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View the Project on GitHub Luzhiled/syakyo-library
// verification-helper: PROBLEM https://judge.yosupo.jp/problem/bitwise_xor_convolution #include "src/math/convolution/bitwise-xor-convolution.hpp" #include "src/math/modular-arithmetic/static-modint.hpp" #include <iostream> #include <vector> namespace luz { void main_() { usize n; std::cin >> n; using mint = modint998244353; std::vector< mint > as(1 << n); for (mint &a: as) { i32 v; std::cin >> v; a = mint(v); } std::vector< mint > bs(1 << n); for (mint &b: bs) { i32 v; std::cin >> v; b = mint(v); } auto cs = bitwise_xor_convolution(as, bs); for (usize i = 0; i < (1 << n); i++) { std::cout << cs[i].val() << (i + 1 == (usize(1) << n) ? "\n" : " "); } } } // namespace luz int main() { luz::main_(); }
#line 1 "test/library-checker/bitwise_xor_convolution.test.cpp" // verification-helper: PROBLEM https://judge.yosupo.jp/problem/bitwise_xor_convolution #line 2 "src/math/convolution/bitwise-xor-convolution.hpp" #line 2 "src/cpp-template/header/size-alias.hpp" #include <cstddef> namespace luz { using isize = std::ptrdiff_t; using usize = std::size_t; } #line 2 "src/math/convolution/fast-walsh-hadamard-transform.hpp" #line 4 "src/math/convolution/fast-walsh-hadamard-transform.hpp" #include <cassert> #include <vector> namespace luz { // length of f must be 2^k template < typename T, typename F > void fast_walsh_hadamard_transform(std::vector< T > &f, F op) { const usize n = f.size(); assert((n & (n - 1)) == 0); usize i = 1; while (i < n) { usize j = 0; while (j < n) { for (usize k = 0; k < i; k++) { op(f[j + k], f[j + k + i]); } j += i << 1; } i <<= 1; } } } // namespace luz #line 5 "src/math/convolution/bitwise-xor-convolution.hpp" #line 8 "src/math/convolution/bitwise-xor-convolution.hpp" namespace luz { // length of f and g must be 2^k template < typename T > std::vector< T > bitwise_xor_convolution(std::vector< T > f, std::vector< T > g) { assert(f.size() == g.size()); T inv2 = T(1) / T(2); auto zeta = [](T &lo, T &hi) { T x = lo + hi; T y = lo - hi; lo = x; hi = y; }; auto mobius = [inv2](T &lo, T &hi) { T x = lo + hi; T y = lo - hi; lo = x * inv2; hi = y * inv2; }; fast_walsh_hadamard_transform(f, zeta); fast_walsh_hadamard_transform(g, zeta); for (usize i = 0; i < f.size(); i++) { f[i] *= g[i]; } fast_walsh_hadamard_transform(f, mobius); return f; } } // namespace luz #line 2 "src/math/modular-arithmetic/static-modint.hpp" #line 2 "src/cpp-template/header/int-alias.hpp" #include <cstdint> namespace luz { using i32 = std::int32_t; using i64 = std::int64_t; using u32 = std::uint32_t; using u64 = std::uint64_t; } #line 4 "src/math/modular-arithmetic/static-modint.hpp" #line 6 "src/math/modular-arithmetic/static-modint.hpp" #include <iostream> namespace luz { template < u32 mod > class StaticPrimeModInt { using modint = StaticPrimeModInt; u32 v; public: StaticPrimeModInt(): v(0) {} template < typename T > StaticPrimeModInt(T t) { i64 x = (i64)(t % (i64)mod); if (x < 0) x += mod; v = (u32)x; } u32 val() const { return v; } modint &operator+=(const modint &rhs) { v += rhs.v; if (v >= mod) v -= mod; return *this; } modint &operator-=(const modint &rhs) { v += mod - rhs.v; // <- if (v >= mod) v -= mod; return *this; } modint &operator*=(const modint &rhs) { v = (u32)(u64(1) * v * rhs.v % mod); return *this; } modint &operator/=(const modint &rhs) { *this *= rhs.inverse(); return *this; } modint operator+() const { return *this; } modint operator-() const { return modint() - *this; } friend modint operator+(const modint &lhs, const modint &rhs) { return modint(lhs) += rhs; } friend modint operator-(const modint &lhs, const modint &rhs) { return modint(lhs) -= rhs; } friend modint operator*(const modint &lhs, const modint &rhs) { return modint(lhs) *= rhs; } friend modint operator/(const modint &lhs, const modint &rhs) { return modint(lhs) /= rhs; } friend bool operator==(const modint &lhs, const modint &rhs) { return lhs.v == rhs.v; } friend bool operator!=(const modint &lhs, const modint &rhs) { return lhs.v != rhs.v; } modint pow(i64 n) const { assert(0 <= n); modint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } modint inverse() const { assert(v != 0); return pow(mod - 2); } static constexpr u32 get_mod() { return mod; } friend std::ostream &operator<<(std::ostream &os, const modint &m) { os << m.val(); return os; } }; using modint998244353 = StaticPrimeModInt< 998244353 >; using modint1000000007 = StaticPrimeModInt< 1000000007 >; } // namespace luz #line 5 "test/library-checker/bitwise_xor_convolution.test.cpp" #line 8 "test/library-checker/bitwise_xor_convolution.test.cpp" namespace luz { void main_() { usize n; std::cin >> n; using mint = modint998244353; std::vector< mint > as(1 << n); for (mint &a: as) { i32 v; std::cin >> v; a = mint(v); } std::vector< mint > bs(1 << n); for (mint &b: bs) { i32 v; std::cin >> v; b = mint(v); } auto cs = bitwise_xor_convolution(as, bs); for (usize i = 0; i < (1 << n); i++) { std::cout << cs[i].val() << (i + 1 == (usize(1) << n) ? "\n" : " "); } } } // namespace luz int main() { luz::main_(); }