Dual Segment Tree (双対セグメント木)
(data_structure/dual_segment_tree.hpp)

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• Last update: 2024-03-24 17:04:51+09:00
• Include: #include "data_structure/dual_segment_tree.hpp"

普通のセグメント木+双対セグメント木=遅延セグメント木というイメージ 普通のセグメント木では区間取得 (prod) が、双対セグメント木では区間作用 (apply) ができる

基本的に algebra/monoid_f 以下のファイルをインクルードして使う

// 区間更新 1 点取得
#include "algebra/monoid_f/monoid_set.hpp"
#include "data_structure/dual_segment_tree.hpp"
int main() {
    vector<int> A;
    DualSegmentTree<MonoidSet<int>> seg(A);
}

• seg[i] は seg.get(i) と同じ

Verified with

• verify/aoj_dsl/aoj_dsl_2_d_dual_segment_tree.test.cpp
• verify/aoj_dsl/aoj_dsl_2_e_dual_segment_tree.test.cpp

Code

#pragma once
#include <vector>
#include <cassert>
template <class MF> struct DualSegmentTree {
   public:
    using F = typename MF::F;
    DualSegmentTree() : DualSegmentTree(0) {}
    DualSegmentTree(int n) : DualSegmentTree(std::vector<F>(n, MF::id())) {}
    DualSegmentTree(const std::vector<F>& v) : n((int)(v.size())) {
        log = 0;
        while ((1U << log) < (unsigned int)(n)) log++;
        size = 1 << log;
        lz = std::vector<F>(size << 1, MF::id());
        for (int i = 0; i < n; i++) lz[i + size] = v[i];
    }

    F operator[](int p) {
        assert(0 <= p and p < n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return lz[p];
    }

    F get(int p) {
        assert(0 <= p and p < n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return lz[p];
    }

    void apply(int p, const F& f) {
        assert(0 <= p and p < n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        lz[p] = f;
    }

    void apply(int l, int r, const F& f) {
        assert(0 <= l and l <= r and r <= n);
        if (l == r) return;

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }
    }

   private:
    int n, log, size;
    std::vector<F> lz;
    void all_apply(int k, const F& f) { lz[k] = MF::composition(f, lz[k]); }
    void push(int k) {
        all_apply(k << 1, lz[k]);
        all_apply((k << 1) | 1, lz[k]);
        lz[k] = MF::id();
    }
};

#line 2 "data_structure/dual_segment_tree.hpp"
#include <vector>
#include <cassert>
template <class MF> struct DualSegmentTree {
   public:
    using F = typename MF::F;
    DualSegmentTree() : DualSegmentTree(0) {}
    DualSegmentTree(int n) : DualSegmentTree(std::vector<F>(n, MF::id())) {}
    DualSegmentTree(const std::vector<F>& v) : n((int)(v.size())) {
        log = 0;
        while ((1U << log) < (unsigned int)(n)) log++;
        size = 1 << log;
        lz = std::vector<F>(size << 1, MF::id());
        for (int i = 0; i < n; i++) lz[i + size] = v[i];
    }

    F operator[](int p) {
        assert(0 <= p and p < n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return lz[p];
    }

    F get(int p) {
        assert(0 <= p and p < n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return lz[p];
    }

    void apply(int p, const F& f) {
        assert(0 <= p and p < n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        lz[p] = f;
    }

    void apply(int l, int r, const F& f) {
        assert(0 <= l and l <= r and r <= n);
        if (l == r) return;

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }
    }

   private:
    int n, log, size;
    std::vector<F> lz;
    void all_apply(int k, const F& f) { lz[k] = MF::composition(f, lz[k]); }
    void push(int k) {
        all_apply(k << 1, lz[k]);
        all_apply((k << 1) | 1, lz[k]);
        lz[k] = MF::id();
    }
};

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