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#include "convolution/subset_convolution.hpp"
長さ $2^N$ の整数列 $a$ と $b$ について、 $c_k = \sum_{i\& j=0, i|j=k} a_i b_j$ を求める。 $O(N^2 2^N)$
#pragma once #include "../template/template.hpp" #include "../math/ranked_subset_transform.hpp" namespace lib { template <class T, int LIM = 20> std::vector<T> subset_convolution(const std::vector<T> &a, const std::vector<T> &b) { auto ra = ranked_zeta<T, LIM>(a); auto rb = ranked_zeta<T, LIM>(b); int n = std::bit_width(a.size()) - 1; for (int s = (1 << n) - 1; s >= 0; s--) { auto &f = ra[s]; const auto &g = rb[s]; for (int d = n; d >= 0; d--) { T x = 0; for (int i = 0; i <= d; i++) { x += f[i] * g[d - i]; } f[d] = x; } } return ranked_mobius<T, LIM>(ra); } } // namespace ebi
#line 2 "convolution/subset_convolution.hpp" #line 2 "template/template.hpp" #include <bits/stdc++.h> #define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++) #define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--) #define all(v) v.begin(), v.end() using ll = long long; using ld = long double; using ull = unsigned long long; template <typename T> bool chmin(T &a, const T &b) { if (a <= b) return false; a = b; return true; } template <typename T> bool chmax(T &a, const T &b) { if (a >= b) return false; a = b; return true; } namespace lib { using namespace std; } // namespace lib // using namespace lib; #line 2 "math/ranked_subset_transform.hpp" #line 4 "math/ranked_subset_transform.hpp" namespace lib { template <class T, int LIM = 20> std::vector<std::array<T, LIM + 1>> ranked_zeta(const std::vector<T> &f) { int n = std::bit_width(f.size()) - 1; assert(n <= LIM); assert((int)f.size() == (1 << n)); std::vector<std::array<T, LIM + 1>> rf(1 << n); for (int s = 0; s < (1 << n); s++) rf[s][std::popcount((unsigned int)(s))] = f[s]; for (int i = 0; i < n; i++) { int w = 1 << i; for (int p = 0; p < (1 << n); p += 2 * w) { for (int s = p; s < p + w; s++) { int t = s | (1 << i); for (int d = 0; d <= n; d++) rf[t][d] += rf[s][d]; } } } return rf; } template <class T, int LIM = 20> std::vector<T> ranked_mobius(std::vector<std::array<T, LIM + 1>> rf) { int n = std::bit_width(rf.size()) - 1; assert((int)rf.size() == (1 << n)); for (int i = 0; i < n; i++) { int w = 1 << i; for (int p = 0; p < (1 << n); p += 2 * w) { for (int s = p; s < p + w; s++) { int t = s | (1 << i); for (int d = 0; d <= n; d++) rf[t][d] -= rf[s][d]; } } } std::vector<T> f(1 << n); for (int s = 0; s < (1 << n); s++) { f[s] = rf[s][std::popcount((unsigned int)(s))]; } return f; } } // namespace ebi #line 5 "convolution/subset_convolution.hpp" namespace lib { template <class T, int LIM = 20> std::vector<T> subset_convolution(const std::vector<T> &a, const std::vector<T> &b) { auto ra = ranked_zeta<T, LIM>(a); auto rb = ranked_zeta<T, LIM>(b); int n = std::bit_width(a.size()) - 1; for (int s = (1 << n) - 1; s >= 0; s--) { auto &f = ra[s]; const auto &g = rb[s]; for (int d = n; d >= 0; d--) { T x = 0; for (int i = 0; i <= d; i++) { x += f[i] * g[d - i]; } f[d] = x; } } return ranked_mobius<T, LIM>(ra); } } // namespace ebi