segTree.cc

/*
  Segment Tree (non-recursive version; including laziness)
  See https://yamate11.github.io/blog/posts/2023/12-03-segment-tree-lib/
 */

//////////////////////////////////////////////////////////////////////
// See help of libins command for dependency spec syntax.
// @@ !! BEGIN(f:<<) ---- segTree.cc

// It seems that we should keep the size power of two,
// considering the binary search.

pair<int, int> segtree_range_of_node(int ht, unsigned i) {
  unsigned m = bit_floor(i);
  unsigned w = ht + 1 - bit_width(i);
  int lo = (i ^ m) << w;
  int hi = lo + (1LL << w);
  return make_pair(lo, hi);
}

vector<int> segtree_nodes_for_range(int ht, unsigned lo, unsigned hi) {
  vector<int> left;
  vector<int> right;
  lo = (1 << ht) + lo;
  hi = (1 << ht) + hi - 1;
  while (lo <= hi) {
    if (lo == hi) {
      left.push_back(lo);
      break;
    }
    if (lo & 1) {
      left.push_back(lo);
      lo++;
    }
    if (not (hi & 1)) {
      right.push_back(hi);
      hi--;
    }
    lo >>= 1;
    hi >>= 1;
  }
  while (not right.empty()) {
    left.push_back(right.back());
    right.pop_back();
  }
  return left;
}

template <typename DAT, typename OP,
	  typename ADD_t, typename COMP_t, typename APPL_t, bool lazy> 
struct GenSegTree {
  using GST = GenSegTree<DAT, OP, ADD_t, COMP_t, APPL_t, lazy>;

  int orig_size;     // size of initdat
  int size;	     // power of two; >= 2
  int height;        // size = 1 << height;
  vector<DAT> node;  // vector of size 2*size.
                     // 0                 : unused
                     // 1    ... size-1   : interval
                     // size ... 2*size-1 : leaf
  vector<OP> susp;   // vector of size size.
                     // suspended operation FOR CHILDREN
                     // (already applied to this node)
  DAT unit_dat;
  OP unit_op;
  ADD_t add;
  COMP_t comp;
  APPL_t appl;
    
  GenSegTree() {}

  GenSegTree(DAT unit_dat_, OP unit_op_, ADD_t add_, COMP_t comp_, APPL_t appl_,
             const vector<DAT>& initdat = vector<DAT>())
    : unit_dat(unit_dat_), unit_op(unit_op_),
      add(add_), comp(comp_), appl(appl_) { set_data(initdat); }

  void set_data(const vector<DAT>& initdat) {
    orig_size = initdat.size();
    if (initdat.size() <= 1) height = 0;
    else   height = sizeof(int) * 8 - __builtin_clz(initdat.size() - 1);
    size = 1 << height;
    node.resize(2*size, unit_dat);
    for (int i = 0; i < (int)initdat.size(); i++) node[size + i] = initdat[i];
    for (int t = size - 1; t >= 1; t--) node[t] = add(node[t<<1|0], node[t<<1|1]);
    susp.resize(size, unit_op);
  }

  void child_updated_sub(int t) {
    node[t] = appl(susp[t], add(node[t<<1|0], node[t<<1|1]));
  }

  void child_updated(int l, int r) {
    r--;
    while (l > 1) {
      l >>= 1;
      r >>= 1;
      child_updated_sub(l);
      if (l < r) child_updated_sub(r);
    }
  }

  void node_op(int i, OP f) {
    node[i] = appl(f, node[i]);
    if (i < size) susp[i] = comp(f, susp[i]);
  }

  // Note that susp[i] HAS ALREADY BEEN APPLIED TO node[i].
  // When push_one(i) is called, susp[j] is updated (for j : i's child) and it is applied to node[j].
  void push_one(int i) {
    node_op(i<<1|0, susp[i]);
    node_op(i<<1|1, susp[i]);
    susp[i] = unit_op;
  }

  void push_upto(int l, int r) {
    for (int s = height; s >= 1; s--) {
      int lz = l >> s;
      int rz = (r-1) >> s;
      push_one(lz);
      if (lz < rz) push_one(rz);
    }
  }

  DAT query(int l, int r) {
    if (l >= r) return unit_dat;
    DAT ret_l = unit_dat;
    DAT ret_r = unit_dat;
    l += size;
    r += size;
    if constexpr(lazy) push_upto(l, r);
    while (l < r) {
      if (l & 1) {
	ret_l = add(ret_l, node[l]);
	l++;
      }
      if (r & 1) {
	ret_r = add(node[r-1], ret_r);
      }
      l >>= 1;
      r >>= 1;
    }
    DAT ret = add(ret_l, ret_r);
    return ret;
  }

  const DAT& get_single(int i) {
    if constexpr(lazy) push_upto(size + i, size + i + 1);
    return node[size + i];
  }

  void set_single(int i, const DAT& t) {
    ll x = size + i;
    if constexpr(lazy) push_upto(x, x + 1);
    node[x] = t;
    for (x >>= 1; x >= 1; x >>= 1) node[x] = add(node[x<<1|0], node[x<<1|1]);
  }

  // obsolete
  template<bool xx = lazy> enable_if_t<! xx> update(int i, DAT t) {
    ll x = size + i;
    node[x] = t;
    for (x >>= 1; x >= 1; x >>= 1) node[x] = add(node[x<<1|0], node[x<<1|1]);
  }

  template<bool xx = lazy> enable_if_t<xx> update(int l, int r, const OP& f) {
    if (l >= r) return;
    l += size;
    r += size;
    push_upto(l, r);
    int l0 = l, r0 = r;
    while (l < r) {
      if (l & 1) {
	node_op(l, f);
	l++;
      }
      if (r & 1) {
	node_op(r-1, f);
      }
      l >>= 1;
      r >>= 1;
    }
    child_updated(l0, r0);
  }

  pair<int, int> range_of_node(unsigned i) { return segtree_range_of_node(height, i); }

  vector<int> nodes_for_range(unsigned lo, unsigned hi) { return segtree_nodes_for_range(height, lo, hi); }

  friend ostream& operator<<(ostream& os, GenSegTree& st) {
    os << '[';
    for (int i = 0; i < st.orig_size; i++) {
      if (i > 0) os << ", ";
      os << st.get_single(i);
    }
    os << ']';
    return os;
  }

  int binsearch_r_until(const auto& check, int l) {
    // DLOGKL("in: binsearch_r_until", l);
    if (not check(unit_dat)) return l - 1;
    if (l == orig_size) return l;
    DAT val = unit_dat;
    int x = l + size;
    if constexpr(lazy) push_upto(x, x + 1);
    while (true) {
      if (x & 1) {
        DAT t = add(val, node[x]);
        if (not check(t)) break;
        val = t;
        x++;
        if (__builtin_popcountll(x) == 1) return orig_size;
      }
      x >>= 1;
      // DLOGKL("1: ", x, val);
    }
    while (x < size) {
      if constexpr(lazy) push_one(x);
      x <<= 1;
      DAT t = add(val, node[x]);
      if (check(t)) {
        x++;
        val = t;
      }
      // DLOGKL("2: ", x, val);
    }
    // DLOGKL("3: ", x - size, orig_size);
    return min(x - size, orig_size);
  }

  int binsearch_r_from(const auto& check, int l) {
    return binsearch_r_until([&](DAT x) { return not check(x); }, l) + 1;
  }

  int binsearch_l_until(const auto& check, int r) {
    if (not check(unit_dat)) return r + 1;
    if (r == 0) return 0;
    DAT val = unit_dat;
    int x = r + size;
    if (x == 2 * size) {
      if (check(node[1])) return 0;
      x = 1;
    }else {
      if constexpr(lazy) push_upto(x - 1, x);
      while (true) {
        if (x & 1) {
          x--;
          DAT t = add(node[x], val);
          if (not check(t)) break;
          val = t;
          if (__builtin_popcountll(x) == 1) return 0;
        }
        x >>= 1;
      }
    }
    while (x < size) {
      if constexpr(lazy) push_one(x);
      x = x << 1 | 1;
      DAT t = add(node[x], val);
      if (check(t)) {
        val = t;
        x--;
      }
    }
    return x + 1 - size;
  }

  int binsearch_l_from(const auto& check, int r) {
    return binsearch_l_until([&](DAT x) { return not check(x); }, r) - 1;
  }

};

template<typename DAT, typename OP>
auto make_seg_tree_lazy(DAT unit_dat, OP unit_op, auto add, auto comp, auto appl,
                        const vector<DAT>& initdat = vector<DAT>()) {
  using ret_t = GenSegTree<DAT, OP, decltype(add), decltype(comp), decltype(appl), true>;
  return ret_t(unit_dat, unit_op, add, comp, appl, initdat);
}

void* dummy_comp(void* x, void* y) { return nullptr; }
template<typename DAT>
DAT dummy_appl(void* x, const DAT& y) { return y; }

template<typename DAT>
auto make_seg_tree(DAT unit_dat, auto add, const vector<DAT>& initdat = vector<DAT>()) {
  using ret_t = GenSegTree<DAT, void*, decltype(add), void* (*)(void*, void*), DAT (*)(void*, const DAT&), false>;
  return ret_t(unit_dat, nullptr, add, dummy_comp, dummy_appl<DAT>, initdat);
}

// @@ !! END() ---- segTree.cc