Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/library-checker/vertex_add_path_sum.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"

#include "../../code/ds/hld.hpp"
#include "../../code/io/fastio.hpp"

using T = std::pair<i64, i32>;
using F = i64;

T op(T a, T b) { return T{a.first + b.first, a.second + b.second}; }
T e() { return T{0, 0}; }
T mapping(F f, T a) { return T{f + a.first, a.second}; }
F composition(F f, F g) { return f + g; }
F id() { return 0; }

int main() {
  u32 n, q;
  tifa_libs::fin >> n >> q;
  vec<i64> b(n);
  vec<T> a(n);
  for (auto& x : b) tifa_libs::fin >> x;
  tifa_libs::graph::tree tr_(n);
  for (u32 i = 1, u, v; i < n; ++i) tifa_libs::fin >> u >> v, tr_.add_arc((u32)u, (u32)v), tr_.add_arc((u32)v, (u32)u);
  tifa_libs::ds::hld<T, op, e, F, mapping, composition, id> tr(tr_);
  for (u32 i = 0; i < n; ++i) a[tr.info.dfn[i]].first = b[i], a[tr.info.dfn[i]].second = 1;
  tr.build(a);
  for (u32 i = 0, opt, u; i < q; ++i) {
    tifa_libs::fin >> opt >> u;
    if (opt == 0) {
      i64 x;
      tifa_libs::fin >> x;
      tr.node_update((u32)u, x);
    } else {
      u32 v;
      tifa_libs::fin >> v;
      tifa_libs::fout << tr.chain_query((u32)u, (u32)v).first << '\n';
    }
  }
  return 0;
}
#line 1 "src/test_cpverifier/library-checker/vertex_add_path_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"

#line 1 "src/code/ds/hld.hpp"



#line 1 "src/code/tree/tree.hpp"



#line 1 "src/code/graph/alist.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
template <class U, class T>
using vecp = vec<std::pair<U, T>>;
template <class U, class T>
using vvecp = vvec<std::pair<U, T>>;
template <class T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};


#line 5 "src/code/graph/alist.hpp"

namespace tifa_libs::graph {

template <bool with_deg = false>
struct alist {
  using weight_type = u32;
  using value_type = vvecu;
  value_type g;
  u32 cnt_arc;
  vecu deg_in;

  //! vertex ID: [0, n)
  explicit constexpr alist(u32 n = 0) : g(n), cnt_arc(0), deg_in(0) {
    if constexpr (with_deg) deg_in.resize(n);
  }

  constexpr void add_arc(u32 u, u32 v) {
    g[u].push_back(v), ++cnt_arc;
    if constexpr (with_deg) ++deg_in[v];
  }
};
template <class G>
concept is_alist = (std::is_base_of_v<alist<true>, G> || std::is_base_of_v<alist<false>, G>);

}  // namespace tifa_libs::graph


#line 5 "src/code/tree/tree.hpp"

namespace tifa_libs::graph {

struct tree : alist<false> {
  u32 root;

  explicit constexpr tree(u32 n, u32 root = 0) : alist(n), root(root) {}
};

}  // namespace tifa_libs::graph


#line 1 "src/code/tree/tree_top.hpp"



#line 1 "src/code/tree/dfs_info.hpp"



#line 1 "src/code/graph/dfs.hpp"



#line 5 "src/code/graph/dfs.hpp"

namespace tifa_libs::graph {
namespace dfs_impl_ {
template <class G, class Fb, class Fp, class Fs, class Fr>
constexpr void dfs_(G const& fg, u32 u, u32 fa, Fb&& init, Fp&& pre_dfs, Fs&& post_dfs, Fr&& before_return) {
  init(u, fa);
  for (auto v : fg.g[u])
    if constexpr (is_alist<G>) {
      if (v != fa) {
        pre_dfs(v, u);
        dfs_(fg, v, u, std::forward<Fb>(init), std::forward<Fp>(pre_dfs), std::forward<Fs>(post_dfs), std::forward<Fr>(before_return));
        post_dfs(v, u);
      }
    } else {
      if (v.first != fa) {
        pre_dfs(v.first, u, v.second);
        dfs_(fg, v.first, u, std::forward<Fb>(init), std::forward<Fp>(pre_dfs), std::forward<Fs>(post_dfs), std::forward<Fr>(before_return));
        post_dfs(v.first, u, v.second);
      }
    }
  before_return(u, fa);
}
}  // namespace dfs_impl_

template <class G, class Fb, class Fp, class Fs, class Fr>
constexpr void dfs(G const& fg, u32 start, Fb&& init, Fp&& pre_dfs, Fs&& post_dfs, Fr&& before_return) { dfs_impl_::dfs_(fg, start, -1_u32, std::forward<Fb>(init), std::forward<Fp>(pre_dfs), std::forward<Fs>(post_dfs), std::forward<Fr>(before_return)); }

}  // namespace tifa_libs::graph


#line 5 "src/code/tree/dfs_info.hpp"

namespace tifa_libs::graph {

enum tree_dfs_info_mask {
  td_dfn = 1,
  td_sz = 2,
  td_fa = 4,
  td_dep = 8,
  td_maxson = 16,
  td_maxdfn = 32,
  td_euler = 64,
  td_go = 128,
  td_dis = 256
};

template <class G>
struct tree_dfs_info {
  using weight_type = typename G::weight_type;

  vecu dfn, sz, fa, dep, maxson, maxdfn, euler;
  vvecu go;
  vec<weight_type> dis;

  template <int state>
  constexpr tree_dfs_info& reset_dfs_info(G const& tree) {
    u32 n = (u32)tree.g.size();
    if constexpr (state & td_dfn) dfn = vecu(n);
    if constexpr (state & (td_sz | td_maxson)) sz = vecu(n);
    if constexpr (state & td_fa) fa = vecu(n);
    if constexpr (state & td_dep) dep = vecu(n);
    if constexpr (state & td_maxson) maxson = vecu(n, n);
    if constexpr (state & td_maxdfn) maxdfn = vecu(n);
    if constexpr (state & td_euler) euler = vecu(n);
    if constexpr (state & td_go) go = vvecu(n, vecu(21u, n));
    if constexpr (state & td_dis) dis = vec<weight_type>(n);

    u32 cnt = 0;
    dfs(
        tree, tree.root,
        [&](u32 u, u32 f) {
          if constexpr (state & td_dfn) dfn[u] = cnt;
          if constexpr (state & td_euler) euler[cnt] = u;
          if constexpr (state & (td_dfn | td_maxdfn | td_euler)) ++cnt;
          if constexpr (state & (td_sz | td_maxson)) sz[u] = 1;
          if constexpr (state & td_fa) fa[u] = f;
          if constexpr (state & td_go) {
            go[u][0] = f;
            for (u32 i = 1; i <= 20u && go[u][i - 1] < n; i++) go[u][i] = go[go[u][i - 1]][i - 1];
          }
        },
        [&](u32 to, u32 u, weight_type const& w = 1) {
          if constexpr (state & td_dep) dep[to] = dep[u] + 1;
          if constexpr (state & td_dis) dis[to] = dis[u] + w;
        },
        [&](u32 to, u32 u, weight_type const& = 1) {
          if constexpr (state & (td_sz | td_maxson)) sz[u] += sz[to];
          if constexpr (state & td_maxson)
            if (maxson[u] == n || sz[to] > sz[maxson[u]]) maxson[u] = to;
        },
        [&](u32 u, u32) {
          if constexpr (state & td_maxdfn) maxdfn[u] = cnt - 1;
        });
    return *this;
  }
};

}  // namespace tifa_libs::graph


#line 5 "src/code/tree/tree_top.hpp"

namespace tifa_libs::graph {

template <class G, bool need_dfn = false>
constexpr vecu tree_top(G const &tr, tree_dfs_info<G> &info) {
  u32 n = (u32)tr.g.size();
  if (info.maxson.empty()) info.template reset_dfs_info<td_maxson>(tr);
  if constexpr (need_dfn) info.dfn = vecu(n);

  vecu top(n, n);
  u32 cnt = 0;
  auto dfs = [&](auto &&dfs, u32 u, u32 top_) -> void {
    if constexpr (need_dfn) info.dfn[u] = cnt++;
    top[u] = top_;
    if (info.maxson[u] == tr.g.size()) return;
    dfs(dfs, info.maxson[u], top_);
    for (auto v : tr.g[u])
      if constexpr (is_alist<G>) {
        if (top[v] == tr.g.size()) dfs(dfs, v, v);
      } else {
        if (top[v.first] == tr.g.size()) dfs(dfs, v.first, v.first);
      }
  };

  dfs(dfs, tr.root, tr.root);
  return top;
}

}  // namespace tifa_libs::graph


#line 1 "src/code/ds/segtree.hpp"



#line 5 "src/code/ds/segtree.hpp"

namespace tifa_libs::ds {
namespace segtree_impl_ {
template <bool use_tag, class T, auto op, auto e, class F, auto mapping, auto composition, auto id>
requires requires(T val, T val_l, T val_r, F tag) {
  { e() } -> std::same_as<T>;
  { op(val_l, val_r) } -> std::same_as<T>;
  { id() } -> std::same_as<F>;
  { mapping(tag, val) } -> std::same_as<T>;
}
class segtree {
  vec<T> t;
  vec<F> sign;
  vecb set_sign;
  u32 n;

 public:
  explicit constexpr segtree(vec<T> const &a) : t(a.size() * 4), sign(), set_sign(), n((u32)a.size()) {
    if constexpr (use_tag) sign.resize(t.size()), set_sign.resize(t.size());
    build(a, 1, 0, n - 1);
  }
  explicit constexpr segtree(u32 N = 0) : t(N * 4), sign(), set_sign(), n(N) {
    if constexpr (use_tag) sign.resize(t.size()), set_sign.resize(t.size());
    if (n) build(vec<T>(n, e()), 1, 0, n - 1);
  }

  constexpr void update(u32 L, u32 R, F f) { update(1, 0, n - 1, L, R, f); }
  constexpr void update(u32 pos, F f) { update(1, 0, n - 1, pos, pos, f); }
  constexpr void set(u32 L, u32 R, T f) { set(1, 0, n - 1, L, R, f); }
  constexpr void set(u32 pos, T f) { set(1, 0, n - 1, pos, pos, f); }
  constexpr T query(u32 L, u32 R) { return query(1, 0, n - 1, L, R); }
  constexpr T query(u32 pos) { return query(1, 0, n - 1, pos, pos); }

 private:
  constexpr void pushup(u32 x) { t[x] = op(t[x * 2], t[x * 2 + 1]); }
  constexpr void all_update(u32 x, F f) {
    t[x] = mapping(f, t[x]);
    if constexpr (use_tag) sign[x] = composition(f, sign[x]);
  }
  constexpr void all_set(u32 x, T f) {
    t[x] = f;
    if constexpr (use_tag) sign[x] = id(), set_sign[x] = 1;
  }
  constexpr void pushdown(u32 x) {
    if constexpr (use_tag) {
      if (set_sign[x]) all_set(x * 2, t[x]), all_set(x * 2 + 1, t[x]), set_sign[x] = 0;
      else all_update(x * 2, sign[x]), all_update(x * 2 + 1, sign[x]), sign[x] = id();
    }
  }
  constexpr void build(vec<T> const &a, u32 x, u32 l, u32 r) {
    if constexpr (use_tag) sign[x] = id();
    if (l == r) return void(t[x] = a[l]);
    u32 mid = l + (r - l) / 2;
    build(a, x * 2, l, mid), build(a, x * 2 + 1, mid + 1, r);
    pushup(x);
  }
  constexpr void update(u32 x, u32 l, u32 r, u32 L, u32 R, F f) {
    assert(R >= l && L <= r);
    if (L <= l && R >= r) return void(all_update(x, f));
    pushdown(x);
    u32 mid = l + (r - l) / 2;
    if (L <= mid) update(x * 2, l, mid, L, R, f);
    if (R > mid) update(x * 2 + 1, mid + 1, r, L, R, f);
    pushup(x);
  }
  constexpr void set(u32 x, u32 l, u32 r, u32 L, u32 R, T f) {
    assert(R >= l && L <= r);
    if (L <= l && R >= r) return void(all_set(x, f));
    pushdown(x);
    u32 mid = l + (r - l) / 2;
    if (L <= mid) set(x * 2, l, mid, L, R, f);
    if (R > mid) set(x * 2 + 1, mid + 1, r, L, R, f);
    pushup(x);
  }
  constexpr T query(u32 x, u32 l, u32 r, u32 L, u32 R) {
    assert(R >= l && L <= r);
    if (L <= l && R >= r) return t[x];
    pushdown(x);
    u32 mid = l + (r - l) / 2;
    T ret = e();
    if (L <= mid) ret = op(ret, query(x * 2, l, mid, L, R));
    if (R > mid) ret = op(ret, query(x * 2 + 1, mid + 1, r, L, R));
    return ret;
  }
};
}  // namespace segtree_impl_

template <class T, auto op, auto e, class F, auto mapping, auto composition, auto id>
requires requires(F tag_l, F tag_r) {
  { composition(tag_l, tag_r) } -> std::same_as<F>;
}
using segtree = segtree_impl_::segtree<true, T, op, e, F, mapping, composition, id>;
template <class T, auto op, auto e>
using segtree_notag = segtree_impl_::segtree<false, T, op, e, T, op, op, e>;

}  // namespace tifa_libs::ds


#line 7 "src/code/ds/hld.hpp"

namespace tifa_libs::ds {

template <class T, auto op, auto e, class F = T, auto mapping = op, auto composition = e, auto id = e>
requires requires(T val, T val_l, T val_r, F tag, F tag_l, F tag_r) {
  { e() } -> std::same_as<T>;
  { id() } -> std::same_as<F>;
  { op(val_l, val_r) } -> std::same_as<T>;
  { mapping(tag, val) } -> std::same_as<T>;
  { composition(tag_l, tag_r) } -> std::same_as<F>;
}
class hld {
  segtree<T, op, e, F, mapping, composition, id> t;

 public:
  graph::tree& tr;
  graph::tree_dfs_info<graph::tree> info;
  vecu top;

  explicit constexpr hld(graph::tree& tr) : t(), tr(tr), info() {
    info.template reset_dfs_info<graph::td_dep | graph::td_fa>(tr);
    top = graph::tree_top<graph::tree, true>(tr, info);
  }
  explicit constexpr hld(graph::tree& tr, vec<T> const& a) : hld(tr) {
    vec<T> b(a.size());
    for (u32 i = 0; i < a.size(); ++i) b[info.dfn[i]] = a[i];
    build(b);
  }

  constexpr void build(vec<T> const& a) { t = segtree<T, op, e, F, mapping, composition, id>(a); }
  constexpr void chain_update(u32 u, u32 v, F f) {
    while (top[u] != top[v]) {
      if (info.dep[top[u]] < info.dep[top[v]]) std::swap(u, v);
      t.update(info.dfn[top[u]], info.dfn[u], f), u = info.fa[top[u]];
    }
    if (info.dfn[u] < info.dfn[v]) std::swap(u, v);
    t.update(info.dfn[v], info.dfn[u], f);
  }
  constexpr void subtree_update(u32 u, F f) { t.update(info.dfn[u], info.dfn[u] + info.sz[u] - 1, f); }
  constexpr void node_update(u32 u, F f) { t.update(info.dfn[u], f); }
  constexpr void chain_set(u32 u, u32 v, T f) {
    while (top[u] != top[v]) {
      if (info.dep[top[u]] < info.dep[top[v]]) std::swap(u, v);
      t.set(info.dfn[top[u]], info.dfn[u], f), u = info.fa[top[u]];
    }
    if (info.dfn[u] < info.dfn[v]) std::swap(u, v);
    t.set(info.dfn[v], info.dfn[u], f);
  }
  constexpr void subtree_set(u32 u, T f) { t.set(info.dfn[u], info.dfn[u] + info.sz[u] - 1, f); }
  constexpr void node_set(u32 u, T f) { t.set(info.dfn[u], f); }
  constexpr T chain_query(u32 u, u32 v) {
    T ret = e();
    while (top[u] != top[v]) {
      if (info.dep[top[u]] < info.dep[top[v]]) std::swap(u, v);
      ret = op(ret, t.query(info.dfn[top[u]], info.dfn[u])), u = info.fa[top[u]];
    }
    if (info.dfn[u] < info.dfn[v]) std::swap(u, v);
    return op(ret, t.query(info.dfn[v], info.dfn[u]));
  }
  constexpr T subtree_query(u32 u) { return t.query(info.dfn[u], info.dfn[u] + info.sz[u] - 1); }
  constexpr T node_query(u32 u) { return t.query(info.dfn[u]); }
};

}  // namespace tifa_libs::ds


#line 1 "src/code/io/fastio.hpp"



#line 1 "src/code/fast/u32tostr.hpp"



#line 5 "src/code/fast/u32tostr.hpp"

namespace tifa_libs {

constexpr u32 u32tostr_si16(u64 x, char *s) {
  if (x <= 9) {
    *s = (char)(x | 0x30);
    return 1;
  } else if (x <= 99) {
    u64 low = x;
    u64 ll = ((low * 103) >> 9) & 0x1E;
    low += ll * 3;
    ll = ((low & 0xF0) >> 4) | ((low & 0x0F) << 8);
    *(u16 *)s = (u16)(ll | 0x3030);
    return 2;
  }
  return 0;
}
constexpr u32 u32tostr_si32(u64 x, char *s) {
  u64 low = 0, ll = 0;
  u32 digits = 0;
  if (x <= 99) return u32tostr_si16(x, s);
  low = x;
  digits = (low > 999) ? 4 : 3;
  ll = ((low * 5243) >> 19) & 0xFF;
  low -= ll * 100;
  low = (low << 16) | ll;
  ll = ((low * 103) >> 9) & 0x1E001E;
  low += ll * 3;
  ll = ((low & 0x00F000F0) << 28) | (low & 0x000F000F) << 40;
  ll |= 0x3030303000000000;
  u8 *p = (u8 *)&ll;
  if (digits == 4) *(u32 *)s = *(u32 *)(&p[4]);
  else {
    *(u16 *)s = *(u16 *)(&p[5]);
    *(((u8 *)s) + 2) = p[7];
  }

  return digits;
}

constexpr u32 u32tostr(u64 x, char *s) {
  u64 low = 0, ll = 0;
  u32 digits = 0;
  if (x <= 9999) return u32tostr_si32(x, s);
  if (x < 100000000) {
    if ((low = x) > 999999) digits = (low > 9999999) ? 8 : 7;
    else digits = (low > 99999) ? 6 : 5;
  } else {
    u64 high = (x * 0x55E63B89) >> 57;
    low = x - (high * 100000000);
    digits = u32tostr_si16(high, s);
    digits += 8;
  }

  ll = (low * 109951163) >> 40;
  (low -= ll * 10000) |= ll << 32;
  ll = ((low * 5243) >> 19) & 0x000000FF000000FF;
  low -= ll * 100;
  low = (low << 16) | ll;
  ll = ((low * 103) >> 9) & 0x001E001E001E001E;
  low += ll * 3;
  ll = ((low & 0x00F000F000F000F0) >> 4) | (low & 0x000F000F000F000F) << 8;
  ll = (ll >> 32) | (ll << 32) | 0x3030303030303030;

  if (digits >= 8) memcpy(s + digits - 8, &ll, 8);
  else {
    u32 d = digits;
    char *s1 = s, *pll = &(((char *)&ll)[8 - digits]);
    if (d >= 4) {
      memcpy(s1, pll, 4);
      s1 += 4, pll += 4, d -= 4;
    }
    if (d >= 2) {
      memcpy(s1, pll, 2);
      s1 += 2, pll += 2, d -= 2;
    }
    if (d > 0) *(u8 *)s1 = *(u8 *)pll;
  }
  return digits;
}

}  // namespace tifa_libs


#line 1 "src/code/util/traits.hpp"



#line 5 "src/code/util/traits.hpp"

namespace tifa_libs {

template <class T>
concept iterable_c = requires(T v) {
  { v.begin() } -> std::same_as<typename T::iterator>;
  { v.end() } -> std::same_as<typename T::iterator>;
};

template <class T>
concept container_c = iterable_c<T> && !std::derived_from<T, std::basic_string<typename T::value_type>>;

template <class T>
constexpr bool is_char_v = std::is_same_v<T, char> || std::is_same_v<T, signed char> || std::is_same_v<T, unsigned char>;
template <class T>
concept char_c = is_char_v<T>;

template <class T>
constexpr bool is_s128_v = std::is_same_v<T, __int128_t> || std::is_same_v<T, __int128>;
template <class T>
concept s128_c = is_s128_v<T>;

template <class T>
constexpr bool is_u128_v = std::is_same_v<T, __uint128_t> || std::is_same_v<T, unsigned __int128>;
template <class T>
concept u128_c = is_u128_v<T>;

template <class T>
constexpr bool is_i128_v = is_s128_v<T> || is_u128_v<T>;
template <class T>
concept i128_c = is_u128_v<T>;

template <class T>
constexpr bool is_int_v = std::is_integral_v<T> || is_i128_v<T>;
template <class T>
concept int_c = is_int_v<T>;

template <class T>
constexpr bool is_sint_v = is_s128_v<T> || (is_int_v<T> && std::is_signed_v<T>);
template <class T>
concept sint_c = is_sint_v<T>;

template <class T>
constexpr bool is_uint_v = is_u128_v<T> || (is_int_v<T> && std::is_unsigned_v<T>);
template <class T>
concept uint_c = is_uint_v<T>;

template <class T>
concept mint_c = requires(T x) {
  { x.mod() } -> uint_c;
  { x.val() } -> uint_c;
};

template <class T>
constexpr bool is_arithm_v = std::is_arithmetic_v<T> || is_int_v<T>;
template <class T>
concept arithm_c = is_arithm_v<T>;

template <class T>
struct to_sint : std::make_signed<T> {};
template <>
struct to_sint<u128> {
  using type = u128;
};
template <>
struct to_sint<i128> {
  using type = u128;
};
template <class T>
using to_sint_t = typename to_sint<T>::type;

template <class T>
struct to_uint : std::make_unsigned<T> {};
template <>
struct to_uint<u128> {
  using type = u128;
};
template <>
struct to_uint<i128> {
  using type = u128;
};
template <class T>
using to_uint_t = typename to_uint<T>::type;

}  // namespace tifa_libs


#line 6 "src/code/io/fastio.hpp"

namespace tifa_libs {
namespace fastio_impl_ {
//! UB if EOF occured during reading
template <u32 BUF>
class fastin {
  char bf_[BUF], *now_ = bf_, *end_ = bf_;
  FILE *f_;

 public:
  explicit fastin(FILE *f = stdin) : f_(f) {}

  char get() { return now_ == end_ && (end_ = (now_ = bf_) + fread(bf_, 1, BUF, f_), now_ == end_) ? EOF : *(now_)++; }
  char peek() { return now_ == end_ && (end_ = (now_ = bf_) + fread(bf_, 1, BUF, f_), now_ == end_) ? EOF : *(now_); }
  void rebind(FILE *f) {
    f_ = f;
    now_ = end_ = bf_;
  }

  bool iseof() { return peek() == EOF; }

  template <class T>
  requires(sint_c<T> && !char_c<T>)
  fastin &read(T &n) {
    bool is_neg = false;
    char ch = get();
    while (!isdigit(ch)) {
      is_neg |= ch == '-';
      ch = get();
    }
    n = 0;
    while (isdigit(ch)) {
      (n *= 10) += ch & 15;
      ch = get();
    }
    if (is_neg) n = -n;
    return *this;
  }
  template <class T>
  requires(uint_c<T> && !char_c<T>)
  fastin &read(T &n) {
    char ch = get();
    while (!isdigit(ch)) ch = get();
    n = 0;
    while (isdigit(ch)) {
      (n *= 10) += ch & 15;
      ch = get();
    }
    return *this;
  }
  template <mint_c T>
  fastin &read(T &n) {
    decltype(std::declval<T>().sval()) x;
    read(x);
    n = T(x);
    return *this;
  }
  //! ignore cntrl and space
  template <char_c T>
  fastin &read(T &n) {
    while (!isgraph(n = get()));
    return *this;
  }
  fastin &read(char *n) {
    char *n_ = n;
    while (!isgraph(*n_ = get()));
    while (isgraph(*(++n_) = get()));
    *n_ = '\0';
    return *this;
  }
  fastin &read(strn &n) {
    n.clear();
    char n_;
    while (!isgraph(n_ = get()));
    n.push_back(n_);
    while (isgraph(n_ = get())) n.push_back(n_);
    return *this;
  }
  template <class T, class U>
  fastin &read(std::pair<T, U> &p) { return read(p.first).read(p.second); }
  template <class... Ts>
  fastin &read(std::tuple<Ts...> &p) {
    std::apply([&](Ts &...targs) { ((read(targs)), ...); }, p);
    return *this;
  }
  template <container_c T>
  fastin &read(T &p) {
    if (p.begin() == p.end()) return *this;
    for (auto &i : p) read(i);
    return *this;
  }

  fastin &getline(char *n) {
    char *n_ = n;
    while (!isprint(*n_ = get()));
    while (isprint(*(++n_) = get()));
    *n_ = '\0';
    return *this;
  }
  fastin &getline(strn &n) {
    char n_;
    while (!isprint(n_ = get()));
    n.push_back(n_);
    while (isprint(n_ = get())) n.push_back(n_);
    return *this;
  }

  //! NOT ignore cntrl and space
  template <char_c T>
  fastin &strict_read(T &n) {
    n = get();
    return *this;
  }

  template <class T>
  fastin &operator>>(T &val) { return read(val); }
};
template <u32 BUF, u32 INTBUF>
class fastout {
  char int_bf_[INTBUF], *now_ib_ = int_bf_;

  FILE *f_;
  char *now_, bf_[BUF];
  const char *const end_ = bf_ + BUF;

 public:
  explicit fastout(FILE *file = stdout) : f_(file), now_(bf_) {}

  fastout &operator=(fastout const &r) {
    f_ = r.f_;
    now_ = bf_ + (r.now_ - r.bf_);
    memcpy(bf_, r.bf_, sizeof(*bf_) * (r.now_ - r.bf_));
    return *this;
  }
  fastout(fastout const &r) { *this = r; }

  ~fastout() { flush(); }

  void flush() {
    fwrite(bf_, 1, usz(now_ - bf_), f_);
    now_ = bf_;
  }
  void rebind(FILE *file) { f_ = file; }

  template <char_c T>
  fastout &write(T const &n) {
    if (now_ == end_) flush();
    *(now_++) = n;
    return *this;
  }
  fastout &write(const char *n) {
    usz len = strlen(n), l_;
    const char *n_ = n;
    while (now_ + len >= end_) {
      memcpy(now_, n_, l_ = usz(end_ - now_));
      now_ += l_;
      n_ += l_;
      len -= l_;
      flush();
    }
    memcpy(now_, n_, len);
    now_ += len;
    return *this;
  }
  template <class T>
  requires(sint_c<T> && !char_c<T>)
  fastout &write(T n) {
    if (n < 0) {
      write('-');
      n = -n;
    }
    return write(to_uint_t<T>(n));
  }
  template <class T>
  requires(uint_c<T> && !char_c<T>)
  fastout &write(T n) {
    if constexpr (sizeof(T) <= 4) {
      memset(now_ib_ = int_bf_, 0, 11);
      u32tostr(n, now_ib_);
      return write(now_ib_);
    }
    now_ib_ = int_bf_ + INTBUF - 1;
    do {
      *(--(now_ib_)) = char(n % 10) | '0';
    } while (n /= 10);
    return write(now_ib_);
  }
  template <mint_c T>
  fastout &write(T n) { return write(n.val()); }
  fastout &write(strn const &str) { return write(str.c_str()); }
  template <class T, class U>
  fastout &write(std::pair<T, U> const &p) { return write(p.first).space().write(p.second); }
  template <class... Ts>
  fastout &write(std::tuple<Ts...> const &p) {
    std::apply(
        [&](Ts const &...targs) {
          usz n{0};
          ((write(targs).space_if(++n != sizeof...(Ts))), ...);
        },
        p);
    return *this;
  }
  template <container_c T>
  fastout &write(T const &p) {
    if (p.begin() == p.end()) return *this;
    auto it = p.begin();
    write(*it++);
    for (; it != p.end(); ++it) space().write(*it);
    return *this;
  }

  fastout &linebreak() { return write('\n'); }
  fastout &linebreak_if(bool flag) { return flag ? linebreak() : *this; }
  fastout &space() { return write(' '); }
  fastout &space_if(bool flag) { return flag ? space() : *this; }

  template <class T>
  fastout &operator<<(T const &val) { return write(val); }
};
}  // namespace fastio_impl_

inline fastio_impl_::fastin<0x200005> fin;
inline fastio_impl_::fastout<0x200005, 41> fout;

}  // namespace tifa_libs


#line 5 "src/test_cpverifier/library-checker/vertex_add_path_sum.test.cpp"

using T = std::pair<i64, i32>;
using F = i64;

T op(T a, T b) { return T{a.first + b.first, a.second + b.second}; }
T e() { return T{0, 0}; }
T mapping(F f, T a) { return T{f + a.first, a.second}; }
F composition(F f, F g) { return f + g; }
F id() { return 0; }

int main() {
  u32 n, q;
  tifa_libs::fin >> n >> q;
  vec<i64> b(n);
  vec<T> a(n);
  for (auto& x : b) tifa_libs::fin >> x;
  tifa_libs::graph::tree tr_(n);
  for (u32 i = 1, u, v; i < n; ++i) tifa_libs::fin >> u >> v, tr_.add_arc((u32)u, (u32)v), tr_.add_arc((u32)v, (u32)u);
  tifa_libs::ds::hld<T, op, e, F, mapping, composition, id> tr(tr_);
  for (u32 i = 0; i < n; ++i) a[tr.info.dfn[i]].first = b[i], a[tr.info.dfn[i]].second = 1;
  tr.build(a);
  for (u32 i = 0, opt, u; i < q; ++i) {
    tifa_libs::fin >> opt >> u;
    if (opt == 0) {
      i64 x;
      tifa_libs::fin >> x;
      tr.node_update((u32)u, x);
    } else {
      u32 v;
      tifa_libs::fin >> v;
      tifa_libs::fout << tr.chain_query((u32)u, (u32)v).first << '\n';
    }
  }
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 almost_line_00 :heavy_check_mark: AC 604 ms 118 MB
g++-12 almost_line_01 :heavy_check_mark: AC 587 ms 117 MB
g++-12 example_00 :heavy_check_mark: AC 10 ms 6 MB
g++-12 line_00 :heavy_check_mark: AC 508 ms 116 MB
g++-12 line_01 :heavy_check_mark: AC 458 ms 122 MB
g++-12 long-path-decomposition_killer_00 :heavy_check_mark: AC 244 ms 105 MB
g++-12 max_random_00 :heavy_check_mark: AC 992 ms 106 MB
g++-12 max_random_01 :heavy_check_mark: AC 1011 ms 106 MB
g++-12 max_random_02 :heavy_check_mark: AC 974 ms 106 MB
g++-12 random_00 :heavy_check_mark: AC 743 ms 84 MB
g++-12 random_01 :heavy_check_mark: AC 820 ms 99 MB
g++-12 random_02 :heavy_check_mark: AC 366 ms 18 MB
g++-12 random_03 :heavy_check_mark: AC 202 ms 91 MB
g++-12 random_04 :heavy_check_mark: AC 228 ms 62 MB
g++-12 small_00 :heavy_check_mark: AC 10 ms 6 MB
g++-12 small_01 :heavy_check_mark: AC 9 ms 6 MB
g++-12 small_02 :heavy_check_mark: AC 9 ms 6 MB
g++-12 small_03 :heavy_check_mark: AC 9 ms 6 MB
g++-12 small_04 :heavy_check_mark: AC 9 ms 6 MB
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