This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub suisen-cp/cp-library-cpp
#include "library/math/product_of_differences.hpp"
#ifndef SUISEN_PRODUCT_OF_DIFFERNCES #define SUISEN_PRODUCT_OF_DIFFERNCES #include <deque> #include "library/polynomial/multi_point_eval.hpp" namespace suisen { /** * O(N(logN)^2) * return the vector p of length xs.size() s.t. p[i]=Π[j!=i](x[i]-x[j]) */ template <typename FPSType, typename T> std::vector<typename FPSType::value_type> product_of_differences(const std::vector<T>& xs) { // f(x):=Π_i(x-x[i]) // => f'(x)=Σ_i Π[j!=i](x-x[j]) // => f'(x[i])=Π[j!=i](x[i]-x[j]) const int n = xs.size(); std::deque<FPSType> dq; for (int i = 0; i < n; ++i) dq.push_back(FPSType{ -xs[i], 1 }); while (dq.size() >= 2) { auto f = std::move(dq.front()); dq.pop_front(); auto g = std::move(dq.front()); dq.pop_front(); dq.push_back(f * g); } auto f = std::move(dq.front()); f.diff_inplace(); return multi_point_eval<FPSType, T>(f, xs); } } // namespace suisen #endif // SUISEN_PRODUCT_OF_DIFFERNCES
#line 1 "library/math/product_of_differences.hpp" #include <deque> #line 1 "library/polynomial/multi_point_eval.hpp" #include <vector> namespace suisen { template <typename FPSType, typename T> std::vector<typename FPSType::value_type> multi_point_eval(const FPSType& f, const std::vector<T>& xs) { int n = xs.size(); if (n == 0) return {}; std::vector<FPSType> seg(2 * n); for (int i = 0; i < n; ++i) seg[n + i] = FPSType{ -xs[i], 1 }; for (int i = n - 1; i > 0; --i) seg[i] = seg[i * 2] * seg[i * 2 + 1]; seg[1] = f % seg[1]; for (int i = 2; i < 2 * n; ++i) seg[i] = seg[i / 2] % seg[i]; std::vector<typename FPSType::value_type> ys(n); for (int i = 0; i < n; ++i) ys[i] = seg[n + i].size() ? seg[n + i][0] : 0; return ys; } } // namespace suisen #line 6 "library/math/product_of_differences.hpp" namespace suisen { /** * O(N(logN)^2) * return the vector p of length xs.size() s.t. p[i]=Π[j!=i](x[i]-x[j]) */ template <typename FPSType, typename T> std::vector<typename FPSType::value_type> product_of_differences(const std::vector<T>& xs) { // f(x):=Π_i(x-x[i]) // => f'(x)=Σ_i Π[j!=i](x-x[j]) // => f'(x[i])=Π[j!=i](x[i]-x[j]) const int n = xs.size(); std::deque<FPSType> dq; for (int i = 0; i < n; ++i) dq.push_back(FPSType{ -xs[i], 1 }); while (dq.size() >= 2) { auto f = std::move(dq.front()); dq.pop_front(); auto g = std::move(dq.front()); dq.pop_front(); dq.push_back(f * g); } auto f = std::move(dq.front()); f.diff_inplace(); return multi_point_eval<FPSType, T>(f, xs); } } // namespace suisen