test/verify/aoj-2450.test.cpp

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Last update: 2024-05-01 23:44:47+09:00
Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2450

Depends on

Code

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

#include "../../template/template.hpp"

#include "../../structure/segment-tree/lazy-segment-tree.hpp"

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

int main() {
  int N, Q, S[200000];
  cin >> N >> Q;
  for(int i = 0; i < N; i++) {
    cin >> S[i];
  }
  HeavyLightDecomposition< int64 > tree(N);
  tree.read(N - 1);
  tree.build();

  struct Node {
    int64 ans, all, left, right, length;

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

    Node(int64 val, int64 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 &a, int64 x) { return Node(x, a.length); };
  auto H = [](int64 x, int64 y) { return y; };
  auto seg = get_lazy_segment_tree(N, F, G, H, Node(), infll);
  for(int i = 0; i < N; i++) seg.set(i, Node(S[tree.rev[i]], 1));

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

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/aoj-2450.test.cpp"

#line 1 "structure/segment-tree/lazy-segment-tree.hpp"
/**
 * @brief Lazy-Segment-Tree(遅延伝搬セグメント木)
 *
 */
template <typename T, typename E, typename F, typename G, typename H>
struct LazySegmentTree {
 private:
  int n{}, sz{}, height{};
  vector<T> data;
  vector<E> lazy;
  const F f;
  const G g;
  const H h;
  const T ti;
  const E ei;

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

  inline void all_apply(int k, const E &x) {
    data[k] = g(data[k], x);
    if (k < sz) lazy[k] = h(lazy[k], x);
  }

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

 public:
  LazySegmentTree() = default;

  explicit LazySegmentTree(int n, const F f, const G g, const H h, const T &ti,
                           const E &ei)
      : n(n), f(f), g(g), h(h), ti(ti), ei(ei) {
    sz = 1;
    height = 0;
    while (sz < n) sz <<= 1, height++;
    data.assign(2 * sz, ti);
    lazy.assign(2 * sz, ei);
  }

  explicit LazySegmentTree(const vector<T> &v, const F f, const G g, const H h,
                           const T &ti, const E &ei)
      : LazySegmentTree(v.size(), f, g, h, ti, ei) {
    build(v);
  }

  void build(const vector<T> &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 T &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);
  }

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

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

  T prod(int l, int r) {
    if (l >= r) return ti;
    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);
    }
    T L = ti, R = ti;
    for (; l < r; l >>= 1, r >>= 1) {
      if (l & 1) L = f(L, data[l++]);
      if (r & 1) R = f(data[--r], R);
    }
    return f(L, R);
  }

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

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

  void apply(int l, int r, const E &x) {
    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++, x);
        if (r & 1) all_apply(--r, x);
      }
      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>
  int find_first(int l, const C &check) {
    if (l >= n) return n;
    l += sz;
    for (int i = height; i > 0; i--) propagate(l >> i);
    T sum = ti;
    do {
      while ((l & 1) == 0) l >>= 1;
      if (check(f(sum, data[l]))) {
        while (l < sz) {
          propagate(l);
          l <<= 1;
          auto nxt = f(sum, data[l]);
          if (not check(nxt)) {
            sum = nxt;
            l++;
          }
        }
        return l + 1 - sz;
      }
      sum = f(sum, data[l++]);
    } while ((l & -l) != l);
    return n;
  }

  template <typename C>
  int find_last(int r, const C &check) {
    if (r <= 0) return -1;
    r += sz;
    for (int i = height; i > 0; i--) propagate((r - 1) >> i);
    T sum = ti;
    do {
      r--;
      while (r > 1 and (r & 1)) r >>= 1;
      if (check(f(data[r], sum))) {
        while (r < sz) {
          propagate(r);
          r = (r << 1) + 1;
          auto nxt = f(data[r], sum);
          if (not check(nxt)) {
            sum = nxt;
            r--;
          }
        }
        return r - sz;
      }
      sum = f(data[r], sum);
    } while ((r & -r) != r);
    return -1;
  }
};

template <typename T, typename E, typename F, typename G, typename H>
LazySegmentTree<T, E, F, G, H> get_lazy_segment_tree(int N, const F &f,
                                                     const G &g, const H &h,
                                                     const T &ti, const E &ei) {
  return LazySegmentTree{N, f, g, h, ti, ei};
}

template <typename T, typename E, typename F, typename G, typename H>
LazySegmentTree<T, E, F, G, H> get_lazy_segment_tree(const vector<T> &v,
                                                     const F &f, const G &g,
                                                     const H &h, const T &ti,
                                                     const E &ei) {
  return LazySegmentTree{v, f, g, h, ti, ei};
}
#line 6 "test/verify/aoj-2450.test.cpp"

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

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

/**
 * @brief Graph Template(グラフテンプレート)
 */
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 {
  vector<vector<Edge<T> > > g;
  int es;

  Graph() = default;

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

  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;
      cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

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

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

template <typename T = int>
using Edges = vector<Edge<T> >;
#line 4 "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;
  vector<int> sz, in, out, head, rev, par, dep;

  void build() {
    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(0, -1, 0);
    int t = 0;
    dfs_hld(0, -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]) 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]) swap(u, v), 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]) 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} */
  vector<pair<int, int> > compress(vector<int> &remark) {
    auto cmp = [&](int a, int b) { return in[a] < in[b]; };
    sort(begin(remark), end(remark), cmp);
    remark.erase(unique(begin(remark), end(remark)), end(remark));
    int K = (int)remark.size();
    for (int k = 1; k < K; k++)
      remark.emplace_back(lca(remark[k - 1], remark[k]));
    sort(begin(remark), end(remark), cmp);
    remark.erase(unique(begin(remark), end(remark)), end(remark));
    vector<pair<int, int> > es;
    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) 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]) 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 8 "test/verify/aoj-2450.test.cpp"

int main() {
  int N, Q, S[200000];
  cin >> N >> Q;
  for(int i = 0; i < N; i++) {
    cin >> S[i];
  }
  HeavyLightDecomposition< int64 > tree(N);
  tree.read(N - 1);
  tree.build();

  struct Node {
    int64 ans, all, left, right, length;

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

    Node(int64 val, int64 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 &a, int64 x) { return Node(x, a.length); };
  auto H = [](int64 x, int64 y) { return y; };
  auto seg = get_lazy_segment_tree(N, F, G, H, Node(), infll);
  for(int i = 0; i < N; i++) seg.set(i, Node(S[tree.rev[i]], 1));

  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	AC	7 ms	4 MB
g++	testcase_01	AC	7 ms	4 MB
g++	testcase_02	AC	7 ms	4 MB
g++	testcase_03	AC	7 ms	4 MB
g++	testcase_04	AC	7 ms	4 MB
g++	testcase_05	AC	67 ms	10 MB
g++	testcase_06	AC	143 ms	31 MB
g++	testcase_07	AC	235 ms	63 MB
g++	testcase_08	AC	8 ms	4 MB
g++	testcase_09	AC	17 ms	5 MB
g++	testcase_10	AC	180 ms	50 MB
g++	testcase_11	AC	7 ms	4 MB
g++	testcase_12	AC	7 ms	4 MB
g++	testcase_13	AC	7 ms	4 MB
g++	testcase_14	AC	8 ms	4 MB
g++	testcase_15	AC	17 ms	5 MB
g++	testcase_16	AC	78 ms	7 MB
g++	testcase_17	AC	154 ms	16 MB
g++	testcase_18	AC	205 ms	28 MB
g++	testcase_19	AC	318 ms	52 MB
g++	testcase_20	AC	8 ms	4 MB
g++	testcase_21	AC	7 ms	4 MB
g++	testcase_22	AC	10 ms	5 MB
g++	testcase_23	AC	58 ms	6 MB
g++	testcase_24	AC	181 ms	26 MB
g++	testcase_25	AC	315 ms	52 MB
g++	testcase_26	AC	7 ms	4 MB
g++	testcase_27	AC	114 ms	10 MB
g++	testcase_28	AC	200 ms	28 MB
g++	testcase_29	AC	306 ms	52 MB
g++	testcase_30	AC	7 ms	4 MB
g++	testcase_31	AC	8 ms	4 MB
g++	testcase_32	AC	20 ms	5 MB
g++	testcase_33	AC	90 ms	14 MB
g++	testcase_34	AC	132 ms	28 MB
g++	testcase_35	AC	204 ms	51 MB
g++	testcase_36	AC	218 ms	51 MB
g++	testcase_37	AC	215 ms	52 MB
g++	testcase_38	AC	215 ms	52 MB
clang++	testcase_00	AC	6 ms	4 MB
clang++	testcase_01	AC	7 ms	4 MB
clang++	testcase_02	AC	6 ms	4 MB
clang++	testcase_03	AC	6 ms	4 MB
clang++	testcase_04	AC	6 ms	4 MB
clang++	testcase_05	AC	72 ms	10 MB
clang++	testcase_06	AC	140 ms	33 MB
clang++	testcase_07	AC	238 ms	71 MB
clang++	testcase_08	AC	7 ms	4 MB
clang++	testcase_09	AC	17 ms	4 MB
clang++	testcase_10	AC	177 ms	50 MB
clang++	testcase_11	AC	7 ms	4 MB
clang++	testcase_12	AC	6 ms	4 MB
clang++	testcase_13	AC	7 ms	4 MB
clang++	testcase_14	AC	7 ms	4 MB
clang++	testcase_15	AC	17 ms	4 MB
clang++	testcase_16	AC	84 ms	6 MB
clang++	testcase_17	AC	162 ms	16 MB
clang++	testcase_18	AC	210 ms	28 MB
clang++	testcase_19	AC	311 ms	52 MB
clang++	testcase_20	AC	7 ms	4 MB
clang++	testcase_21	AC	6 ms	4 MB
clang++	testcase_22	AC	9 ms	4 MB
clang++	testcase_23	AC	61 ms	5 MB
clang++	testcase_24	AC	183 ms	25 MB
clang++	testcase_25	AC	307 ms	52 MB
clang++	testcase_26	AC	7 ms	4 MB
clang++	testcase_27	AC	120 ms	9 MB
clang++	testcase_28	AC	214 ms	28 MB
clang++	testcase_29	AC	322 ms	52 MB
clang++	testcase_30	AC	7 ms	4 MB
clang++	testcase_31	AC	7 ms	4 MB
clang++	testcase_32	AC	20 ms	4 MB
clang++	testcase_33	AC	93 ms	14 MB
clang++	testcase_34	AC	136 ms	28 MB
clang++	testcase_35	AC	223 ms	51 MB
clang++	testcase_36	AC	225 ms	51 MB
clang++	testcase_37	AC	247 ms	52 MB
clang++	testcase_38	AC	237 ms	52 MB