src/DataStructure/SegmentTree.hpp

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• Last update: 2020-03-31 17:02:31+09:00
• Include: #include "src/DataStructure/SegmentTree.hpp"

概要

配列の長さが$2n$($n$は扱いたい範囲の要素数)でよいセグメント木。 実装方針の参考: https://codeforces.com/blog/entry/18051

使い方

変数

• op(T a, T b) -> T: T上のモノイド
• e: モノイドの単位元

メソッド

• query(int l, int r) -> T: [l, r)の範囲のモノイドの合成を返す
• update(int i, T x): $i$番目の要素を$x$に変更
• operate(int i, T x): $i$番目の要素に$x$を作用

初期化例

• Intに対するmin

  auto seg = make_segment_tree<Int>([](Int a, Int b) { return std::min(a, b); }, 1e18);
  

• Intに対するmax

  auto seg = make_segment_tree<Int>([](Int a, Int b) { return std::max(a, b); }, -1e18);
  

• Intに対するsum

  auto seg = make_segment_tree<Int>(std::plus<Int>(), 0);
  

• gcd

  auto seg = make_segment_tree<Int>([](Int x, Int y) { return std::gcd(x, y); }, 0);
  

• Intに対するAffine

  auto seg = make_segment_tree<std::pair<Int, Int>>(
    [](std::pair<Int, Int> a, std::pair<Int, Int> b) -> std::pair<Int, Int> {
        return {a.first * b.first, b.first * a.second + b.second};
    },
    {1, 0});
  

Verified with

• test/aoj/DSL_2_A.test.cpp
• test/aoj/DSL_2_B.test.cpp
• test/yosupo/point_add_range_sum.test.cpp
• test/yosupo/point_set_range_composite.test.cpp
• test/yosupo/staticrmq.test.cpp
• test/yukicoder/1036_segment_tree.test.cpp

Code

/// @docs src/DataStructure/SegmentTree.md
template <class T, class F> struct SegmentTree {
    const F op;
    const T e;
    SegmentTree(F op_, T e_) : op(op_), e(e_) {}
    int n;
    std::vector<T> t;
    void set_by_identity(int n_) {
        n = n_;
        t.clear(), t.resize(2 * n, e);
    }
    void set_by_vector(const std::vector<T>& a) {
        n = a.size();
        t.clear(), t.resize(2 * n, e);
        for (int i = 0; i < n; i++) t[i + n] = a[i];
        build();
    }
    void build() {
        for (int i = n - 1; i; --i) t[i] = op(t[2 * i], t[2 * i + 1]);
    }
    T& operator[](int i) { return t[i + n]; }
    // [l, r)
    T query(int l, int r) const {
        assert(0 <= l && l <= r && r <= n);
        T resl = e, resr = e;
        for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
            if (l & 1) resl = op(resl, t[l++]);
            if (r & 1) resr = op(t[--r], resr);
        }
        return op(resl, resr);
    }
    // i番目をxに変更
    void update(int i, const T& x) {
        assert(0 <= i && i < n);
        t[i += n] = x;
        while (i >>= 1) t[i] = op(t[2 * i], t[2 * i + 1]);
    }
    // i番目にxを作用 (a[i] = op(a[i], x))
    void operate(int i, const T& x) {
        assert(0 <= i && i < n);
        i += n;
        t[i] = op(t[i], x);
        while (i >>= 1) t[i] = op(t[2 * i], t[2 * i + 1]);
    }
    friend std::string to_string(const SegmentTree<T, F>& seg) {
        return to_string(std::vector<T>(seg.t.begin() + seg.n, seg.t.end()));
    }
};
template <class T, class F> auto make_segment_tree(F op, T e) { return SegmentTree<T, F>(op, e); }

#line 1 "src/DataStructure/SegmentTree.hpp"
/// @docs src/DataStructure/SegmentTree.md
template <class T, class F> struct SegmentTree {
    const F op;
    const T e;
    SegmentTree(F op_, T e_) : op(op_), e(e_) {}
    int n;
    std::vector<T> t;
    void set_by_identity(int n_) {
        n = n_;
        t.clear(), t.resize(2 * n, e);
    }
    void set_by_vector(const std::vector<T>& a) {
        n = a.size();
        t.clear(), t.resize(2 * n, e);
        for (int i = 0; i < n; i++) t[i + n] = a[i];
        build();
    }
    void build() {
        for (int i = n - 1; i; --i) t[i] = op(t[2 * i], t[2 * i + 1]);
    }
    T& operator[](int i) { return t[i + n]; }
    // [l, r)
    T query(int l, int r) const {
        assert(0 <= l && l <= r && r <= n);
        T resl = e, resr = e;
        for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
            if (l & 1) resl = op(resl, t[l++]);
            if (r & 1) resr = op(t[--r], resr);
        }
        return op(resl, resr);
    }
    // i番目をxに変更
    void update(int i, const T& x) {
        assert(0 <= i && i < n);
        t[i += n] = x;
        while (i >>= 1) t[i] = op(t[2 * i], t[2 * i + 1]);
    }
    // i番目にxを作用 (a[i] = op(a[i], x))
    void operate(int i, const T& x) {
        assert(0 <= i && i < n);
        i += n;
        t[i] = op(t[i], x);
        while (i >>= 1) t[i] = op(t[2 * i], t[2 * i + 1]);
    }
    friend std::string to_string(const SegmentTree<T, F>& seg) {
        return to_string(std::vector<T>(seg.t.begin() + seg.n, seg.t.end()));
    }
};
template <class T, class F> auto make_segment_tree(F op, T e) { return SegmentTree<T, F>(op, e); }

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