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#include "library/util/step_sum.hpp"
#ifndef SUISEN_STEP_SUM #define SUISEN_STEP_SUM #include <vector> #include "library/number/barrett_reduction.hpp" namespace suisen { template <typename T> struct StepSum { using value_type = T; StepSum() : StepSum(std::vector<value_type>{}, 1) {} template <typename Sequence> StepSum(const Sequence &a, int step) : _sum(a.begin(), a.end()), _step(step), _n(_sum.size()), _br(_step) { for (int i = _step; i < _n; ++i) { _sum[i] += _sum[i - _step]; } } // sum A_i for i = k (mod step) and i in [l, r) value_type sum(int k, int l, int r) const { if (r <= k or r <= l or l >= _n) return 0; const int t = _br.quo(std::min(_n, r) - 1 - k); T ans = _sum[t * _step + k]; if (l > k) { const int s = _br.quo(l - 1 - k); ans -= _sum[s * _step + k]; } return ans; } // sum A_i for i = k (mod step) and i in [l, r) value_type operator()(int k, int l, int r) const { return sum(k, l, r); } // sum[i] = a[i] + a[i - step] + a[i - 2 * step] + ... std::vector<value_type>& data() { return _sum; } // sum[i] = a[i] + a[i - step] + a[i - 2 * step] + ... const std::vector<value_type>& data() const { return _sum; } private: std::vector<value_type> _sum; int _step, _n; barrett _br; }; template <typename Sequence> StepSum(Sequence, int) -> StepSum<std::decay_t<decltype(*std::declval<Sequence>().begin())>>; } // namespace suisen #endif // SUISEN_STEP_SUM
#line 1 "library/util/step_sum.hpp" #include <vector> #line 1 "library/number/barrett_reduction.hpp" #include <array> #include <cassert> #include <cstdint> #include <utility> namespace suisen { struct barrett { constexpr barrett() : M(1), L(0) {} constexpr explicit barrett(uint32_t M) : M(M), L(uint64_t(-1) / M + 1) { assert(M); } constexpr int32_t mod() { return M; } constexpr uint32_t umod() const { return M; } // floor(x/M) (correctly works for all 0<=x<2^64) template <bool care_M1 = true> constexpr uint64_t quo(uint64_t x) const { return quorem<care_M1>(x).first; } // x%M (correctly works for all 0<=x<2^64) template <bool care_M1 = true> constexpr uint32_t rem(uint64_t x) const { return quorem<care_M1>(x).second; } // { floor(x/M), x%M } (correctly works for all 0<=x<2^64) template <bool care_M1 = true> constexpr std::pair<uint64_t, uint32_t> quorem(uint64_t x) const { if constexpr (care_M1) if (M == 1) return { x, 0 }; uint64_t q = (__uint128_t(x) * L) >> 64; int32_t r = x - q * M; if (r < 0) --q, r += M; return { q, uint32_t(r) }; } // a*b mod M template <bool care_M1 = true> constexpr uint32_t mul(uint32_t a, uint32_t b) const { return rem<care_M1>(uint64_t(a) * b); } private: uint32_t M; // mod uint64_t L; // ceil(2^K / M), where K = 64 (if M != 1) }; } // namespace suisen #line 7 "library/util/step_sum.hpp" namespace suisen { template <typename T> struct StepSum { using value_type = T; StepSum() : StepSum(std::vector<value_type>{}, 1) {} template <typename Sequence> StepSum(const Sequence &a, int step) : _sum(a.begin(), a.end()), _step(step), _n(_sum.size()), _br(_step) { for (int i = _step; i < _n; ++i) { _sum[i] += _sum[i - _step]; } } // sum A_i for i = k (mod step) and i in [l, r) value_type sum(int k, int l, int r) const { if (r <= k or r <= l or l >= _n) return 0; const int t = _br.quo(std::min(_n, r) - 1 - k); T ans = _sum[t * _step + k]; if (l > k) { const int s = _br.quo(l - 1 - k); ans -= _sum[s * _step + k]; } return ans; } // sum A_i for i = k (mod step) and i in [l, r) value_type operator()(int k, int l, int r) const { return sum(k, l, r); } // sum[i] = a[i] + a[i - step] + a[i - 2 * step] + ... std::vector<value_type>& data() { return _sum; } // sum[i] = a[i] + a[i - step] + a[i - 2 * step] + ... const std::vector<value_type>& data() const { return _sum; } private: std::vector<value_type> _sum; int _step, _n; barrett _br; }; template <typename Sequence> StepSum(Sequence, int) -> StepSum<std::decay_t<decltype(*std::declval<Sequence>().begin())>>; } // namespace suisen