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:heavy_check_mark: ds/segtree/sortable_segtree.hpp

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Code

#include "ds/fastset.hpp"
#include "ds/segtree/segtree.hpp"

template <typename Monoid>
struct Sortable_SegTree {
  using MX = Monoid;
  using X = typename MX::value_type;
  const int N, KEY_MAX;

  struct Node {
    X x, rev_x;
    int size;
    Node *l, *r;
  };
  Node* pool;
  const int NODES;
  int pid;
  using np = Node*;

  FastSet ss;      // 区間の左端全体を表す fastset
  SegTree<MX> seg; // 区間を集約した値を区間の左端にのせた segtree
  vector<np> root; // 区間の左端に、dynamic segtree の node を乗せる
  vector<bool> rev;

  Sortable_SegTree(int NODES, int KEY_MAX, vector<int> key, vector<X> dat) : N(key.size()), KEY_MAX(KEY_MAX), NODES(NODES), pid(0), ss(key.size()), seg(dat) {
    pool = new Node[NODES];
    init(key, dat);
  }
  ~Sortable_SegTree() { delete[] pool; }
  void set(int i, int key, const X& x) {
    assert(key < KEY_MAX);
    split_at(i), split_at(i + 1);
    rev[i] = 0, root[i] = new_node();
    set_rec(root[i], 0, KEY_MAX, key, x);
    seg.set(i, x);
  }

  X prod_all() { return seg.prod_all(); }

  X prod(int l, int r) {
    if (pid > NODES * 0.9) rebuild();
    split_at(l), split_at(r);
    return seg.prod(l, r);
  }

  void sort_inc(int l, int r) {
    split_at(l), split_at(r);
    while (1) {
      if (pid > NODES * 0.9) rebuild();
      np c = root[l];
      int i = ss.next(l + 1);
      if (i == r) break;
      root[l] = merge(c, root[i]);
      ss.erase(i), seg.set(i, MX::unit());
    }
    rev[l] = 0, seg.set(l, root[l]->x);
  };

  void sort_dec(int l, int r) {
    if (pid > NODES * 0.9) rebuild();
    sort_inc(l, r), rev[l] = 1;
    seg.set(l, root[l]->rev_x);
  };

  pair<vc<int>, vc<X>> get_all() {
    vector<int> key;
    vector<X> dat;
    key.reserve(N);
    dat.reserve(N);
    auto dfs = [&](auto& dfs, np n, int l, int r, bool rev) -> void {
      if (!n) return;
      if (r == l + 1) {
        key.eb(l), dat.eb(n->x);
        return;
      }
      int m = (l + r) / 2;
      if (!rev) { dfs(dfs, n->l, l, m, rev), dfs(dfs, n->r, m, r, rev); }
      if (rev) { dfs(dfs, n->r, m, r, rev), dfs(dfs, n->l, l, m, rev); }
    };
    for (int i = 0; i < N; ++i) {
      if (ss[i]) dfs(dfs, root[i], 0, KEY_MAX, rev[i]);
    }
    return {key, dat};
  }

private:
  void init(vector<int>& key, vector<X>& dat) {
    rev.assign(N, 0), root.clear(), root.reserve(N);
    seg.build(N, [&](int i) -> X { return dat[i]; });
    for (int i = 0; i < N; ++i) {
      ss.insert(i);
      root.eb(new_node(MX::unit()));
      assert(key[i] < KEY_MAX);
      set_rec(root[i], 0, KEY_MAX, key[i], dat[i]);
    }
  }

  // x が左端になるようにする
  void split_at(int x) {
    if (x == N || ss[x]) return;
    int a = ss.prev(x), b = ss.next(a + 1);
    ss.insert(x);
    if (!rev[a]) {
      auto [nl, nr] = split(root[a], x - a);
      root[a] = nl, root[x] = nr;
      rev[a] = rev[x] = 0;
      seg.set(a, root[a]->x), seg.set(x, root[x]->x);
    } else {
      auto [nl, nr] = split(root[a], b - x);
      root[a] = nr, root[x] = nl;
      rev[a] = rev[x] = 1;
      seg.set(a, root[a]->rev_x), seg.set(x, root[x]->rev_x);
    }
  }

  void rebuild() {
    auto [key, dat] = get_all();
    pid = 0;
    init(key, dat);
  }

  np new_node(X x = MX::unit()) {
    assert(pid < NODES);
    pool[pid].x = pool[pid].rev_x = x;
    pool[pid].l = pool[pid].r = nullptr;
    pool[pid].size = 1;
    return &(pool[pid++]);
  }

  pair<np, np> split(np n, int k) {
    if (k == 0) { return {nullptr, n}; }
    if (k == n->size) { return {n, nullptr}; }
    int s = (n->l ? n->l->size : 0);
    Node* b = new_node();
    if (k <= s) {
      auto [nl, nr] = split(n->l, k);
      b->l = nr, b->r = n->r, n->l = nl, n->r = nullptr;
    }
    if (k > s) {
      auto [nl, nr] = split(n->r, k - s);
      n->l = n->l, n->r = nl, b->l = nullptr, b->r = nr;
    }
    update(n), update(b);
    return {n, b};
  }

  np merge(np a, np b) {
    if (!a) return b;
    if (!b) return a;
    a->l = merge(a->l, b->l), a->r = merge(a->r, b->r);
    update(a);
    return a;
  }

  void update(np n) {
    if (!(n->l) && !(n->r)) { return; }
    if (!(n->l)) {
      n->x = n->r->x, n->rev_x = n->r->rev_x, n->size = n->r->size;
      return;
    }
    if (!(n->r)) {
      n->x = n->l->x, n->rev_x = n->l->rev_x, n->size = n->l->size;
      return;
    }
    n->x = MX::op(n->l->x, n->r->x);
    n->rev_x = MX::op(n->r->rev_x, n->l->rev_x);
    n->size = n->l->size + n->r->size;
  }

  void set_rec(np n, int l, int r, int k, const X& x) {
    if (r == l + 1) {
      n->x = n->rev_x = x;
      return;
    }
    int m = (l + r) / 2;
    if (k < m) {
      if (!(n->l)) n->l = new_node();
      set_rec(n->l, l, m, k, x);
    }
    if (m <= k) {
      if (!(n->r)) n->r = new_node();
      set_rec(n->r, m, r, k, x);
    }
    update(n);
  }
};
#line 2 "ds/fastset.hpp"

// 64-ary tree

// space: (N/63) * u64

struct FastSet {
  static constexpr u32 B = 64;
  int n, log;
  vvc<u64> seg;

  FastSet() {}
  FastSet(int n) { build(n); }

  int size() { return n; }

  template <typename F>
  FastSet(int n, F f) {
    build(n, f);
  }

  void build(int m) {
    seg.clear();
    n = m;
    do {
      seg.push_back(vc<u64>((m + B - 1) / B));
      m = (m + B - 1) / B;
    } while (m > 1);
    log = len(seg);
  }
  template <typename F>
  void build(int n, F f) {
    build(n);
    FOR(i, n) { seg[0][i / B] |= u64(f(i)) << (i % B); }
    FOR(h, log - 1) {
      FOR(i, len(seg[h])) {
        seg[h + 1][i / B] |= u64(bool(seg[h][i])) << (i % B);
      }
    }
  }

  bool operator[](int i) const { return seg[0][i / B] >> (i % B) & 1; }
  void insert(int i) {
    for (int h = 0; h < log; h++) {
      seg[h][i / B] |= u64(1) << (i % B), i /= B;
    }
  }
  void add(int i) { insert(i); }
  void erase(int i) {
    u64 x = 0;
    for (int h = 0; h < log; h++) {
      seg[h][i / B] &= ~(u64(1) << (i % B));
      seg[h][i / B] |= x << (i % B);
      x = bool(seg[h][i / B]);
      i /= B;
    }
  }
  void remove(int i) { erase(i); }

  // min[x,n) or n

  int next(int i) {
    assert(i <= n);
    chmax(i, 0);
    for (int h = 0; h < log; h++) {
      if (i / B == seg[h].size()) break;
      u64 d = seg[h][i / B] >> (i % B);
      if (!d) {
        i = i / B + 1;
        continue;
      }
      i += lowbit(d);
      for (int g = h - 1; g >= 0; g--) {
        i *= B;
        i += lowbit(seg[g][i / B]);
      }
      return i;
    }
    return n;
  }

  // max [0,x], or -1

  int prev(int i) {
    assert(i >= -1);
    if (i >= n) i = n - 1;
    for (int h = 0; h < log; h++) {
      if (i == -1) break;
      u64 d = seg[h][i / B] << (63 - i % B);
      if (!d) {
        i = i / B - 1;
        continue;
      }
      i -= __builtin_clzll(d);
      for (int g = h - 1; g >= 0; g--) {
        i *= B;
        i += topbit(seg[g][i / B]);
      }
      return i;
    }
    return -1;
  }

  bool any(int l, int r) { return next(l) < r; }

  // [l, r)

  template <typename F>
  void enumerate(int l, int r, F f) {
    for (int x = next(l); x < r; x = next(x + 1)) f(x);
  }

  string to_string() {
    string s(n, '?');
    for (int i = 0; i < n; ++i) s[i] = ((*this)[i] ? '1' : '0');
    return s;
  }
};
#line 2 "ds/segtree/segtree.hpp"

template <class Monoid>
struct SegTree {
  using MX = Monoid;
  using X = typename MX::value_type;
  using value_type = X;
  vc<X> dat;
  int n, log, size;

  SegTree() {}
  SegTree(int n) { build(n); }
  template <typename F>
  SegTree(int n, F f) {
    build(n, f);
  }
  SegTree(const vc<X>& v) { build(v); }

  void build(int m) {
    build(m, [](int i) -> X { return MX::unit(); });
  }
  void build(const vc<X>& v) {
    build(len(v), [&](int i) -> X { return v[i]; });
  }
  template <typename F>
  void build(int m, F f) {
    n = m, log = 1;
    while ((1 << log) < n) ++log;
    size = 1 << log;
    dat.assign(size << 1, MX::unit());
    FOR(i, n) dat[size + i] = f(i);
    FOR_R(i, 1, size) update(i);
  }

  X get(int i) { return dat[size + i]; }
  vc<X> get_all() { return {dat.begin() + size, dat.begin() + size + n}; }

  void update(int i) { dat[i] = Monoid::op(dat[2 * i], dat[2 * i + 1]); }
  void set(int i, const X& x) {
    assert(i < n);
    dat[i += size] = x;
    while (i >>= 1) update(i);
  }

  void multiply(int i, const X& x) {
    assert(i < n);
    i += size;
    dat[i] = Monoid::op(dat[i], x);
    while (i >>= 1) update(i);
  }

  X prod(int L, int R) {
    assert(0 <= L && L <= R && R <= n);
    X vl = Monoid::unit(), vr = Monoid::unit();
    L += size, R += size;
    while (L < R) {
      if (L & 1) vl = Monoid::op(vl, dat[L++]);
      if (R & 1) vr = Monoid::op(dat[--R], vr);
      L >>= 1, R >>= 1;
    }
    return Monoid::op(vl, vr);
  }

  X prod_all() { return dat[1]; }

  template <class F>
  int max_right(F check, int L) {
    assert(0 <= L && L <= n && check(Monoid::unit()));
    if (L == n) return n;
    L += size;
    X sm = Monoid::unit();
    do {
      while (L % 2 == 0) L >>= 1;
      if (!check(Monoid::op(sm, dat[L]))) {
        while (L < size) {
          L = 2 * L;
          if (check(Monoid::op(sm, dat[L]))) { sm = Monoid::op(sm, dat[L++]); }
        }
        return L - size;
      }
      sm = Monoid::op(sm, dat[L++]);
    } while ((L & -L) != L);
    return n;
  }

  template <class F>
  int min_left(F check, int R) {
    assert(0 <= R && R <= n && check(Monoid::unit()));
    if (R == 0) return 0;
    R += size;
    X sm = Monoid::unit();
    do {
      --R;
      while (R > 1 && (R % 2)) R >>= 1;
      if (!check(Monoid::op(dat[R], sm))) {
        while (R < size) {
          R = 2 * R + 1;
          if (check(Monoid::op(dat[R], sm))) { sm = Monoid::op(dat[R--], sm); }
        }
        return R + 1 - size;
      }
      sm = Monoid::op(dat[R], sm);
    } while ((R & -R) != R);
    return 0;
  }

  // prod_{l<=i<r} A[i xor x]
  X xor_prod(int l, int r, int xor_val) {
    static_assert(Monoid::commute);
    X x = Monoid::unit();
    for (int k = 0; k < log + 1; ++k) {
      if (l >= r) break;
      if (l & 1) { x = Monoid::op(x, dat[(size >> k) + ((l++) ^ xor_val)]); }
      if (r & 1) { x = Monoid::op(x, dat[(size >> k) + ((--r) ^ xor_val)]); }
      l /= 2, r /= 2, xor_val /= 2;
    }
    return x;
  }
};
#line 3 "ds/segtree/sortable_segtree.hpp"

template <typename Monoid>
struct Sortable_SegTree {
  using MX = Monoid;
  using X = typename MX::value_type;
  const int N, KEY_MAX;

  struct Node {
    X x, rev_x;
    int size;
    Node *l, *r;
  };
  Node* pool;
  const int NODES;
  int pid;
  using np = Node*;

  FastSet ss;      // 区間の左端全体を表す fastset
  SegTree<MX> seg; // 区間を集約した値を区間の左端にのせた segtree
  vector<np> root; // 区間の左端に、dynamic segtree の node を乗せる
  vector<bool> rev;

  Sortable_SegTree(int NODES, int KEY_MAX, vector<int> key, vector<X> dat) : N(key.size()), KEY_MAX(KEY_MAX), NODES(NODES), pid(0), ss(key.size()), seg(dat) {
    pool = new Node[NODES];
    init(key, dat);
  }
  ~Sortable_SegTree() { delete[] pool; }
  void set(int i, int key, const X& x) {
    assert(key < KEY_MAX);
    split_at(i), split_at(i + 1);
    rev[i] = 0, root[i] = new_node();
    set_rec(root[i], 0, KEY_MAX, key, x);
    seg.set(i, x);
  }

  X prod_all() { return seg.prod_all(); }

  X prod(int l, int r) {
    if (pid > NODES * 0.9) rebuild();
    split_at(l), split_at(r);
    return seg.prod(l, r);
  }

  void sort_inc(int l, int r) {
    split_at(l), split_at(r);
    while (1) {
      if (pid > NODES * 0.9) rebuild();
      np c = root[l];
      int i = ss.next(l + 1);
      if (i == r) break;
      root[l] = merge(c, root[i]);
      ss.erase(i), seg.set(i, MX::unit());
    }
    rev[l] = 0, seg.set(l, root[l]->x);
  };

  void sort_dec(int l, int r) {
    if (pid > NODES * 0.9) rebuild();
    sort_inc(l, r), rev[l] = 1;
    seg.set(l, root[l]->rev_x);
  };

  pair<vc<int>, vc<X>> get_all() {
    vector<int> key;
    vector<X> dat;
    key.reserve(N);
    dat.reserve(N);
    auto dfs = [&](auto& dfs, np n, int l, int r, bool rev) -> void {
      if (!n) return;
      if (r == l + 1) {
        key.eb(l), dat.eb(n->x);
        return;
      }
      int m = (l + r) / 2;
      if (!rev) { dfs(dfs, n->l, l, m, rev), dfs(dfs, n->r, m, r, rev); }
      if (rev) { dfs(dfs, n->r, m, r, rev), dfs(dfs, n->l, l, m, rev); }
    };
    for (int i = 0; i < N; ++i) {
      if (ss[i]) dfs(dfs, root[i], 0, KEY_MAX, rev[i]);
    }
    return {key, dat};
  }

private:
  void init(vector<int>& key, vector<X>& dat) {
    rev.assign(N, 0), root.clear(), root.reserve(N);
    seg.build(N, [&](int i) -> X { return dat[i]; });
    for (int i = 0; i < N; ++i) {
      ss.insert(i);
      root.eb(new_node(MX::unit()));
      assert(key[i] < KEY_MAX);
      set_rec(root[i], 0, KEY_MAX, key[i], dat[i]);
    }
  }

  // x が左端になるようにする
  void split_at(int x) {
    if (x == N || ss[x]) return;
    int a = ss.prev(x), b = ss.next(a + 1);
    ss.insert(x);
    if (!rev[a]) {
      auto [nl, nr] = split(root[a], x - a);
      root[a] = nl, root[x] = nr;
      rev[a] = rev[x] = 0;
      seg.set(a, root[a]->x), seg.set(x, root[x]->x);
    } else {
      auto [nl, nr] = split(root[a], b - x);
      root[a] = nr, root[x] = nl;
      rev[a] = rev[x] = 1;
      seg.set(a, root[a]->rev_x), seg.set(x, root[x]->rev_x);
    }
  }

  void rebuild() {
    auto [key, dat] = get_all();
    pid = 0;
    init(key, dat);
  }

  np new_node(X x = MX::unit()) {
    assert(pid < NODES);
    pool[pid].x = pool[pid].rev_x = x;
    pool[pid].l = pool[pid].r = nullptr;
    pool[pid].size = 1;
    return &(pool[pid++]);
  }

  pair<np, np> split(np n, int k) {
    if (k == 0) { return {nullptr, n}; }
    if (k == n->size) { return {n, nullptr}; }
    int s = (n->l ? n->l->size : 0);
    Node* b = new_node();
    if (k <= s) {
      auto [nl, nr] = split(n->l, k);
      b->l = nr, b->r = n->r, n->l = nl, n->r = nullptr;
    }
    if (k > s) {
      auto [nl, nr] = split(n->r, k - s);
      n->l = n->l, n->r = nl, b->l = nullptr, b->r = nr;
    }
    update(n), update(b);
    return {n, b};
  }

  np merge(np a, np b) {
    if (!a) return b;
    if (!b) return a;
    a->l = merge(a->l, b->l), a->r = merge(a->r, b->r);
    update(a);
    return a;
  }

  void update(np n) {
    if (!(n->l) && !(n->r)) { return; }
    if (!(n->l)) {
      n->x = n->r->x, n->rev_x = n->r->rev_x, n->size = n->r->size;
      return;
    }
    if (!(n->r)) {
      n->x = n->l->x, n->rev_x = n->l->rev_x, n->size = n->l->size;
      return;
    }
    n->x = MX::op(n->l->x, n->r->x);
    n->rev_x = MX::op(n->r->rev_x, n->l->rev_x);
    n->size = n->l->size + n->r->size;
  }

  void set_rec(np n, int l, int r, int k, const X& x) {
    if (r == l + 1) {
      n->x = n->rev_x = x;
      return;
    }
    int m = (l + r) / 2;
    if (k < m) {
      if (!(n->l)) n->l = new_node();
      set_rec(n->l, l, m, k, x);
    }
    if (m <= k) {
      if (!(n->r)) n->r = new_node();
      set_rec(n->r, m, r, k, x);
    }
    update(n);
  }
};
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