Step Sum
(library/util/step_sum.hpp)

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• Last update: 2023-09-15 20:02:25+09:00
• Include: #include "library/util/step_sum.hpp"

Step Sum

Depends on

• Barrett Reduction (library/number/barrett_reduction.hpp)

Verified with

• test/src/util/step_sum/dummy.test.cpp

Code

#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

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