Luzhiled's Library

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View the Project on GitHub ei1333/library

:heavy_check_mark: test/verify/aoj-2450.test.cpp

Depends on

Code

// clang-format off
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2450
// clang-format on

#include <algorithm>
#include <cstdint>
#include <iostream>
#include <limits>
#include <utility>
#include <vector>

#include "../../graph/tree/heavy-light-decomposition.hpp"
#include "../../structure/segment-tree/lazy-segment-tree.hpp"

using namespace std;

constexpr int64_t kInfinity = (1LL << 62) - 1;

int main() {
  int N, Q;
  cin >> N >> Q;
  vector<int> S(N);
  for (int i = 0; i < N; i++) {
    cin >> S[i];
  }
  HeavyLightDecomposition<int64_t> tree(N);
  tree.read(N - 1);
  tree.build();

  struct Node {
    int64_t ans, all, left, right, length;

    Node()
        : ans(-kInfinity),
          all(0),
          left(-kInfinity),
          right(-kInfinity),
          length(0) {}

    Node(int64_t val, int64_t len) {
      length = len;
      all = val * length;
      ans = left = right = (val > 0 ? all : val);
    }

    Node operator+(const Node& s) const {
      Node ret;
      ret.length = length + s.length;
      ret.ans = max({ans, s.ans, right + s.left});
      ret.all = all + s.all;
      ret.left = max(left, all + s.left);
      ret.right = max(s.right, right + s.all);
      return ret;
    }
  };
  auto F = [](const Node& a, const Node& b) { return a + b; };
  auto G = [](const Node& x, int64_t f) -> Node { return {f, x.length}; };
  auto H = [](int64_t f, int64_t g) { return g; };
  auto e = []() { return Node(); };
  auto id = []() { return kInfinity; };

  vector<Node> vs(N);
  for (int i = 0; i < N; i++) vs[i] = {S[tree.rev[i]], 1};
  LazySegmentTree seg(LambdaActedMonoid(F, e, G, H, id), vs);

  auto QF = [&](int a, int b) { return seg.prod(a, b); };
  auto QG = [](const Node& a, const Node& b) { return a + b; };
  auto QS = [](Node l, const Node& r) {
    swap(l.left, l.right);
    return l + r;
  };

  while (Q--) {
    int T, A, B, C;
    cin >> T >> A >> B >> C;
    --A, --B;
    if (T == 1) {
      tree.add(A, B, [&](int a, int b) { seg.apply(a, b, C); });
    } else {
      cout << tree.query(A, B, Node(), QF, QG, QS).ans << "\n";
    }
  }
}

#line 1 "test/verify/aoj-2450.test.cpp"
// clang-format off
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2450
// clang-format on

#include <algorithm>
#include <cstdint>
#include <iostream>
#include <limits>
#include <utility>
#include <vector>

#line 2 "graph/tree/heavy-light-decomposition.hpp"

#line 4 "graph/tree/heavy-light-decomposition.hpp"
#include <stack>
#line 7 "graph/tree/heavy-light-decomposition.hpp"

#line 2 "graph/graph-template.hpp"

#include <cstddef>
#line 6 "graph/graph-template.hpp"

template <typename T = int>
struct Edge {
  int from, to;
  T cost;
  int idx;

  Edge() = default;

  Edge(int from, int to, T cost = 1, int idx = -1)
      : from(from), to(to), cost(cost), idx(idx) {}

  operator int() const { return to; }
};

template <typename T = int>
struct Graph {
  std::vector<std::vector<Edge<T> > > g;
  int es;

  Graph() = default;

  explicit Graph(int n) : g(n), es(0) {}

  std::size_t size() const { return g.size(); }

  void add_directed_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es++);
  }

  void add_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es);
    g[to].emplace_back(to, from, cost, es++);
  }

  void read(int M, int padding = -1, bool weighted = false,
            bool directed = false) {
    for (int i = 0; i < M; i++) {
      int a, b;
      std::cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) std::cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

  inline std::vector<Edge<T> >& operator[](const int& k) { return g[k]; }

  inline const std::vector<Edge<T> >& operator[](const int& k) const {
    return g[k];
  }
};

template <typename T = int>
using Edges = std::vector<Edge<T> >;
#line 9 "graph/tree/heavy-light-decomposition.hpp"

/**
 * @brief Heavy-Light-Decomposition(HL分解)
 * @see https://smijake3.hatenablog.com/entry/2019/09/15/200200
 */
template <typename T = int>
struct HeavyLightDecomposition : Graph<T> {
 public:
  using Graph<T>::Graph;
  using Graph<T>::g;
  std::vector<int> sz, in, out, head, rev, par, dep;

  void build(int root = 0) {
    sz.assign(g.size(), 0);
    in.assign(g.size(), 0);
    out.assign(g.size(), 0);
    head.assign(g.size(), 0);
    rev.assign(g.size(), 0);
    par.assign(g.size(), 0);
    dep.assign(g.size(), 0);
    dfs_sz(root, -1, 0);
    int t = 0;
    head[root] = root;
    dfs_hld(root, -1, t);
  }

  /* k: 0-indexed */
  int la(int v, int k) {
    while (1) {
      int u = head[v];
      if (in[v] - k >= in[u]) return rev[in[v] - k];
      k -= in[v] - in[u] + 1;
      v = par[u];
    }
  }

  int lca(int u, int v) const {
    for (;; v = par[head[v]]) {
      if (in[u] > in[v]) std::swap(u, v);
      if (head[u] == head[v]) return u;
    }
  }

  int dist(int u, int v) const { return dep[u] + dep[v] - 2 * dep[lca(u, v)]; }

  template <typename E, typename Q, typename F, typename S>
  E query(int u, int v, const E& ti, const Q& q, const F& f, const S& s,
          bool edge = false) {
    E l = ti, r = ti;
    for (;; v = par[head[v]]) {
      if (in[u] > in[v]) std::swap(u, v), std::swap(l, r);
      if (head[u] == head[v]) break;
      l = f(q(in[head[v]], in[v] + 1), l);
    }
    return s(f(q(in[u] + edge, in[v] + 1), l), r);
  }

  template <typename E, typename Q, typename F>
  E query(int u, int v, const E& ti, const Q& q, const F& f,
          bool edge = false) {
    return query(u, v, ti, q, f, f, edge);
  }

  template <typename Q>
  void add(int u, int v, const Q& q, bool edge = false) {
    for (;; v = par[head[v]]) {
      if (in[u] > in[v]) std::swap(u, v);
      if (head[u] == head[v]) break;
      q(in[head[v]], in[v] + 1);
    }
    q(in[u] + edge, in[v] + 1);
  }

  /* {parent, child} */
  std::vector<std::pair<int, int> > compress(std::vector<int>& remark) {
    auto cmp = [&](int a, int b) { return in[a] < in[b]; };
    std::sort(std::begin(remark), std::end(remark), cmp);
    remark.erase(std::unique(std::begin(remark), std::end(remark)),
                 std::end(remark));
    int K = (int)remark.size();
    for (int k = 1; k < K; k++)
      remark.emplace_back(lca(remark[k - 1], remark[k]));
    std::sort(std::begin(remark), std::end(remark), cmp);
    remark.erase(std::unique(std::begin(remark), std::end(remark)),
                 std::end(remark));
    std::vector<std::pair<int, int> > es;
    std::stack<int> st;
    for (auto& k : remark) {
      while (!st.empty() && out[st.top()] <= in[k]) st.pop();
      if (!st.empty()) es.emplace_back(st.top(), k);
      st.emplace(k);
    }
    return es;
  }

  explicit HeavyLightDecomposition(const Graph<T>& g) : Graph<T>(g) {}

 private:
  void dfs_sz(int idx, int p, int d) {
    dep[idx] = d;
    par[idx] = p;
    sz[idx] = 1;
    if (g[idx].size() && g[idx][0] == p) std::swap(g[idx][0], g[idx].back());
    for (auto& to : g[idx]) {
      if (to == p) continue;
      dfs_sz(to, idx, d + 1);
      sz[idx] += sz[to];
      if (sz[g[idx][0]] < sz[to]) std::swap(g[idx][0], to);
    }
  }

  void dfs_hld(int idx, int p, int& times) {
    in[idx] = times++;
    rev[in[idx]] = idx;
    for (auto& to : g[idx]) {
      if (to == p) continue;
      head[to] = (g[idx][0] == to ? head[idx] : to);
      dfs_hld(to, idx, times);
    }
    out[idx] = times;
  }
};
#line 2 "structure/segment-tree/lazy-segment-tree.hpp"

#include <cassert>
#include <optional>
#include <set>
#line 7 "structure/segment-tree/lazy-segment-tree.hpp"

#line 2 "structure/class/acted-monoid.hpp"

template <typename S2, typename Op, typename E, typename F2, typename Mapping,
          typename Composition, typename Id>
struct LambdaActedMonoid {
  using S = S2;
  using F = F2;

  S op(const S& a, const S& b) const { return _op(a, b); }

  S e() const { return _e(); }

  S mapping(const S& x, const F& f) const { return _mapping(x, f); }

  F composition(const F& f, const F& g) const { return _composition(f, g); }

  F id() const { return _id(); }

  LambdaActedMonoid(Op _op, E _e, Mapping _mapping, Composition _composition,
                    Id _id)
      : _op(_op),
        _e(_e),
        _mapping(_mapping),
        _composition(_composition),
        _id(_id) {}

 private:
  Op _op;

  E _e;

  Mapping _mapping;

  Composition _composition;

  Id _id;
};

template <typename Op, typename E, typename Mapping, typename Composition,
          typename Id>
LambdaActedMonoid(Op _op, E _e, Mapping _mapping, Composition _composition,
                  Id _id)
    -> LambdaActedMonoid<decltype(_e()), Op, E, decltype(_id()), Mapping,
                         Composition, Id>;

/*
struct ActedMonoid {
  using S = ?;
  using F = ?;
  static constexpr S op(const S& a, const S& b) {}
  static constexpr S e() {}
  static constexpr S mapping(const S &x, const F &f) {}
  static constexpr F composition(const F &f, const F &g) {}
  static constexpr F id() {}
};
*/
#line 9 "structure/segment-tree/lazy-segment-tree.hpp"

template <typename ActedMonoid>
struct LazySegmentTree {
  using S = typename ActedMonoid::S;
  using F = typename ActedMonoid::F;

 private:
  ActedMonoid m;

  int n{}, sz{}, height{};

  std::vector<S> data;

  std::vector<F> lazy;

  inline void update(int k) {
    data[k] = m.op(data[2 * k + 0], data[2 * k + 1]);
  }

  inline void all_apply(int k, const F& x) {
    data[k] = m.mapping(data[k], x);
    if (k < sz) lazy[k] = m.composition(lazy[k], x);
  }

  inline void propagate(int k) {
    if (lazy[k] != m.id()) {
      all_apply(2 * k + 0, lazy[k]);
      all_apply(2 * k + 1, lazy[k]);
      lazy[k] = m.id();
    }
  }

 public:
  LazySegmentTree() = default;

  explicit LazySegmentTree(ActedMonoid m, int n) : m(m), n(n) {
    sz = 1;
    height = 0;
    while (sz < n) sz <<= 1, height++;
    data.assign(2 * sz, m.e());
    lazy.assign(2 * sz, m.id());
  }

  explicit LazySegmentTree(ActedMonoid m, const std::vector<S>& v)
      : LazySegmentTree(m, static_cast<int>(v.size())) {
    build(v);
  }

  void build(const std::vector<S>& v) {
    assert(n == (int)v.size());
    for (int k = 0; k < n; k++) data[k + sz] = v[k];
    for (int k = sz - 1; k > 0; k--) update(k);
  }

  void set(int k, const S& x) {
    k += sz;
    for (int i = height; i > 0; i--) propagate(k >> i);
    data[k] = x;
    for (int i = 1; i <= height; i++) update(k >> i);
  }

  S get(int k) {
    k += sz;
    for (int i = height; i > 0; i--) propagate(k >> i);
    return data[k];
  }

  S operator[](int k) { return get(k); }

  S prod(int l, int r) {
    if (l >= r) return m.e();
    l += sz;
    r += sz;
    for (int i = height; i > 0; i--) {
      if (((l >> i) << i) != l) propagate(l >> i);
      if (((r >> i) << i) != r) propagate((r - 1) >> i);
    }
    S L = m.e(), R = m.e();
    for (; l < r; l >>= 1, r >>= 1) {
      if (l & 1) L = m.op(L, data[l++]);
      if (r & 1) R = m.op(data[--r], R);
    }
    return m.op(L, R);
  }

  S all_prod() const { return data[1]; }

  void apply(int k, const F& f) {
    k += sz;
    for (int i = height; i > 0; i--) propagate(k >> i);
    data[k] = m.mapping(data[k], f);
    for (int i = 1; i <= height; i++) update(k >> i);
  }

  void apply(int l, int r, const F& f) {
    if (l >= r) return;
    l += sz;
    r += sz;
    for (int i = height; i > 0; i--) {
      if (((l >> i) << i) != l) propagate(l >> i);
      if (((r >> i) << i) != r) propagate((r - 1) >> i);
    }
    {
      int l2 = l, r2 = r;
      for (; l < r; l >>= 1, r >>= 1) {
        if (l & 1) all_apply(l++, f);
        if (r & 1) all_apply(--r, f);
      }
      l = l2, r = r2;
    }
    for (int i = 1; i <= height; i++) {
      if (((l >> i) << i) != l) update(l >> i);
      if (((r >> i) << i) != r) update((r - 1) >> i);
    }
  }

  template <typename C>
  std::optional<int> find_first(int l, const C& check) {
    if (l >= n) return std::nullopt;
    l += sz;
    for (int i = height; i > 0; i--) propagate(l >> i);
    S sum = m.e();
    do {
      while ((l & 1) == 0) l >>= 1;
      if (check(m.op(sum, data[l]))) {
        while (l < sz) {
          propagate(l);
          l <<= 1;
          auto nxt = m.op(sum, data[l]);
          if (not check(nxt)) {
            sum = nxt;
            l++;
          }
        }
        return l + 1 - sz;
      }
      sum = m.op(sum, data[l++]);
    } while ((l & -l) != l);
    return std::nullopt;
  }

  template <typename C>
  std::optional<int> find_last(int r, const C& check) {
    if (r <= 0) return std::nullopt;
    r += sz;
    for (int i = height; i > 0; i--) propagate((r - 1) >> i);
    S sum = m.e();
    do {
      r--;
      while (r > 1 and (r & 1)) r >>= 1;
      if (check(m.op(data[r], sum))) {
        while (r < sz) {
          propagate(r);
          r = (r << 1) + 1;
          auto nxt = m.op(data[r], sum);
          if (not check(nxt)) {
            sum = nxt;
            r--;
          }
        }
        return r - sz;
      }
      sum = m.op(data[r], sum);
    } while ((r & -r) != r);
    return std::nullopt;
  }
};
#line 14 "test/verify/aoj-2450.test.cpp"

using namespace std;

constexpr int64_t kInfinity = (1LL << 62) - 1;

int main() {
  int N, Q;
  cin >> N >> Q;
  vector<int> S(N);
  for (int i = 0; i < N; i++) {
    cin >> S[i];
  }
  HeavyLightDecomposition<int64_t> tree(N);
  tree.read(N - 1);
  tree.build();

  struct Node {
    int64_t ans, all, left, right, length;

    Node()
        : ans(-kInfinity),
          all(0),
          left(-kInfinity),
          right(-kInfinity),
          length(0) {}

    Node(int64_t val, int64_t len) {
      length = len;
      all = val * length;
      ans = left = right = (val > 0 ? all : val);
    }

    Node operator+(const Node& s) const {
      Node ret;
      ret.length = length + s.length;
      ret.ans = max({ans, s.ans, right + s.left});
      ret.all = all + s.all;
      ret.left = max(left, all + s.left);
      ret.right = max(s.right, right + s.all);
      return ret;
    }
  };
  auto F = [](const Node& a, const Node& b) { return a + b; };
  auto G = [](const Node& x, int64_t f) -> Node { return {f, x.length}; };
  auto H = [](int64_t f, int64_t g) { return g; };
  auto e = []() { return Node(); };
  auto id = []() { return kInfinity; };

  vector<Node> vs(N);
  for (int i = 0; i < N; i++) vs[i] = {S[tree.rev[i]], 1};
  LazySegmentTree seg(LambdaActedMonoid(F, e, G, H, id), vs);

  auto QF = [&](int a, int b) { return seg.prod(a, b); };
  auto QG = [](const Node& a, const Node& b) { return a + b; };
  auto QS = [](Node l, const Node& r) {
    swap(l.left, l.right);
    return l + r;
  };

  while (Q--) {
    int T, A, B, C;
    cin >> T >> A >> B >> C;
    --A, --B;
    if (T == 1) {
      tree.add(A, B, [&](int a, int b) { seg.apply(a, b, C); });
    } else {
      cout << tree.query(A, B, Node(), QF, QG, QS).ans << "\n";
    }
  }
}

Test cases

Env Name Status Elapsed Memory
g++ testcase_00 :heavy_check_mark: AC 3 ms 4 MB
g++ testcase_01 :heavy_check_mark: AC 2 ms 4 MB
g++ testcase_02 :heavy_check_mark: AC 2 ms 4 MB
g++ testcase_03 :heavy_check_mark: AC 2 ms 4 MB
g++ testcase_04 :heavy_check_mark: AC 3 ms 4 MB
g++ testcase_05 :heavy_check_mark: AC 168 ms 10 MB
g++ testcase_06 :heavy_check_mark: AC 260 ms 34 MB
g++ testcase_07 :heavy_check_mark: AC 406 ms 71 MB
g++ testcase_08 :heavy_check_mark: AC 3 ms 4 MB
g++ testcase_09 :heavy_check_mark: AC 44 ms 4 MB
g++ testcase_10 :heavy_check_mark: AC 359 ms 59 MB
g++ testcase_11 :heavy_check_mark: AC 3 ms 4 MB
g++ testcase_12 :heavy_check_mark: AC 3 ms 4 MB
g++ testcase_13 :heavy_check_mark: AC 4 ms 4 MB
g++ testcase_14 :heavy_check_mark: AC 10 ms 4 MB
g++ testcase_15 :heavy_check_mark: AC 54 ms 4 MB
g++ testcase_16 :heavy_check_mark: AC 272 ms 6 MB
g++ testcase_17 :heavy_check_mark: AC 281 ms 17 MB
g++ testcase_18 :heavy_check_mark: AC 460 ms 32 MB
g++ testcase_19 :heavy_check_mark: AC 560 ms 60 MB
g++ testcase_20 :heavy_check_mark: AC 2 ms 3 MB
g++ testcase_21 :heavy_check_mark: AC 3 ms 4 MB
g++ testcase_22 :heavy_check_mark: AC 13 ms 4 MB
g++ testcase_23 :heavy_check_mark: AC 133 ms 5 MB
g++ testcase_24 :heavy_check_mark: AC 361 ms 28 MB
g++ testcase_25 :heavy_check_mark: AC 568 ms 60 MB
g++ testcase_26 :heavy_check_mark: AC 3 ms 4 MB
g++ testcase_27 :heavy_check_mark: AC 297 ms 10 MB
g++ testcase_28 :heavy_check_mark: AC 451 ms 32 MB
g++ testcase_29 :heavy_check_mark: AC 602 ms 60 MB
g++ testcase_30 :heavy_check_mark: AC 3 ms 4 MB
g++ testcase_31 :heavy_check_mark: AC 6 ms 4 MB
g++ testcase_32 :heavy_check_mark: AC 46 ms 4 MB
g++ testcase_33 :heavy_check_mark: AC 198 ms 15 MB
g++ testcase_34 :heavy_check_mark: AC 273 ms 32 MB
g++ testcase_35 :heavy_check_mark: AC 390 ms 58 MB
g++ testcase_36 :heavy_check_mark: AC 387 ms 59 MB
g++ testcase_37 :heavy_check_mark: AC 406 ms 60 MB
g++ testcase_38 :heavy_check_mark: AC 485 ms 60 MB
clang++ testcase_00 :heavy_check_mark: AC 2 ms 4 MB
clang++ testcase_01 :heavy_check_mark: AC 2 ms 4 MB
clang++ testcase_02 :heavy_check_mark: AC 2 ms 4 MB
clang++ testcase_03 :heavy_check_mark: AC 2 ms 4 MB
clang++ testcase_04 :heavy_check_mark: AC 4 ms 4 MB
clang++ testcase_05 :heavy_check_mark: AC 215 ms 11 MB
clang++ testcase_06 :heavy_check_mark: AC 269 ms 37 MB
clang++ testcase_07 :heavy_check_mark: AC 402 ms 79 MB
clang++ testcase_08 :heavy_check_mark: AC 3 ms 4 MB
clang++ testcase_09 :heavy_check_mark: AC 68 ms 4 MB
clang++ testcase_10 :heavy_check_mark: AC 484 ms 58 MB
clang++ testcase_11 :heavy_check_mark: AC 2 ms 4 MB
clang++ testcase_12 :heavy_check_mark: AC 2 ms 4 MB
clang++ testcase_13 :heavy_check_mark: AC 3 ms 4 MB
clang++ testcase_14 :heavy_check_mark: AC 6 ms 4 MB
clang++ testcase_15 :heavy_check_mark: AC 31 ms 4 MB
clang++ testcase_16 :heavy_check_mark: AC 159 ms 6 MB
clang++ testcase_17 :heavy_check_mark: AC 360 ms 17 MB
clang++ testcase_18 :heavy_check_mark: AC 376 ms 32 MB
clang++ testcase_19 :heavy_check_mark: AC 730 ms 60 MB
clang++ testcase_20 :heavy_check_mark: AC 2 ms 4 MB
clang++ testcase_21 :heavy_check_mark: AC 3 ms 4 MB
clang++ testcase_22 :heavy_check_mark: AC 13 ms 4 MB
clang++ testcase_23 :heavy_check_mark: AC 127 ms 5 MB
clang++ testcase_24 :heavy_check_mark: AC 303 ms 28 MB
clang++ testcase_25 :heavy_check_mark: AC 538 ms 60 MB
clang++ testcase_26 :heavy_check_mark: AC 3 ms 4 MB
clang++ testcase_27 :heavy_check_mark: AC 231 ms 10 MB
clang++ testcase_28 :heavy_check_mark: AC 471 ms 32 MB
clang++ testcase_29 :heavy_check_mark: AC 491 ms 60 MB
clang++ testcase_30 :heavy_check_mark: AC 3 ms 4 MB
clang++ testcase_31 :heavy_check_mark: AC 6 ms 4 MB
clang++ testcase_32 :heavy_check_mark: AC 45 ms 4 MB
clang++ testcase_33 :heavy_check_mark: AC 283 ms 15 MB
clang++ testcase_34 :heavy_check_mark: AC 287 ms 32 MB
clang++ testcase_35 :heavy_check_mark: AC 414 ms 58 MB
clang++ testcase_36 :heavy_check_mark: AC 425 ms 59 MB
clang++ testcase_37 :heavy_check_mark: AC 430 ms 60 MB
clang++ testcase_38 :heavy_check_mark: AC 455 ms 60 MB
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