test/aoj_2450.test.cpp

#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2450"

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

#include "DataStructure/segment_tree.cpp"
#include "Graph/hl_decomposition.cpp"
#include "utility/monoid/set.cpp"
#include "utility/monoid/max_subsum.cpp"

template <typename Tp>
struct action_set_to_max_subsum {
  using operand_type = max_subsum_monoid<Tp>;
  using action_type = set_monoid<Tp>;

  static void act(operand_type& op, action_type const& a) {
    if (a.empty()) return;
    op = operand_type(a.get(), op.length());
  }
};

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

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

  std::vector<std::pair<size_t, size_t>> es(n-1);
  for (auto& [u, v]: es) scanf("%zu %zu", &u, &v), --u, --v;

  hl_decomposed_tree<segment_tree<action_set_to_max_subsum<intmax_t>>,
                     value_on_vertex_tag> g(a, es);

  for (size_t i = 0; i < q; ++i) {
    int t;
    size_t u, v;
    intmax_t w;
    scanf("%d %zu %zu %jd", &t, &u, &v, &w);
    --u, --v;

    if (t == 1) {
      g.act(u, v, w);
    } else if (t == 2) {
      printf("%jd\n", g.fold(u, v).get());
    }
  }
}

#line 1 "test/aoj_2450.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2450"

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

#line 1 "DataStructure/segment_tree.cpp"



/**
 * @brief 区間作用・区間和セグメント木
 * @author えびちゃん
 */

#include <cstddef>
#line 11 "DataStructure/segment_tree.cpp"

#line 1 "integer/bit.cpp"



/** 
 * @brief ビット演算
 * @author えびちゃん
 */

// XXX integral promotion 関連の注意をあまりしていません

#include <climits>
#include <type_traits>

template <typename Tp>
constexpr auto countl_zero(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  using value_type = typename std::make_unsigned<Tp>::type;
  int bits = (sizeof(value_type) * CHAR_BIT);
  if (n == 0) return bits;
  int res = 0;
  for (int i = bits / 2; i > 0; i /= 2) {
    value_type mask = ((static_cast<value_type>(1) << i) - 1) << i;
    if (n & mask) n >>= i;
    else res += i;
  }
  return res;
}
template <typename Tp>
constexpr auto countl_one(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  using value_type = typename std::make_unsigned<Tp>::type;
  return countl_zero(static_cast<value_type>(~n));
}

template <typename Tp>
constexpr auto countr_zero(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  using value_type = typename std::make_unsigned<Tp>::type;
  int bits = (sizeof(value_type) * CHAR_BIT);
  if (n == 0) return bits;
  int res = 0;
  for (int i = bits / 2; i > 0; i /= 2) {
    value_type mask = ((static_cast<value_type>(1) << i) - 1);
    if (!(n & mask)) res += i, n >>= i;
  }
  return res;
}
template <typename Tp>
constexpr auto countr_one(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  using value_type = typename std::make_unsigned<Tp>::type;
  return countr_zero(static_cast<value_type>(~n));
}

constexpr unsigned long long half_mask[] = {
  0x5555555555555555uLL, 0x3333333333333333uLL, 0x0F0F0F0F0F0F0F0FuLL,
  0x00FF00FF00FF00FFuLL, 0x0000FFFF0000FFFFuLL, 0x00000000FFFFFFFFuLL
};

template <typename Tp>
constexpr auto popcount(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  int bits = static_cast<int>((sizeof n) * CHAR_BIT);
  for (int i = 0, j = 1; j < bits; ++i, j *= 2) {
    if (j <= 8) n = (n & half_mask[i]) + ((n >> j) & half_mask[i]);
    else n += n >> j;
  }
  return n & 0xFF;
}

template <typename Tp>
constexpr auto parity(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{ return popcount(n) & 1; }


template <typename Tp>
int clz(Tp n) { return countl_zero(static_cast<typename std::make_unsigned<Tp>::type>(n)); }
template <typename Tp>
int ctz(Tp n) { return countr_zero(static_cast<typename std::make_unsigned<Tp>::type>(n)); }

template <typename Tp>
int ilog2(Tp n) {
  return (CHAR_BIT * sizeof(Tp) - 1) - clz(static_cast<typename std::make_unsigned<Tp>::type>(n));
}
template <typename Tp>
bool is_pow2(Tp n) { return (n > 0) && ((n & (n-1)) == 0); }
template <typename Tp>
Tp floor2(Tp n) { return is_pow2(n)? n: static_cast<Tp>(1) << ilog2(n); }
template <typename Tp>
Tp ceil2(Tp n) { return is_pow2(n)? n: static_cast<Tp>(2) << ilog2(n); }

template <typename Tp>
constexpr auto reverse(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, Tp>::type
{
  int bits = static_cast<int>((sizeof n) * CHAR_BIT);
  for (int i = 0, j = 1; j < bits; ++i, j *= 2) {
    n = ((n & half_mask[i]) << j) | ((n >> j) & half_mask[i]);
  }
  return n;
}


#line 13 "DataStructure/segment_tree.cpp"

template <typename Operation>
class segment_tree {
public:
  using size_type = size_t;
  using operation = Operation;
  using operand_type = typename operation::operand_type;
  using action_type = typename operation::action_type;
  using value_type = operand_type;

private:
  size_type M_n;
  std::vector<operand_type> M_c;
  std::vector<action_type> M_d;  // deferred

  void M_build(size_type i) {
    while (i > 1) {
      i >>= 1;
      M_c[i] = (M_c[i<<1|0] + M_c[i<<1|1]);
      operation::act(M_c[i], M_d[i]);
    }
  }

  void M_resolve(size_type i) {
    size_type h = ilog2(M_n) + 2;  // ilog2p1(M_n*2)
    for (size_type s = h; s > 0; --s) {
      size_type p = i >> s;
      action_type id{};
      if (M_d[p] != id) {
        M_apply(p<<1|0, M_d[p]);
        M_apply(p<<1|1, M_d[p]);
        M_d[p] = id;
      }
    }
  }

  void M_apply(size_type i, action_type const& x) {
    operation::act(M_c[i], x);
    if (i < M_n) M_d[i] += x;
  }

public:
  segment_tree() = default;
  explicit segment_tree(size_type n):
    M_n(n), M_c(n+n, operand_type{}), M_d(n, action_type{}) {}

  segment_tree(size_type n, operand_type const& x):
    M_n(n), M_c(n+n, x), M_d(n, action_type{})
  {
    for (size_type i = n; i--;) M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
  }

  template <typename InputIt>
  segment_tree(InputIt first, InputIt last): M_c(first, last) {
    M_n = M_c.size();
    M_d.assign(M_n, action_type{});
    M_c.insert(M_c.begin(), M_n, operand_type{});
    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) {
    M_n = n;
    M_c(n+n, operand_type{});
    M_d(n, action_type{});
  }

  void assign(size_type n, operand_type const& x) {
    M_n = n;
    M_c(n+n, x);
    M_d(n, action_type{});
    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) {
    M_c.assign(first, last);
    M_n = M_c.size();
    M_d.assign(M_n, action_type{});
    M_c.insert(M_c.begin(), M_n, operand_type{});
    for (size_type i = M_n; i--;) M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
  }

  void act(size_type l, size_type r, action_type const& x) {
    if (l == r) return;
    l += M_n;
    r += M_n;
    size_type l0 = l;
    size_type r0 = r;
    M_resolve(l0);
    M_resolve(r0-1);
    while (l < r) {
      if (l & 1) M_apply(l++, x);
      if (r & 1) M_apply(--r, x);
      l >>= 1;
      r >>= 1;
    }
    M_build(l0);
    M_build(r0-1);
  }

  operand_type fold(size_type l, size_type r) {
    operand_type resl{}, resr{};
    if (l == r) return resl;

    l += M_n;
    r += M_n;
    M_resolve(l);
    M_resolve(r-1);
    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;
  }

  operand_type operator [](size_type i) {
    i += M_n;
    M_resolve(i);
    return M_c[i];
  }
};


#line 1 "Graph/hl_decomposition.cpp"



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

#line 11 "Graph/hl_decomposition.cpp"
#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 "utility/monoid/set.cpp"



/**
 * @brief モノイドクラス
 * @author えびちゃん
 */

template <typename Tp>
class set_monoid {
public:
  using value_type = Tp;

private:
  bool M_empty = true;
  value_type M_x;

public:
  set_monoid() = default;  // identity

  set_monoid(value_type const& x): M_empty(false), M_x(x) {}

  set_monoid& operator +=(set_monoid const& that) {
    M_empty = that.M_empty;
    if (!that.M_empty) M_x = that.M_x;
    return *this;
  }
  friend bool operator ==(set_monoid const& lhs, set_monoid const& rhs) {
    if (lhs.M_empty && rhs.M_empty) return true;
    if (lhs.M_empty != rhs.M_empty) return false;
    return lhs.M_x == rhs.M_x;
  }

  friend set_monoid operator +(set_monoid lhs, set_monoid const& rhs) { return lhs += rhs; }
  friend bool operator !=(set_monoid const& lhs, set_monoid const& rhs) {
    return !(lhs == rhs);
  }

  bool empty() const noexcept { return M_empty; }
  value_type const& get() const { return M_x; }
};


#line 1 "utility/monoid/max_subsum.cpp"



/**
 * @brief 部分和の最大値を得る演算のモノイドクラス
 * @author えびちゃん
 */

#line 11 "utility/monoid/max_subsum.cpp"

template <typename Tp>
class max_subsum_monoid {
public:
  using size_type = size_t;
  using value_type = Tp;

private:
  value_type M_pre = 0, M_suf = 0, M_sub = 0, M_whole = 0;
  size_type M_length = 0;

public:
  max_subsum_monoid() = default;  // identity

  max_subsum_monoid(value_type const& x):
    M_pre(x), M_suf(x), M_sub(x), M_whole(x), M_length(1) {}

  max_subsum_monoid(value_type const& x, value_type n):
    M_pre(x*n), M_suf(x*n), M_sub(x*n), M_whole(x*n), M_length(n)
  {
    if (x < 0) M_pre = M_suf = M_sub = x;
  }

  max_subsum_monoid& operator +=(max_subsum_monoid const& that) {
    if (that.M_length == 0) return *this;
    if (M_length == 0) return (*this = that);
    M_sub = std::max({M_sub, M_suf + that.M_pre, that.M_sub});
    M_suf = std::max(M_suf + that.M_whole, that.M_suf);
    M_pre = std::max(M_pre, M_whole + that.M_pre);
    M_whole += that.M_whole;
    M_length += that.M_length;
    return *this;
  }
  friend bool operator ==(max_subsum_monoid const& lhs, max_subsum_monoid const& rhs) {
    if (lhs.M_length == 0 && rhs.M_length == 0) return true;
    return (
        lhs.M_length == rhs.M_length
        && lhs.M_pre == rhs.M_pre
        && lhs.M_suf == rhs.M_suf
        && lhs.M_sub == rhs.M_sub
        && lhs.M_whole == rhs.M_whole
    );
  }

  friend max_subsum_monoid operator +(max_subsum_monoid lhs, max_subsum_monoid const& rhs) {
    return lhs += rhs;
  }
  friend bool operator !=(max_subsum_monoid const& lhs, max_subsum_monoid const& rhs) {
    return !(lhs == rhs);
  }

  size_type length() const noexcept { return M_length; }
  value_type const& get() const { return M_sub; }
};


#line 13 "test/aoj_2450.test.cpp"

template <typename Tp>
struct action_set_to_max_subsum {
  using operand_type = max_subsum_monoid<Tp>;
  using action_type = set_monoid<Tp>;

  static void act(operand_type& op, action_type const& a) {
    if (a.empty()) return;
    op = operand_type(a.get(), op.length());
  }
};

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

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

  std::vector<std::pair<size_t, size_t>> es(n-1);
  for (auto& [u, v]: es) scanf("%zu %zu", &u, &v), --u, --v;

  hl_decomposed_tree<segment_tree<action_set_to_max_subsum<intmax_t>>,
                     value_on_vertex_tag> g(a, es);

  for (size_t i = 0; i < q; ++i) {
    int t;
    size_t u, v;
    intmax_t w;
    scanf("%d %zu %zu %jd", &t, &u, &v, &w);
    --u, --v;

    if (t == 1) {
      g.act(u, v, w);
    } else if (t == 2) {
      printf("%jd\n", g.fold(u, v).get());
    }
  }
}