;
static constexpr double cos_3_32 = 0.83146961230254523707878837761791;
static constexpr double sin_3_32 = 0.55557023301960222474283081394853;
static constexpr Complex w1(cos_1_32, -sin_1_32), w2(cos_1_16, -sin_1_16), w3(cos_3_32, -sin_3_32);
static constexpr Complex w5(sin_3_32, -cos_3_32), w6(sin_1_16, -cos_1_16), w7(sin_1_32, -cos_1_32);
static constexpr Complex w9(-sin_1_32, -cos_1_32), w10(-sin_1_16, -cos_1_16), w11(-sin_3_32, -cos_3_32);
static constexpr Complex w13(-cos_3_32, -sin_3_32), w14(-cos_1_16, -sin_1_16), w15(-cos_1_32, -sin_1_32);
Complex tmp0 = input[0];
Complex tmp1 = input[rank];
Complex tmp2 = input[rank * 16];
Complex tmp3 = input[rank * 17];
input[0] = tmp0 + tmp2;
input[rank] = tmp1 + tmp3;
input[rank * 16] = tmp0 - tmp2;
input[rank * 17] = (tmp1 - tmp3) * w1;
tmp0 = input[rank * 2];
tmp1 = input[rank * 3];
tmp2 = input[rank * 18];
tmp3 = input[rank * 19];
input[rank * 2] = tmp0 + tmp2;
input[rank * 3] = tmp1 + tmp3;
input[rank * 18] = (tmp0 - tmp2) * w2;
input[rank * 19] = (tmp1 - tmp3) * w3;
tmp0 = input[rank * 4];
tmp1 = input[rank * 5];
tmp2 = input[rank * 20];
tmp3 = input[rank * 21];
fft_2point(tmp0, tmp2);
tmp2 = cos_1_8 * Complex(tmp2.imag() + tmp2.real(), tmp2.imag() - tmp2.real());
input[rank * 4] = tmp0;
input[rank * 5] = tmp1 + tmp3;
input[rank * 20] = tmp2;
input[rank * 21] = (tmp1 - tmp3) * w5;
tmp0 = input[rank * 6];
tmp1 = input[rank * 7];
tmp2 = input[rank * 22];
tmp3 = input[rank * 23];
input[rank * 6] = tmp0 + tmp2;
input[rank * 7] = tmp1 + tmp3;
input[rank * 22] = (tmp0 - tmp2) * w6;
input[rank * 23] = (tmp1 - tmp3) * w7;
tmp0 = input[rank * 8];
tmp1 = input[rank * 9];
tmp2 = input[rank * 24];
tmp3 = input[rank * 25];
fft_2point(tmp0, tmp2);
tmp2 = Complex(tmp2.imag(), -tmp2.real());
input[rank * 8] = tmp0;
input[rank * 9] = tmp1 + tmp3;
input[rank * 24] = tmp2;
input[rank * 25] = (tmp1 - tmp3) * w9;
tmp0 = input[rank * 10];
tmp1 = input[rank * 11];
tmp2 = input[rank * 26];
tmp3 = input[rank * 27];
input[rank * 10] = tmp0 + tmp2;
input[rank * 11] = tmp1 + tmp3;
input[rank * 26] = (tmp0 - tmp2) * w10;
input[rank * 27] = (tmp1 - tmp3) * w11;
tmp0 = input[rank * 12];
tmp1 = input[rank * 13];
tmp2 = input[rank * 28];
tmp3 = input[rank * 29];
fft_2point(tmp0, tmp2);
tmp2 = -cos_1_8 * Complex(tmp2.real() - tmp2.imag(), tmp2.real() + tmp2.imag());
input[rank * 12] = tmp0;
input[rank * 13] = tmp1 + tmp3;
input[rank * 28] = tmp2;
input[rank * 29] = (tmp1 - tmp3) * w13;
tmp0 = input[rank * 14];
tmp1 = input[rank * 15];
tmp2 = input[rank * 30];
tmp3 = input[rank * 31];
input[rank * 14] = tmp0 + tmp2;
input[rank * 15] = tmp1 + tmp3;
input[rank * 30] = (tmp0 - tmp2) * w14;
input[rank * 31] = (tmp1 - tmp3) * w15;
fft_dif_16point(input, rank);
fft_dif_16point(input + rank * 16, rank);
}
// fft分裂基时间抽取蝶形变换
inline void fft_split_radix_dit_butterfly(Complex omega, Complex omega_cube,
Complex *input, size_t rank)
{
Complex tmp0 = input[0];
Complex tmp1 = input[rank];
Complex tmp2 = input[rank * 2] * omega;
Complex tmp3 = input[rank * 3] * omega_cube;
fft_2point(tmp2, tmp3);
tmp3 = Complex(tmp3.imag(), -tmp3.real());
input[0] = tmp0 + tmp2;
input[rank] = tmp1 + tmp3;
input[rank * 2] = tmp0 - tmp2;
input[rank * 3] = tmp1 - tmp3;
}
// fft分裂基频率抽取蝶形变换
inline void fft_split_radix_dif_butterfly(Complex omega, Complex omega_cube,
Complex *input, size_t rank)
{
Complex tmp0 = input[0];
Complex tmp1 = input[rank];
Complex tmp2 = input[rank * 2];
Complex tmp3 = input[rank * 3];
fft_2point(tmp0, tmp2);
fft_2point(tmp1, tmp3);
tmp3 = Complex(-tmp3.imag(), tmp3.real());
input[0] = tmp0;
input[rank] = tmp1;
input[rank * 2] = (tmp2 - tmp3) * omega;
input[rank * 3] = (tmp2 + tmp3) * omega_cube;
}
// 模板化时间抽取分裂基fft
template <size_t LEN>
void fft_split_radix_dit_template(Complex *input)
{
constexpr size_t log_len = hint_log2(LEN);
constexpr size_t half_len = LEN / 2, quarter_len = LEN / 4;
fft_split_radix_dit_template<half_len>(input);
fft_split_radix_dit_template<quarter_len>(input + half_len);
fft_split_radix_dit_template<quarter_len>(input + half_len + quarter_len);
for (size_t i = 0; i < quarter_len; i++)
{
Complex omega = TABLE.get_complex_conj(log_len, i);
Complex omega_cube = TABLE.get_complex_conj(log_len, i * 3);
fft_split_radix_dit_butterfly(omega, omega_cube, input + i, quarter_len);
}
}
template <>
void fft_split_radix_dit_template<0>(Complex *input) {}
template <>
void fft_split_radix_dit_template<1>(Complex *input) {}
template <>
void fft_split_radix_dit_template<2>(Complex *input)
{
fft_2point(input[0], input[1]);
}
template <>
void fft_split_radix_dit_template<4>(Complex *input)
{
fft_dit_4point(input, 1);
}
template <>
void fft_split_radix_dit_template<8>(Complex *input)
{
fft_dit_8point(input, 1);
}
template <>
void fft_split_radix_dit_template<16>(Complex *input)
{
// fft_radix2_dit_template<16>(input);
fft_dit_16point(input, 1);
}
template <>
void fft_split_radix_dit_template<32>(Complex *input)
{
// fft_radix2_dit_template<32>(input);
fft_dit_32point(input, 1);
}
// 模板化频率抽取分裂基fft
template <size_t LEN>
void fft_split_radix_dif_template(Complex *input)
{
constexpr size_t log_len = hint_log2(LEN);
constexpr size_t half_len = LEN / 2, quarter_len = LEN / 4;
for (size_t i = 0; i < quarter_len; i++)
{
Complex omega = TABLE.get_complex_conj(log_len, i);
Complex omega_cube = TABLE.get_complex_conj(log_len, i * 3);
fft_split_radix_dif_butterfly(omega, omega_cube, input + i, quarter_len);
}
fft_split_radix_dif_template<half_len>(input);
fft_split_radix_dif_template<quarter_len>(input + half_len);
fft_split_radix_dif_template<quarter_len>(input + half_len + quarter_len);
}
template <>
void fft_split_radix_dif_template<0>(Complex *input) {}
template <>
void fft_split_radix_dif_template<1>(Complex *input) {}
template <>
void fft_split_radix_dif_template<2>(Complex *input)
{
fft_2point(input[0], input[1]);
}
template <>
void fft_split_radix_dif_template<4>(Complex *input)
{
fft_dif_4point(input, 1);
}
template <>
void fft_split_radix_dif_template<8>(Complex *input)
{
fft_dif_8point(input, 1);
}
template <>
void fft_split_radix_dif_template<16>(Complex *input)
{
// fft_radix2_dif_template<16>(input);
fft_dif_16point(input, 1);
}
template <>
void fft_split_radix_dif_template<32>(Complex *input)
{
// fft_radix2_dif_template<32>(input);
fft_dif_32point(input, 1);
}
template <size_t LEN = 1>
void fft_dit_template(Complex *input, size_t fft_len, bool bit_inv = true)
{
if (fft_len > LEN)
{
fft_dit_template<LEN * 2>(input, fft_len, bit_inv);
return;
}
TABLE.expend(hint_log2(LEN));
if (bit_inv)
{
binary_inverse_swap(input, LEN);
}
fft_split_radix_dit_template<LEN>(input);
}
template <>
void fft_dit_template<1 << 24>(Complex *input, size_t fft_len, bool bit_inv) {}
template <size_t LEN = 1>
void fft_dif_template(Complex *input, size_t fft_len, bool bit_inv = true)
{
if (fft_len > LEN)
{
fft_dif_template<LEN * 2>(input, fft_len, bit_inv);
return;
}
TABLE.expend(hint_log2(LEN));
fft_split_radix_dif_template<LEN>(input);
if (bit_inv)
{
binary_inverse_swap(input, LEN);
}
}
template <>
void fft_dif_template<1 << 24>(Complex *input, size_t fft_len, bool is_ifft) {}
/// @brief 时间抽取基2fft
/// @param input 复数组
/// @param fft_len 数组长度
/// @param bit_inv 是否逆序
inline void fft_dit(Complex *input, size_t fft_len, bool bit_inv = true)
{
fft_len = max_2pow(fft_len);
fft_dit_template<1>(input, fft_len, bit_inv);
}
/// @brief 频率抽取基2fft
/// @param input 复数组
/// @param fft_len 数组长度
/// @param bit_inv 是否逆序
inline void fft_dif(Complex *input, size_t fft_len, bool bit_inv = true)
{
fft_len = max_2pow(fft_len);
fft_dif_template<1>(input, fft_len, bit_inv);
}
}
std::string ui64to_string(UINT_64 input, UINT_8 digits)
{
std::string result(digits, '0');
for (UINT_8 i = 0; i < digits; i++)
{
result[digits - i - 1] = static_cast<char>(input % 10 + '0');
input /= 10;
}
return result;
}
constexpr UINT_64 stoui64(char *s, size_t dig = 4)
{
UINT_64 result = 0;
for (size_t i = 0; i < dig; i++)
{
result *= 10;
result += (s[i] - '0');
}
return result;
}
static constexpr INT_64 DIGIT = 4;
size_t char_to_real(char *buffer, Complex *comary, size_t str_len)
{
hint::INT_64 len = str_len, pos = len, i = 0;
len = (len + DIGIT - 1) / DIGIT;
while (pos - DIGIT > 0)
{
hint::UINT_64 tmp = hint::stoui64(buffer + pos - DIGIT, 4);
comary[i].real(tmp);
i++;
pos -= DIGIT;
}
if (pos > 0)
{
hint::UINT_64 tmp = hint::stoui64(buffer, pos);
comary[i].real(tmp);
}
return len;
}
size_t char_to_imag(char *buffer, Complex *comary, size_t str_len)
{
hint::INT_64 len = str_len, pos = len, i = 0;
len = (len + DIGIT - 1) / DIGIT;
while (pos - DIGIT > 0)
{
hint::UINT_64 tmp = hint::stoui64(buffer + pos - DIGIT, 4);
comary[i].imag(tmp);
i++;
pos -= DIGIT;
}
if (pos > 0)
{
hint::UINT_64 tmp = hint::stoui64(buffer, pos);
comary[i].imag(tmp);
}
return len;
}
void num_to_s(char *s, UINT_64 num)
{
char c = '0';
std::tie(num, c) = div_mod<UINT_64>(num, 10);
s[3] = c + '0';
std::tie(num, c) = div_mod<UINT_64>(num, 10);
s[2] = c + '0';
std::tie(num, c) = div_mod<UINT_64>(num, 10);
s[1] = c + '0';
std::tie(num, c) = div_mod<UINT_64>(num, 10);
s[0] = c + '0';
}
size_t read_string(char *s)
{
size_t len = 0;
char c = getchar();
// 处理多余回车或空格
while (c == ' ' || c == '\n' || c == '\r')
{
c = getchar();
}
// 不断读入直到遇到回车或空格
while (c != ' ' && c != '\n' && c != '\r')
{
s[len] = c;
len++;
c = getchar();
}
s[len] = '\0';
return len;
}
}
using namespace std;
using namespace hint;
using namespace hint_transform;
// char in[1 << 20];
char out[1 << 21 + 1];
Complex fft_ary[1 << 19];
int main()
{
size_t len_a = 0, len_b = 0;
scanf("%s", out);
while (isdigit(out[len_a]))
{
len_a++;
}
if (len_a == 1 && out[0] == '0')
{
printf("0");
return 0;
}
size_t len1 = char_to_real(out, fft_ary, len_a);
scanf("%s", out);
while (isdigit(out[len_b]))
{
len_b++;
}
if (len_b == 1 && out[0] == '0')
{
printf("0");
return 0;
}
size_t len2 = char_to_imag(out, fft_ary, len_b);
size_t fft_len = min_2pow(len1 + len2 - 1);
fft_dif(fft_ary, fft_len, false); // 优化FFT
for (size_t i = 0; i < fft_len; i++)
{
Complex tmp = fft_ary[i];
fft_ary[i] = std::conj(tmp * tmp);
}
fft_dit(fft_ary, fft_len, false); // 优化FFT
double inv = -0.5 / fft_len;
UINT_64 carry = 0;
size_t pos = 1 << 21;
for (size_t i = 0; i < len1 + len2 - 1; i++)
{
carry += UINT_64(fft_ary[i].imag() * inv + 0.5);
UINT_64 num = 0;
std::tie(carry, num) = div_mod<UINT_64>(carry, 10000);
num_to_s(out + pos - 4, num);
pos -= 4;
}
num_to_s(out + pos - 4, carry);
pos -= 4;
while (out[pos] == '0')
{
pos++;
}
puts(out + pos);
}
| Compilation | N/A | N/A | Compile OK | Score: N/A | 显示更多 |
| Testcase #1 | 1.635 ms | 4 MB + 220 KB | Accepted | Score: 100 | 显示更多 |