test/yj_vertex_add_path_sum.test.cpp

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

#include <cstdint>
#include <cstdio>
#include <utility>
#include <vector>

#include "Graph/hl_decomposition.cpp"
#include "DataStructure/basic_segment_tree.cpp"

int main() {
  size_t n, q;
  scanf("%zu %zu", &n, &q);

  std::vector<intmax_t> a(n);
  for (auto& ai: a) scanf("%jd", &ai);

  std::vector<std::pair<size_t, size_t>> es;
  es.reserve(n-1);
  for (size_t i = 1; i < n; ++i) {
    size_t u, v;
    scanf("%zu %zu", &u, &v);
    es.emplace_back(u, v);
  }

  hl_decomposed_tree<basic_segment_tree<intmax_t>, value_on_vertex_tag> g(a, es);
  for (size_t i = 0; i < q; ++i) {
    int t;
    scanf("%d", &t);

    if (t == 0) {
      size_t p;
      intmax_t x;
      scanf("%zu %jd", &p, &x);
      a[p] += x;
      g.set(p, a[p]);
    } else if (t == 1) {
      size_t u, v;
      scanf("%zu %zu", &u, &v);
      printf("%jd\n", g.fold(u, v));
    }
  }
}

#line 1 "test/yj_vertex_add_path_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"

#include <cstdint>
#include <cstdio>
#include <utility>
#include <vector>

#line 1 "Graph/hl_decomposition.cpp"



/**
 * @brief HL 分解
 * @author えびちゃん
 * @see https://codeforces.com/blog/entry/53170
 */

#include <cstddef>
#include <tuple>
#include <type_traits>
#line 15 "Graph/hl_decomposition.cpp"

struct value_on_directed_edge_tag {};
struct value_on_undirected_edge_tag {};
struct value_on_vertex_tag {};

template <typename RangeQuery, typename ValueAttribute>
class hl_decomposed_tree {
public:
  using size_type = size_t;
  using range_query_type = RangeQuery;
  using value_type = typename range_query_type::value_type;
  using attribute = ValueAttribute;

private:
  size_type M_n = 0;
  std::vector<size_type> M_p, M_hp;  // parent, heavy path root
  std::vector<size_type> M_in;
  range_query_type M_fa, M_fd;

  void M_dfs_size(
      std::vector<std::vector<size_type>>& al, std::vector<size_type>& ss,
      size_type v, size_type p
  ) {
    ss[v] = 1;
    M_p[v] = p;
    if (al[v][0] == p) std::swap(al[v][0], al[v].back());
    for (auto& u: al[v]) {
      if (u == p) continue;
      M_dfs_size(al, ss, u, v);
      ss[v] += ss[u];
      if (ss[u] > ss[al[v][0]]) std::swap(u, al[v][0]);
    }
  }

  void M_dfs_heavy_path(
      std::vector<std::vector<size_type>> const& al, std::vector<size_type> const& ss,
      size_type v, size_type& t
  ) {
    M_in[v] = t++;
    for (auto u: al[v]) {
      if (u == M_p[v]) continue;
      M_hp[u] = ((u == al[v][0])? M_hp[v]: u);
      M_dfs_heavy_path(al, ss, u, t);
    }
  }

  void M_decompose(std::vector<std::vector<size_type>>& al, size_type r = 0) {
    std::vector<size_type> ss(M_n, 0);
    M_dfs_size(al, ss, r, M_n);
    size_type in = 0;
    M_dfs_heavy_path(al, ss, r, in);
  }

  size_type M_lca(size_type u, size_type v) const {
    if (M_in[u] > M_in[v]) std::swap(u, v);
    if (M_hp[u] == M_hp[v]) return u;
    return M_lca(u, M_p[M_hp[v]]);
  }

  static void S_fold(value_type& this_, value_type that, bool foldl) {
    if (foldl) {
      this_ += that;
    } else {
      this_ = that + std::move(this_);
    }
  }

  value_type M_fold_one_way(size_type u, size_type v, bool asc) {
    value_type res{};
    if (asc) {
      while (M_hp[u] != M_hp[v]) {
        size_type l = M_n-1 - M_in[u];
        size_type r = M_n-1 - M_in[M_hp[u]];
        S_fold(res, M_fa.fold(l, r+1), true);
        u = M_p[M_hp[u]];
      }
      size_type l = M_n-1 - M_in[u];
      size_type r = M_n-1 - M_in[v];
      S_fold(res, M_fa.fold(l, r), true);
    } else {
      while (M_hp[u] != M_hp[v]) {
        size_type l = M_in[M_hp[u]];
        size_type r = M_in[u];
        S_fold(res, M_fd.fold(l, r+1), false);
        u = M_p[M_hp[u]];
      }
      size_type l = M_in[v]+1;
      size_type r = M_in[u]+1;
      S_fold(res, M_fd.fold(l, r), false);
    }
    return res;
  }

  template <typename Tp>
  void M_act_one_way(size_type u, size_type v, Tp x, bool asc) {
    if (asc) {
      while (M_hp[u] != M_hp[v]) {
        size_type l = M_n-1 - M_in[u];
        size_type r = M_n-1 - M_in[M_hp[u]];
        M_fa.act(l, r+1, x);
        u = M_p[M_hp[u]];
      }
      size_type l = M_n-1 - M_in[u];
      size_type r = M_n-1 - M_in[v];
      M_fa.act(l, r, x);
    } else {
      while (M_hp[u] != M_hp[v]) {
        size_type l = M_in[M_hp[u]];
        size_type r = M_in[u];
        M_fd.act(l, r+1, x);
        u = M_p[M_hp[u]];
      }
      size_type l = M_in[v]+1;
      size_type r = M_in[u]+1;
      M_fd.act(l, r, x);
    }
  }

  value_type M_fold(size_type u, size_type v) {
    size_type w = M_lca(u, v);
    value_type resl = M_fold_one_way(u, w, true);
    value_type resr = M_fold_one_way(v, w, false);
    if (std::is_same<attribute, value_on_vertex_tag>::value) {
      resl += M_fd.fold(M_in[w], M_in[w]+1);
    }
    return resl += resr;
  }

  void M_set(size_type v, value_type x, bool asc) {
    // on directed edges or on vertices
    bool dir = std::is_same<ValueAttribute, value_on_directed_edge_tag>::value;
    if (asc || !dir) M_fa.set(M_n-1 - M_in[v], x);
    if (!asc || !dir) M_fd.set(M_in[v], x);
  }

  template <typename Tp>
  void M_act(size_type u, size_type v, Tp x) {
    size_type w = M_lca(u, v);
    M_act_one_way(u, w, x, true);
    M_act_one_way(v, w, x, false);
    if (!std::is_same<attribute, value_on_directed_edge_tag>::value) {
      M_act_one_way(v, w, x, true);
      M_act_one_way(u, w, x, false);
      if (std::is_same<attribute, value_on_vertex_tag>::value) {
        M_act_one_way(w, M_p[w], x, true);
        M_act_one_way(w, M_p[w], x, false);
      }
    }
  }

public:
  hl_decomposed_tree() = default;

  template <
    typename Va = ValueAttribute,
    typename Tp = typename std::enable_if<std::is_same<Va, value_on_vertex_tag>::value, value_type>::type
  >
  hl_decomposed_tree(
      std::vector<Tp> const& vs,
      std::vector<std::pair<size_type, size_type>> const& es, size_type r = 0
  ): M_n(vs.size()+1), M_p(M_n, M_n), M_hp(M_n, r), M_in(M_n) {
    size_type n = M_n-1;
    std::vector<std::vector<size_type>> al(M_n);
    for (auto const& [u, v]: es) {
      al[u].push_back(v);
      al[v].push_back(u);
    }
    al[r].push_back(n);
    al[n].push_back(r);
    M_decompose(al, n);

    std::vector<value_type> a(M_n), d(M_n);
    for (size_type i = 0; i < n; ++i) a[M_in[i]] = d[M_in[i]] = vs[i];
    M_fa.assign(a.rbegin(), a.rend());
    M_fd.assign(d.begin(), d.end());
  }

  template <
    typename Va = ValueAttribute,
    typename Sz = typename std::enable_if<!std::is_same<Va, value_on_vertex_tag>::value, size_type>::type
  >
  hl_decomposed_tree(
      Sz n, std::vector<std::tuple<size_type, size_type, value_type>> const& es,
      size_type r = 0
  ): M_n(n), M_p(n, n), M_hp(n, r), M_in(n) {
    std::vector<std::vector<size_type>> al(n);
    bool undir = std::is_same<Va, value_on_undirected_edge_tag>::value;
    for (auto const& e: es) {
      size_type u, v;
      std::tie(u, v, std::ignore) = e;
      al[u].push_back(v);
      if (undir) al[v].push_back(u);
    }
    M_decompose(al);

    std::vector<value_type> a(n), d(n);
    for (auto const& [u, v, w]: es) {
      if (u == M_p[v]) {
        d[M_in[v]] = w;
        if (undir) a[M_in[v]] = w;
      } else {
        a[M_in[u]] = w;
        if (undir) d[M_in[u]] = w;
      }
    }

    M_fa.assign(a.rbegin(), a.rend());
    M_fd.assign(d.begin(), d.end());
  }

  value_type fold(size_type u, size_type v) { return M_fold(u, v); }
  void set(size_type v, value_type x, bool asc = true) { M_set(v, x, asc); }
  template <typename Rq = RangeQuery, typename Ta = typename Rq::action_type>
  void act(size_type u, size_type v, Ta x) { M_act(u, v, x); }
};


#line 1 "DataStructure/basic_segment_tree.cpp"



/**
 * @brief 単一更新セグメント木
 * @author えびちゃん
 * @docs docs/basic_segment_tree.md
 */

#line 11 "DataStructure/basic_segment_tree.cpp"
#include <algorithm>
#line 13 "DataStructure/basic_segment_tree.cpp"

template <typename Monoid>
class basic_segment_tree {
public:
  using value_type = Monoid;
  using size_type = size_t;

private:
  std::vector<value_type> M_c;
  size_type M_n;

public:
  basic_segment_tree() = default;

  explicit basic_segment_tree(size_type n): M_c(n+n), M_n(n) {}
  explicit basic_segment_tree(size_type n, value_type const& x):
    M_c(n+n, x), M_n(n)
  {
    for (size_type i = n; i--;) M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
  }

  template <typename InputIt>
  basic_segment_tree(InputIt first, InputIt last) {
    std::vector<value_type> tmp(first, last);
    M_n = tmp.size();
    M_c.resize(M_n);
    M_c.insert(M_c.end(), tmp.begin(), tmp.end());
    for (size_type i = M_n; i--;) M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
  }

  void assign(size_type n, value_type const& x) {
    M_c.assign(n+n, x);
    M_n = n;
    for (size_type i = n; i--;) M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
  }

  template <typename InputIt>
  void assign(InputIt first, InputIt last) {
    std::vector<value_type> tmp(first, last);
    M_n = tmp.size();
    M_c.resize(M_n);
    M_c.insert(M_c.end(), tmp.begin(), tmp.end());
    for (size_type i = M_n; i--;) M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
  }

  void set(size_type i, value_type const& x) {
    i += M_n;
    M_c[i] = x;
    while (i > 1) {
      i >>= 1;
      M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
    }
  }

  void set(size_type i, value_type&& x) {
    i += M_n;
    M_c[i] = std::move(x);
    while (i > 1) {
      i >>= 1;
      M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
    }
  }

  value_type const& operator [](size_type i) const { return M_c[i + M_n]; }

  value_type fold(size_type l, size_type r) const {
    value_type resl{}, resr{};
    l += M_n;
    r += M_n;
    while (l < r) {
      if (l & 1) resl += M_c[l++];
      if (r & 1) resr = M_c[--r] + std::move(resr);
      l >>= 1;
      r >>= 1;
    }
    return resl += resr;
  }

  template <typename Predicate>
  size_type foldl_bisect(size_type l, Predicate pred) const {
    size_type r = M_n+M_n;
    value_type x{};
    size_type h = 0;
    if (l == M_n) return pred(x)? -1: l;
    l += M_n;
    auto bisect = [&](size_type v) -> size_type {
      while (v < M_n) {
        v <<= 1;
        if (pred(x + M_c[v])) x += M_c[v++];
      }
      return v - M_n;
    };
    for (; l < r; ++h, l >>= 1, r >>= 1) {
      if (l & 1) {
        if (!pred(x + M_c[l])) return bisect(l);
        x += M_c[l];
        ++l;
      }
      if (r & 1) --r;
    }
    while (r <<= 1, h--) {
      if (((r+1) << h) <= M_n+M_n) {
        if (!pred(x + M_c[r])) return bisect(r);
        x += M_c[r];
        ++r;
      }
    }
    return -1;
  }

  template <typename Predicate>
  size_type foldr_bisect(size_type r, Predicate pred) const {
    size_type l = M_n;
    value_type x{};
    size_type h = 0;
    if (r == 0) return pred(x)? -1: 0;
    r += M_n;
    auto bisect = [&](size_type v) -> size_type {
      while (v < M_n) {
        v = (v << 1 | 1);
        if (pred(M_c[v] + x)) x = M_c[v--] + std::move(x);
      }
      return v - M_n;
    };
    for (; l < r; ++h, l >>= 1, r >>= 1) {
      if (l & 1) ++l;
      if (r & 1) {
        --r;
        if (!pred(M_c[r] + x)) return bisect(r);
        x = M_c[r] + std::move(x);
      }
    }
    while (l <<= 1, h--) {
      if (((l-1) << h) >= M_n) {
        --l;
        if (!pred(M_c[l] + x)) return bisect(l);
        x = M_c[l] + std::move(x);
      }
    }
    return -1;
  }
};


#line 10 "test/yj_vertex_add_path_sum.test.cpp"

int main() {
  size_t n, q;
  scanf("%zu %zu", &n, &q);

  std::vector<intmax_t> a(n);
  for (auto& ai: a) scanf("%jd", &ai);

  std::vector<std::pair<size_t, size_t>> es;
  es.reserve(n-1);
  for (size_t i = 1; i < n; ++i) {
    size_t u, v;
    scanf("%zu %zu", &u, &v);
    es.emplace_back(u, v);
  }

  hl_decomposed_tree<basic_segment_tree<intmax_t>, value_on_vertex_tag> g(a, es);
  for (size_t i = 0; i < q; ++i) {
    int t;
    scanf("%d", &t);

    if (t == 0) {
      size_t p;
      intmax_t x;
      scanf("%zu %jd", &p, &x);
      a[p] += x;
      g.set(p, a[p]);
    } else if (t == 1) {
      size_t u, v;
      scanf("%zu %zu", &u, &v);
      printf("%jd\n", g.fold(u, v));
    }
  }
}