Segment Tree (ds/segtree.hpp)

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• Last update: 2025-09-18 22:02:23+07:00
• Include: #include "ds/segtree.hpp"

Description

Segment tree can handle range queries with point updates under a monoid in $\mathcal O(\log n)$ time. Example monoid:

struct Sum {
  using T = int;
  static T id() { return 0; }
  static T op(T l, T r) { return l + r; }
};

Operations

• SegTree<M>(int n)
  • Construct segment tree with identity elements
  • Time complexity: $\mathcal O(n)$
• SegTree<M>(const vector<T> &v)
  • Constructs segment tree using v
  • Time complexity: $\mathcal O(n)$
• SegTree<M>(int n, Gen gen)
  • Constructs segment tree using gen(i)
  • Time complexity: $\mathcal O(n)$
• void set(int p, T x)
  • Sets the value at p to be x, consider using operator[]
  • Time complexity: $\mathcal O(\log n)$
• void mul(int p, T x)
  • Sets the value at p (denoted as a[p]) to be M::op(a[p], x)
  • Time complexity: $\mathcal O(\log n)$
• T operator()(int l, int r) or T prod(int l, int r)
  • Returns the product of the range [l, r)
  • Time complexity: $\mathcal O(\log n)$
• int max_right(int l, G g)
  • Finds the maximum r such that g(prod(l, r)) == true. For requirements of g, please visit ac-library’s segtree docs
  • Time complexity: $\mathcal O(\log n)$
• int min_left(int r, G g)
  • Finds the maximum l such that g(prod(l, r)) == true. For requirements of g, please visit ac-library’s segtree docs
  • Time complexity: $\mathcal O(\log n)$
• vector<T> to_vec()
  • Returns a vector of leaf nodes
  • Time complexity: $\mathcal O(n)$

Depends on

• other/update_proxy.hpp

Verified with

• test/yosupo/ds/point_add_range_sum.test.cpp
• test/yosupo/ds/segment_tree/point_set_range_composite.test.cpp
• test/yosupo/tree/vertex_add_path_sum_hld.test.cpp

Code

#pragma once

#include "../other/update_proxy.hpp"

// Modified version of atcoder library's segtree.hpp
template<class M> struct SegTree {
    using T = typename M::T;

    int n, m;
    vector<T> t;

    SegTree() = default;
    SegTree(int _n) : n(_n), m(bit_ceil(n)), t(2 * m, M::id()) {}
    template<class G> SegTree(int _n, G &&gen) : SegTree(_n) {
        for (int i = 0; i < n; i++) t[i + m] = gen(i);
        for (int i = m; --i;) update(i);
    }
    template<class V>
    SegTree(const V &v) :
        SegTree((int)v.size(), [&](int i) { return T(v[i]); }) {}

    vector<T> to_vec() {
        vector<T> r(n);
        for (int i = 0; i < n; i++) r[i] = t[i + m];
        return r;
    }
    void set(int p, const T &x) {
        assert(0 <= p && p < n);
        t[p + m] = x, update_from(p);
    }
    void mul(int p, const T &x) {
        assert(0 <= p && p < n);
        t[p + m] = M::op(t[p + m], x), update_from(p);
    }
    auto operator[](int p) {
        assert(0 <= p && p < n);
        UpdateProxy up(t[p + m], [this, p]() { update_from(p); });
        return up;
    }
    T operator[](int p) const {
        assert(0 <= p && p < n);
        return t[p + m];
    }
    T get(int p) const { return (*this)[p]; }
    T operator()(int l, int r) const {
        assert(0 <= l && l <= r && r <= n);
        T resl = M::id(), resr = M::id();
        for (l += m, r += m; l < r; l >>= 1, r >>= 1) {
            if (l & 1) resl = M::op(resl, t[l++]);
            if (r & 1) resr = M::op(t[--r], resr);
        }
        return M::op(resl, resr);
    }
    T pref(int r) const { return (*this)(0, r); }
    T suff(int l) const { return (*this)(l, n); }
    T prod(int l, int r) const { return (*this)(l, r); }
    T all_prod() const { return t[1]; }
    template<class G> int max_right(int l, G &&g) const {
        assert(0 <= l && l <= n);
        assert(g(M::id()));
        if (l == n) return n;
        l += m;
        T sm = M::id();
        do {
            for (; l % 2 == 0; l >>= 1);
            if (!g(M::op(sm, t[l]))) {
                while (l < m) {
                    l = l << 1;
                    if (g(M::op(sm, t[l]))) sm = M::op(sm, t[l++]);
                }
                return l - m;
            }
            sm = M::op(sm, t[l++]);
        } while ((l & -l) != l);
        return n;
    }
    template<class G> int min_left(int r, G &&g) const {
        assert(0 <= r && r <= n);
        assert(g(M::id()));
        if (r == 0) return 0;
        r += m;
        T sm = M::id();
        do {
            for (r--; r > 1 && r & 1; r >>= 1);
            if (!g(M::op(t[r], sm))) {
                while (r < m) {
                    r = r << 1 | 1;
                    if (g(M::op(t[r], sm))) sm = M::op(t[r--], sm);
                }
                return r + 1 - m;
            }
            sm = M::op(t[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    // clang-format off
    static int bit_ceil(int n) { int m = 1; while (m < n) m *= 2; return m; }
    // clang-format on
    void update(int p) { t[p] = M::op(t[p << 1], t[p << 1 | 1]); }
    void update_from(int p) {
        for (p += m; p >>= 1;) update(p);
    }
};

#line 2 "ds/segtree.hpp"

#line 2 "other/update_proxy.hpp"

// clang-format off
template<class T, class Cb> struct UpdateProxy {
    T &x;
    Cb cb;

    UpdateProxy(T &_x, Cb _cb) : x(_x), cb(_cb) {}

    operator const T &() const { return x; }
    auto &operator*() && { return x; }
    auto operator->() && { return &x; }
    auto operator++(int) && { T old = x; return ++x, cb(), old; }
    auto operator--(int) && { T old = x; return --x, cb(), old; }
    auto &operator++() && { ++x, cb(); return *this; }
    auto &operator--() && { --x, cb(); return *this; }
    auto &operator+=(const T &r) && { x += r, cb(); return *this; }
    auto &operator-=(const T &r) && { x -= r, cb(); return *this; }
    auto &operator*=(const T &r) && { x *= r, cb(); return *this; }
    auto &operator/=(const T &r) && { x /= r, cb(); return *this; }
    auto &operator%=(const T &r) && { x %= r, cb(); return *this; }
    auto &operator=(const T &r) && { x = r, cb(); return *this; }
    auto &operator<<=(const T &r) && { x <<= r, cb(); return *this; }
    auto &operator>>=(const T &r) && { x >>= r, cb(); return *this; }
    template<class F> auto &apply(F &&f) && { f(x), cb(); return *this; }
};
// clang-format on
#line 4 "ds/segtree.hpp"

// Modified version of atcoder library's segtree.hpp
template<class M> struct SegTree {
    using T = typename M::T;

    int n, m;
    vector<T> t;

    SegTree() = default;
    SegTree(int _n) : n(_n), m(bit_ceil(n)), t(2 * m, M::id()) {}
    template<class G> SegTree(int _n, G &&gen) : SegTree(_n) {
        for (int i = 0; i < n; i++) t[i + m] = gen(i);
        for (int i = m; --i;) update(i);
    }
    template<class V>
    SegTree(const V &v) :
        SegTree((int)v.size(), [&](int i) { return T(v[i]); }) {}

    vector<T> to_vec() {
        vector<T> r(n);
        for (int i = 0; i < n; i++) r[i] = t[i + m];
        return r;
    }
    void set(int p, const T &x) {
        assert(0 <= p && p < n);
        t[p + m] = x, update_from(p);
    }
    void mul(int p, const T &x) {
        assert(0 <= p && p < n);
        t[p + m] = M::op(t[p + m], x), update_from(p);
    }
    auto operator[](int p) {
        assert(0 <= p && p < n);
        UpdateProxy up(t[p + m], [this, p]() { update_from(p); });
        return up;
    }
    T operator[](int p) const {
        assert(0 <= p && p < n);
        return t[p + m];
    }
    T get(int p) const { return (*this)[p]; }
    T operator()(int l, int r) const {
        assert(0 <= l && l <= r && r <= n);
        T resl = M::id(), resr = M::id();
        for (l += m, r += m; l < r; l >>= 1, r >>= 1) {
            if (l & 1) resl = M::op(resl, t[l++]);
            if (r & 1) resr = M::op(t[--r], resr);
        }
        return M::op(resl, resr);
    }
    T pref(int r) const { return (*this)(0, r); }
    T suff(int l) const { return (*this)(l, n); }
    T prod(int l, int r) const { return (*this)(l, r); }
    T all_prod() const { return t[1]; }
    template<class G> int max_right(int l, G &&g) const {
        assert(0 <= l && l <= n);
        assert(g(M::id()));
        if (l == n) return n;
        l += m;
        T sm = M::id();
        do {
            for (; l % 2 == 0; l >>= 1);
            if (!g(M::op(sm, t[l]))) {
                while (l < m) {
                    l = l << 1;
                    if (g(M::op(sm, t[l]))) sm = M::op(sm, t[l++]);
                }
                return l - m;
            }
            sm = M::op(sm, t[l++]);
        } while ((l & -l) != l);
        return n;
    }
    template<class G> int min_left(int r, G &&g) const {
        assert(0 <= r && r <= n);
        assert(g(M::id()));
        if (r == 0) return 0;
        r += m;
        T sm = M::id();
        do {
            for (r--; r > 1 && r & 1; r >>= 1);
            if (!g(M::op(t[r], sm))) {
                while (r < m) {
                    r = r << 1 | 1;
                    if (g(M::op(t[r], sm))) sm = M::op(t[r--], sm);
                }
                return r + 1 - m;
            }
            sm = M::op(t[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    // clang-format off
    static int bit_ceil(int n) { int m = 1; while (m < n) m *= 2; return m; }
    // clang-format on
    void update(int p) { t[p] = M::op(t[p << 1], t[p << 1 | 1]); }
    void update_from(int p) {
        for (p += m; p >>= 1;) update(p);
    }
};

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