kpr/data_structure/SegmentTree.hpp

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Last update: 2023-06-22 14:29:46+09:00
Include: #include "kpr/data_structure/SegmentTree.hpp"

Depends on

Required by

Verified with

verify/yosupo/point_set_range_composite.test.cpp

Code

#pragma once
#include <algorithm>
#include <cstdint>
#include <utility>
#include <vector>
#include "../algorithm/bit.hpp"
#include "../function/monoid.hpp"
#include "../meta/setting.hpp"

namespace kpr {
    template<class T, class Op = Add<T>>
    struct SegmentTree {
        using value_type = T;
        using num_type = std::size_t;
        using reference = T&;
        using const_reference = const T&;
        using operator_type = Op;

    private:
        int n, log, num;
        std::vector<T> tree;
        Op op;

        void update(int k) {
            tree[k] = op(tree[2 * k], tree[2 * k + 1]);
        }

    public:
        SegmentTree() noexcept = default;
        template<class... Args>
        explicit SegmentTree(Args&&... args) {
            std::vector<T> v(std::forward<Args>(args)...);
            n = v.size();
            log = ceil_bit(n);
            num = 1 << log;
            tree = std::vector<T>(num * 2, op.id());
            std::move(v.begin(), v.end(), tree.begin() + num);
            for (int i = num - 1; i >= 1; --i) update(i);
        }

        std::size_t size() const noexcept {
            return n;
        }

        void set(int p, const T& x) {
            p += num;
            tree[p] = x;
            for (int i = 1; i <= log; ++i) update(p >> i);
        }

        T get(int p) const {
            return tree[p + num];
        }

        T prod(int r) const {
            T sl = op.id(), sr = op.id();
            int l = num;
            r += num;
            while (l < r) {
                if (l & 1) {
                    sl = op(std::move(sl), tree[l]);
                    ++l;
                }
                if (r & 1) {
                    --r;
                    sr = op(tree[r], std::move(sr));
                }
                l >>= 1;
                r >>= 1;
            }
            return op(sl, sr);
        }
        T prod(int l, int r) const {
            T sl = op.id(), sr = op.id();
            l += num;
            r += num;
            while (l < r) {
                if (l & 1) {
                    sl = op(std::move(sl), tree[l]);
                    ++l;
                }
                if (r & 1) {
                    --r;
                    sr = op(tree[r], std::move(sr));
                }
                l >>= 1;
                r >>= 1;
            }
            return op(sl, sr);
        }

        T all_prod() const {
            return tree[1];
        }

        template<class F>
        KYOPRO_BASE_INT max_right(int l, F&& func) const {
            if (l == n) return n;
            l += num;
            T s = op.id();
            do {
                while (!(l & 1)) l >>= 1;
                if (!func(op(s, tree[l]))) {
                    while (l < num) {
                        l *= 2;
                        if (func(op(s, tree[l]))) {
                            s = op(std::move(s), tree[l]);
                            ++l;
                        }
                    }
                    return l - num;
                }
                s = op(std::move(s), tree[l]);
                ++l;
            } while ((l & -l) != l);
            return n;
        }

        template<class F>
        KYOPRO_BASE_INT min_left(int r, F&& func) const {
            if (r == 0) return 0;
            r += num;
            T s = op.id();
            do {
                --r;
                while (r > 1 && (r & 1)) r >>= 1;
                if (!func(op(tree[r], s))) {
                    while (r < num) {
                        r = r * 2 + 1;
                        if (func(op(tree[r], s))) {
                            s = op(tree[r], std::move(s));
                            --r;
                        }
                    }
                    return r + 1 - num;
                }
                s = op(tree[r], std::move(s));
            } while ((r & -r) != r);
            return 0;
        }
    };
} // namespace kpr

#line 2 "kpr/data_structure/SegmentTree.hpp"
#include <algorithm>
#include <cstdint>
#include <utility>
#include <vector>
#line 2 "kpr/algorithm/bit.hpp"
#include <limits>
#include <type_traits>
#line 3 "kpr/meta/setting.hpp"

#ifndef KYOPRO_BASE_INT
// 基本符号付き整数型

#define KYOPRO_BASE_INT std::int64_t
#endif

#ifndef KYOPRO_BASE_UINT
// 基本符号なし整数型

#define KYOPRO_BASE_UINT std::uint64_t
#endif

#ifndef KYOPRO_BASE_FLOAT
// 基本浮動小数点数型

#define KYOPRO_BASE_FLOAT double
#endif

#ifndef KYOPRO_LL
// ll

#define KYOPRO_LL long long
#endif

#ifndef KYOPRO_LF
// lf

#define KYOPRO_LF double
#endif

#ifndef KYOPRO_MINT
// mint

#define KYOPRO_MINT kpr::ModInt<mod>
#endif

#ifndef KYOPRO_DEFAULT_MOD
// 問題で設定されたmod

#define KYOPRO_DEFAULT_MOD (static_cast<KYOPRO_BASE_UINT>(998244353))
#endif

#ifndef KYOPRO_DECIMAL_PRECISION
// 小数精度(桁)

#define KYOPRO_DECIMAL_PRECISION (static_cast<KYOPRO_BASE_UINT>(12))
#endif

#ifndef KYOPRO_INF_DIV
// 無限大を表す整数が最大値の何分の一かを表す

#define KYOPRO_INF_DIV (static_cast<KYOPRO_BASE_UINT>(3))
#endif

#ifndef KYOPRO_BUFFER_SIZE
// デフォルトのバッファサイズ

#define KYOPRO_BUFFER_SIZE (static_cast<KYOPRO_BASE_UINT>(2048))
#endif

#ifndef KYOPRO_BINOM_MOD_MAX
// デフォルトのBinomModの計算上限

#define KYOPRO_BINOM_MOD_MAX (static_cast<KYOPRO_BASE_UINT>(1000000))
#endif
#line 2 "kpr/meta/trait.hpp"
#include <cstddef>
#include <iterator>
#include <tuple>
#line 7 "kpr/meta/trait.hpp"

namespace kpr {
    namespace helper {
        template<class T>
        struct is_integer_helper {
            static constexpr bool value = std::is_integral_v<T>;
        };

        #ifdef __SIZEOF_INT128__
        template<>
        struct is_integer_helper<__int128_t> {
            static constexpr bool value = true;
        };
        template<>
        struct is_integer_helper<__uint128_t> {
            static constexpr bool value = true;
        };
        #endif
    } // namespace helper


    // 型Tが整数か調べる

    template<class T>
    struct is_integer {
        static constexpr bool value = helper::is_integer_helper<std::remove_cv_t<T>>::value;
    };
    // 型Tが整数か調べる

    template<class T>
    inline constexpr bool is_integer_v = is_integer<T>::value;

    // 型Tが符号付き整数か調べる

    template<class T>
    struct is_signed_integer {
        static constexpr bool value = is_integer_v<T> && std::is_signed_v<T>;
    };
    // 型Tが符号付き整数か調べる

    template<class T>
    inline constexpr bool is_signed_integer_v = is_signed_integer<T>::value;

    // 型Tが符号無し整数か調べる

    template<class T>
    struct is_unsigned_integer {
        static constexpr bool value = is_integer_v<T> && !std::is_signed_v<T>;
    };
    // 型Tが符号無し整数か調べる

    template<class T>
    inline constexpr bool is_unsigned_integer_v = is_unsigned_integer<T>::value;

    namespace helper {
        template<class T>
        struct is_floating_point_helper {
            static constexpr bool value = std::is_floating_point_v<T>;
        };

        #ifdef __SIZEOF_FLOAT128__
        template<>
        struct is_floating_point_helper<__float128> {
            static constexpr bool value = true;
        };
        #endif
    } // namespace helper


    // 型Tが浮動小数点数か調べる

    template<class T>
    struct is_floating_point {
        static constexpr bool value = helper::is_floating_point_helper<std::remove_cv_t<T>>::value;
    };
    // 型Tが浮動小数点数か調べる

    template<class T>
    inline constexpr bool is_floating_point_v = is_floating_point<T>::value;

    // 型Tが算術型か調べる

    template<class T>
    struct is_arithmetic {
        static constexpr bool value = is_integer_v<T> || is_floating_point_v<T>;
    };
    // 型Tが算術型か調べる

    template<class T>
    inline constexpr bool is_arithmetic_v = is_arithmetic<T>::value;

    // 型Tがスカラーか調べる

    template<class T>
    struct is_scalar {
        static constexpr bool value = is_arithmetic_v<T> || std::is_enum_v<T> || std::is_pointer_v<T> || std::is_member_pointer_v<T> || std::is_null_pointer_v<T>;
    };
    // 型Tがスカラーか調べる

    template<class T>
    inline constexpr bool is_scalar_v = is_scalar<T>::value;

    // size以上の大きさを持つ最小の符号付き整数を調べる

    template<std::size_t size>
    struct int_least {
    private:
        static constexpr auto get_type() noexcept {
            static_assert(size <= 128, "The given integer type is too large");
            if constexpr (size <= 8) return std::int_least8_t{};
            else if constexpr (size <= 16) return std::int_least16_t{};
            else if constexpr (size <= 32) return std::int_least32_t{};
            else if constexpr (size <= 64) return std::int_least64_t{};
            else return __int128_t{};
        }

    public:
        using type = decltype(get_type());
    };
    // size以上の大きさを持つ最小の符号付き整数を調べる

    template<std::size_t size>
    using int_least_t = typename int_least<size>::type;

    // size以上の大きさを持つ最小の符号無し整数を調べる

    template<std::size_t size>
    struct uint_least {
    private:
        static constexpr auto get_type() noexcept {
            static_assert(size <= 128, "The give integer type is too large");
            if constexpr (size <= 8) return std::uint_least8_t{};
            else if constexpr (size <= 16) return std::uint_least16_t{};
            else if constexpr (size <= 32) return std::uint_least32_t{};
            else if constexpr (size <= 64) return std::uint_least64_t{};
            else return __uint128_t{};
        }

    public:
        using type = decltype(get_type());
    };
    // size以上の大きさを持つ最小の符号無し整数を調べる

    template<std::size_t size>
    using uint_least_t = typename uint_least<size>::type;

    // Tの次に大きい整数型を調べる

    template<class T>
    struct next_integer {
        static_assert(is_integer_v<T>, "The given type must be an integer type");
        static_assert(sizeof(T) <= 8, "The given integer type is too large");
        using type = std::conditional_t<std::is_signed_v<T>, int_least_t<sizeof(T) * 16>, uint_least_t<sizeof(T) * 16>>;
    };
    // Tの次に大きい整数型を調べる

    template<class T>
    using next_integer_t = typename next_integer<T>::type;

    // Tの次に小さい整数型を調べる

    template<class T>
    struct prev_integer {
        static_assert(is_integer_v<T>, "The given type must be an integer type");
        static_assert(sizeof(T) >= 2, "The given integer type is too large");
        using type = std::conditional_t<std::is_signed_v<T>, int_least_t<sizeof(T) * 4>, uint_least_t<sizeof(T) * 4>>;
    };
    // Tの次に小さい整数型を調べる

    template<class T>
    using prev_integer_t = typename prev_integer<T>::type;

    // 型Tがイテレータか調べる

    template<class T, class = void>
    struct is_iterator {
        static constexpr bool value = false;
    };
    template<class T>
    struct is_iterator<T, std::void_t<typename std::iterator_traits<T>::iterator_category>> {
        static constexpr bool value = true;
    };
    // 型Tがイテレータか調べる

    template<class T>
    inline constexpr bool is_iterator_v = is_iterator<T>::value;

    // 型TがRangeか調べる

    template<class T, class = void>
    struct is_range {
        static constexpr bool value = false;
    };
    template<class T>
    struct is_range<T, std::void_t<decltype(std::begin(std::declval<std::add_lvalue_reference_t<T>>()), std::end(std::declval<std::add_lvalue_reference_t<T>>()))>> {
        static constexpr bool value = true;
    };
     // 型TがRangeか調べる

    template<class T>
    inline constexpr bool is_range_v = is_range<T>::value;

    // Range型Tからイテレータの型を調べる

    template<class T>
    struct range_iterator {
        using type = std::decay_t<decltype(std::begin(std::declval<T>()))>;
    };
    // Range型Tからイテレータの型を調べる

    template<class T>
    using range_iterator_t = typename range_iterator<T>::type;

    // Range型Tから読み取り専用イテレータの型を調べる

    template<class T>
    struct range_const_iterator {
        using type = std::decay_t<decltype(std::cbegin(std::declval<T>()))>;
    };
    // Range型Tから読み取り専用イテレータの型を調べる

    template<class T>
    using range_const_iterator_t = typename range_iterator<T>::type;

    // Range型Tから要素の型を調べる

    template<class T>
    struct range_value {
        using type = std::decay_t<decltype(*std::begin(std::declval<T>()))>;
    };
    // Range型Tから要素の型を調べる

    template<class T>
    using range_value_t = typename range_value<T>::type;
} // namespace kpr

#line 6 "kpr/algorithm/bit.hpp"

namespace kpr {
    // 立っているbitの個数を返す

    [[maybe_unused]] inline constexpr struct {
        template<class T>
        constexpr KYOPRO_BASE_INT operator ()(T x) const noexcept {
            static_assert(is_integer_v<T>, "The argument must be an integer");
            constexpr auto digits = std::numeric_limits<std::make_unsigned_t<T>>::digits;
            static_assert(digits <= std::numeric_limits<unsigned long long>::digits, "The integer type of the argument is too large");
            if constexpr (digits <= std::numeric_limits<unsigned int>::digits) return __builtin_popcount(x);
            else if constexpr (digits <= std::numeric_limits<unsigned long>::digits) return __builtin_popcountl(x);
            else return __builtin_popcountll(x);
        }
    } pop_count;

    // 最上位bitより左の連続した0ビットの数を返す

    [[maybe_unused]] inline constexpr struct {
        template<class T>
        constexpr KYOPRO_BASE_INT operator ()(T x) const noexcept {
            static_assert(is_integer_v<T>, "The argument must be an integer");
            constexpr auto digits = std::numeric_limits<std::make_unsigned_t<T>>::digits;
            static_assert(digits <= std::numeric_limits<unsigned long long>::digits, "The integer type of the argument is too large");
            if (x == 0) return 0;
            if constexpr (digits <= std::numeric_limits<unsigned int>::digits) return __builtin_clz(x) + digits - std::numeric_limits<unsigned int>::digits;
            else if constexpr (digits <= std::numeric_limits<unsigned long>::digits) return __builtin_clzl(x) + digits - std::numeric_limits<unsigned long>::digits;
            else return __builtin_clzll(x) + digits - std::numeric_limits<unsigned long long>::digits;
        }
    } lzero_count;

    // 1の位から連続した0ビットの数を返す

    [[maybe_unused]] inline constexpr struct {
        template<class T>
        constexpr KYOPRO_BASE_INT operator ()(T x) const noexcept {
            static_assert(is_integer_v<T>, "The argument must be an integer");
            constexpr auto digits = std::numeric_limits<std::make_unsigned_t<T>>::digits;
            if (x == 0) return digits;
            static_assert(digits <= std::numeric_limits<unsigned long long>::digits, "The integer type of the argument is too large");
            if constexpr (digits <= std::numeric_limits<unsigned int>::digits) return __builtin_ctz(x);
            else if constexpr (digits <= std::numeric_limits<unsigned long>::digits) return __builtin_ctzl(x);
            else return __builtin_ctzll(x);
        }
    } rzero_count;

    // ビット幅を返す

    [[maybe_unused]] inline constexpr struct {
        template<class T>
        constexpr KYOPRO_BASE_INT operator ()(T x) const noexcept {
            static_assert(is_integer_v<T>, "The argument must be an integer");
            constexpr auto digits = std::numeric_limits<std::make_unsigned_t<T>>::digits;
            static_assert(digits <= std::numeric_limits<unsigned long long>::digits, "The integer type of the argument is too large");
            if (x == 0) return 0;
            if constexpr (digits <= std::numeric_limits<unsigned int>::digits) return std::numeric_limits<unsigned int>::digits - __builtin_clz(x);
            else if constexpr (digits <= std::numeric_limits<unsigned long>::digits) return std::numeric_limits<unsigned long>::digits - __builtin_clzl(x);
            else return std::numeric_limits<unsigned long long>::digits - __builtin_clzll(x);
        }
    } bit_len;

    // 1 << n が与えられた数以下である最大の n を返す (0 の場合、0を返す)

    [[maybe_unused]] inline constexpr struct {
        template<class T>
        constexpr KYOPRO_BASE_INT operator ()(T x) const noexcept {
            return bit_len(x >> static_cast<T>(1));
        }
    } floor_bit;

    // 1 << n が与えられた数以上である最小の n を返す

    [[maybe_unused]] inline constexpr struct {
        template<class T>
        constexpr KYOPRO_BASE_INT operator ()(T x) const noexcept {
            if (x == 0) return 0;
            return bit_len(x - static_cast<T>(1));
        }
    } ceil_bit;
} // namespace kpr

#line 6 "kpr/function/monoid.hpp"

namespace kpr {
    // 足し算のmonoid

    template<class T>
    struct Add {
        using value_type = T;

        static constexpr T id() noexcept {
            return T{};
        }

        constexpr T operator ()(const T& a, const T& b) const noexcept {
            return a + b;
        }

        static constexpr T inv(const T& a) noexcept {
            return -a;
        }
    };

    // 掛け算のmonoid

    template<class T>
    struct Mul {
        using value_type = T;

        static constexpr T id() noexcept {
            return 1;
        }

        constexpr T operator ()(const T& a, const T& b) const noexcept {
            return a * b;
        }

        static constexpr T inv(const T& a) noexcept {
            return 1 / a;
        }
    };

    // minのmonoid

    template<class T>
    struct Min {
        using value_type = T;

        static constexpr T id() noexcept {
            if constexpr (std::numeric_limits<T>::has_infinity) return std::numeric_limits<T>::infinity();
            return std::numeric_limits<T>::max() / KYOPRO_INF_DIV;
        }

        constexpr T operator ()(const T& a, const T& b) const noexcept {
            return a < b ? a : b;
        }
    };

    // maxのmonoid

    template<class T>
    struct Max {
        using value_type = T;

        static constexpr T id() noexcept {
            if constexpr (std::numeric_limits<T>::has_infinity) return -std::numeric_limits<T>::infinity();
            if constexpr (std::is_signed_v<T>) return -(std::numeric_limits<T>::max() / KYOPRO_INF_DIV);
            return 0;
        }

        constexpr  T operator ()(const T& a, const T& b) const noexcept {
            return a > b ? a : b;
        }
    };


    // invを持つか調べる

    template<class, class = void>
    struct has_inv {
        static constexpr bool value = false;
    };

    template<class T>
    struct has_inv<T, std::void_t<decltype(&T::inv)>> {
        static constexpr bool value = true;
    };

    // invを持つか調べる

    template<class T>
    inline constexpr bool has_inv_v = has_inv<T>::value;
} // namespace kpr

#line 9 "kpr/data_structure/SegmentTree.hpp"

namespace kpr {
    template<class T, class Op = Add<T>>
    struct SegmentTree {
        using value_type = T;
        using num_type = std::size_t;
        using reference = T&;
        using const_reference = const T&;
        using operator_type = Op;

    private:
        int n, log, num;
        std::vector<T> tree;
        Op op;

        void update(int k) {
            tree[k] = op(tree[2 * k], tree[2 * k + 1]);
        }

    public:
        SegmentTree() noexcept = default;
        template<class... Args>
        explicit SegmentTree(Args&&... args) {
            std::vector<T> v(std::forward<Args>(args)...);
            n = v.size();
            log = ceil_bit(n);
            num = 1 << log;
            tree = std::vector<T>(num * 2, op.id());
            std::move(v.begin(), v.end(), tree.begin() + num);
            for (int i = num - 1; i >= 1; --i) update(i);
        }

        std::size_t size() const noexcept {
            return n;
        }

        void set(int p, const T& x) {
            p += num;
            tree[p] = x;
            for (int i = 1; i <= log; ++i) update(p >> i);
        }

        T get(int p) const {
            return tree[p + num];
        }

        T prod(int r) const {
            T sl = op.id(), sr = op.id();
            int l = num;
            r += num;
            while (l < r) {
                if (l & 1) {
                    sl = op(std::move(sl), tree[l]);
                    ++l;
                }
                if (r & 1) {
                    --r;
                    sr = op(tree[r], std::move(sr));
                }
                l >>= 1;
                r >>= 1;
            }
            return op(sl, sr);
        }
        T prod(int l, int r) const {
            T sl = op.id(), sr = op.id();
            l += num;
            r += num;
            while (l < r) {
                if (l & 1) {
                    sl = op(std::move(sl), tree[l]);
                    ++l;
                }
                if (r & 1) {
                    --r;
                    sr = op(tree[r], std::move(sr));
                }
                l >>= 1;
                r >>= 1;
            }
            return op(sl, sr);
        }

        T all_prod() const {
            return tree[1];
        }

        template<class F>
        KYOPRO_BASE_INT max_right(int l, F&& func) const {
            if (l == n) return n;
            l += num;
            T s = op.id();
            do {
                while (!(l & 1)) l >>= 1;
                if (!func(op(s, tree[l]))) {
                    while (l < num) {
                        l *= 2;
                        if (func(op(s, tree[l]))) {
                            s = op(std::move(s), tree[l]);
                            ++l;
                        }
                    }
                    return l - num;
                }
                s = op(std::move(s), tree[l]);
                ++l;
            } while ((l & -l) != l);
            return n;
        }

        template<class F>
        KYOPRO_BASE_INT min_left(int r, F&& func) const {
            if (r == 0) return 0;
            r += num;
            T s = op.id();
            do {
                --r;
                while (r > 1 && (r & 1)) r >>= 1;
                if (!func(op(tree[r], s))) {
                    while (r < num) {
                        r = r * 2 + 1;
                        if (func(op(tree[r], s))) {
                            s = op(tree[r], std::move(s));
                            --r;
                        }
                    }
                    return r + 1 - num;
                }
                s = op(tree[r], std::move(s));
            } while ((r & -r) != r);
            return 0;
        }
    };
} // namespace kpr