test/verify/aoj-2270.test.cpp

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• Last update: 2026-08-10 15:36:17+00:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2270

Depends on

• Graph Template (グラフテンプレート) (graph/graph-template.hpp)
• Offline LCA(オフライン最小共通祖先) (graph/tree/offline-lca.hpp)
• Mo Tree(木上のMo) (other/mo-tree.hpp)
• Binary Indexed Tree (structure/others/binary-indexed-tree.hpp)
• Union Find (structure/union-find/union-find.hpp)

Code

// clang-format off
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2270
// clang-format on

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

#include "../../other/mo-tree.hpp"
#include "../../structure/others/binary-indexed-tree.hpp"

using namespace std;

int main() {
  int N, Q;
  cin >> N >> Q;
  vector<int> A(N);
  for (auto& a : A) cin >> a;
  auto vs = A;
  sort(begin(vs), end(vs));
  vs.erase(unique(begin(vs), end(vs)), end(vs));
  for (auto& a : A) a = lower_bound(begin(vs), end(vs), a) - begin(vs);
  MoTree<> g(N);
  g.read(N - 1);
  vector<int> K(Q);
  for (int i = 0; i < Q; i++) {
    int a, b;
    cin >> a >> b >> K[i];
    --a, --b;
    g.add(a, b);
  }
  vector<int64_t> ans(Q);
  BinaryIndexedTree<int> bit(N);
  auto add = [&](int i) { bit.apply(A[i], 1); };
  auto erase = [&](int i) { bit.apply(A[i], -1); };
  auto out = [&](int q) { ans[q] = vs[bit.lower_bound(K[q])]; };
  g.build(add, erase, out);
  for (auto& p : ans) cout << p << "\n";
}

#line 1 "test/verify/aoj-2270.test.cpp"
// clang-format off
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2270
// clang-format on

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

#line 2 "other/mo-tree.hpp"

#line 4 "other/mo-tree.hpp"
#include <cmath>
#include <iterator>
#include <numeric>
#include <utility>
#line 9 "other/mo-tree.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 2 "graph/tree/offline-lca.hpp"

#line 5 "graph/tree/offline-lca.hpp"

#line 2 "structure/union-find/union-find.hpp"

#line 7 "structure/union-find/union-find.hpp"

struct UnionFind {
  std::vector<int> data;

  UnionFind() = default;

  explicit UnionFind(std::size_t sz) : data(sz, -1) {}

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return false;
    if (data[x] > data[y]) std::swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return true;
  }

  int find(int k) {
    if (data[k] < 0) return (k);
    return data[k] = find(data[k]);
  }

  int size(int k) { return -data[find(k)]; }

  bool same(int x, int y) { return find(x) == find(y); }

  std::vector<std::vector<int>> groups() {
    int n = (int)data.size();
    std::vector<std::vector<int>> ret(n);
    for (int i = 0; i < n; i++) {
      ret[find(i)].emplace_back(i);
    }
    ret.erase(
        std::remove_if(ret.begin(), ret.end(),
                       [&](const std::vector<int>& v) { return v.empty(); }),
        ret.end());
    return ret;
  }
};
#line 8 "graph/tree/offline-lca.hpp"

/**
 * @brief Offline LCA(オフライン最小共通祖先)
 **/
template <typename T>
std::vector<int> offline_lca(const Graph<T>& g,
                             std::vector<std::pair<int, int> >& qs,
                             int root = 0) {
  int n = (int)g.size();
  UnionFind uf(n);
  std::vector<int> st(n), mark(n), ptr(n), ans(qs.size(), -1);
  int top = 0;
  st[top] = root;
  for (auto& [l, r] : qs) mark[l]++, mark[r]++;
  std::vector<std::vector<std::pair<int, int> > > q(n);
  for (int i = 0; i < n; i++) {
    q[i].reserve(mark[i]);
    mark[i] = -1;
    ptr[i] = (int)g[i].size();
  }
  for (int i = 0; i < qs.size(); i++) {
    q[qs[i].first].emplace_back(qs[i].second, i);
    q[qs[i].second].emplace_back(qs[i].first, i);
  }
  auto run = [&](int u) -> bool {
    while (ptr[u]) {
      int v = g[u][--ptr[u]];
      if (mark[v] == -1) {
        st[++top] = v;
        return true;
      }
    }
    return false;
  };
  while (~top) {
    int u = st[top];
    if (mark[u] == -1) {
      mark[u] = u;
    } else {
      uf.unite(u, g[u][ptr[u]]);
      mark[uf.find(u)] = u;
    }
    if (not run(u)) {
      for (auto& [v, i] : q[u]) {
        if (~mark[v] and ans[i] == -1) {
          ans[i] = mark[uf.find(v)];
        }
      }
      --top;
    }
  }
  return ans;
}
#line 12 "other/mo-tree.hpp"

/**
 * @brief Mo Tree(木上のMo)
 **/
template <typename T = int>
struct MoTree : Graph<T> {
  using Graph<T>::Graph;
  using Graph<T>::g;
  std::vector<int> in, vs;
  std::vector<std::pair<int, int> > qs;

 public:
  void add(int l, int r) { /* [l, r) */ qs.emplace_back(l, r); }

 private:
  void dfs(int u, int p) {
    in[u] = (int)vs.size();
    vs.emplace_back(u);
    for (auto& v : g[u]) {
      if (v != p) {
        dfs(v, u);
        vs.emplace_back(v);
      }
    }
  }

 public:
  template <typename A, typename E, typename O>
  void build(const A& add, const E& erase, const O& out) {
    int n = (int)g.size() * 2 - 1;
    vs.reserve(n);
    in.resize(g.size());
    dfs(0, -1);
    std::vector<std::pair<int, int> > lr;
    lr.reserve(qs.size());
    auto lca = offline_lca(*this, qs);
    for (auto& [l, r] : qs) {
      lr.emplace_back(std::minmax(in[l] + 1, in[r] + 1));
    }
    int q = (int)lr.size();
    int bs = n / std::min<int>(n, std::sqrt(q));
    std::vector<int> ord(q);
    std::iota(std::begin(ord), std::end(ord), 0);
    std::sort(std::begin(ord), std::end(ord), [&](int a, int b) {
      int ablock = lr[a].first / bs, bblock = lr[b].first / bs;
      if (ablock != bblock) return ablock < bblock;
      return (ablock & 1) ? lr[a].second > lr[b].second
                          : lr[a].second < lr[b].second;
    });
    int l = 0, r = 0;
    std::vector<int> flip(g.size());
    auto f = [&](int u) {
      flip[u] ^= 1;
      if (flip[u])
        add(u);
      else
        erase(u);
    };
    for (auto& idx : ord) {
      while (l > lr[idx].first) f(vs[--l]);
      while (r < lr[idx].second) f(vs[r++]);
      while (l < lr[idx].first) f(vs[l++]);
      while (r > lr[idx].second) f(vs[--r]);
      f(lca[idx]);
      out(idx);
      f(lca[idx]);
    }
  }
};
#line 2 "structure/others/binary-indexed-tree.hpp"

#include <cassert>
#line 5 "structure/others/binary-indexed-tree.hpp"

template <typename T>
struct BinaryIndexedTree {
 private:
  int n;
  std::vector<T> data;

 public:
  BinaryIndexedTree() = default;

  explicit BinaryIndexedTree(int n) : n(n) { data.assign(n + 1, T()); }

  explicit BinaryIndexedTree(const std::vector<T>& v)
      : BinaryIndexedTree((int)v.size()) {
    build(v);
  }

  void build(const std::vector<T>& v) {
    assert(n == (int)v.size());
    for (int i = 1; i <= n; i++) data[i] = v[i - 1];
    for (int i = 1; i <= n; i++) {
      int j = i + (i & -i);
      if (j <= n) data[j] += data[i];
    }
  }

  void apply(int k, const T& x) {
    for (++k; k <= n; k += k & -k) data[k] += x;
  }

  T prod(int r) const {
    T ret = T();
    for (; r > 0; r -= r & -r) ret += data[r];
    return ret;
  }

  T prod(int l, int r) const { return prod(r) - prod(l); }

  int lower_bound(T x) const {
    int i = 0;
    for (int k = 1 << (32 - __builtin_clz(n)); k > 0; k >>= 1) {
      if (i + k <= n && data[i + k] < x) {
        x -= data[i + k];
        i += k;
      }
    }
    return i;
  }

  int upper_bound(T x) const {
    int i = 0;
    for (int k = 1 << (32 - __builtin_clz(n)); k > 0; k >>= 1) {
      if (i + k <= n && data[i + k] <= x) {
        x -= data[i + k];
        i += k;
      }
    }
    return i;
  }
};
#line 12 "test/verify/aoj-2270.test.cpp"

using namespace std;

int main() {
  int N, Q;
  cin >> N >> Q;
  vector<int> A(N);
  for (auto& a : A) cin >> a;
  auto vs = A;
  sort(begin(vs), end(vs));
  vs.erase(unique(begin(vs), end(vs)), end(vs));
  for (auto& a : A) a = lower_bound(begin(vs), end(vs), a) - begin(vs);
  MoTree<> g(N);
  g.read(N - 1);
  vector<int> K(Q);
  for (int i = 0; i < Q; i++) {
    int a, b;
    cin >> a >> b >> K[i];
    --a, --b;
    g.add(a, b);
  }
  vector<int64_t> ans(Q);
  BinaryIndexedTree<int> bit(N);
  auto add = [&](int i) { bit.apply(A[i], 1); };
  auto erase = [&](int i) { bit.apply(A[i], -1); };
  auto out = [&](int q) { ans[q] = vs[bit.lower_bound(K[q])]; };
  g.build(add, erase, out);
  for (auto& p : ans) cout << p << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	testcase_00	AC	3 ms	4 MB
g++	testcase_01	AC	2 ms	4 MB
g++	testcase_02	AC	2 ms	4 MB
g++	testcase_03	AC	2 ms	4 MB
g++	testcase_04	AC	2 ms	4 MB
g++	testcase_05	AC	2 ms	4 MB
g++	testcase_06	AC	2 ms	4 MB
g++	testcase_07	AC	2 ms	4 MB
g++	testcase_08	AC	2 ms	4 MB
g++	testcase_09	AC	2 ms	4 MB
g++	testcase_10	AC	2 ms	4 MB
g++	testcase_11	AC	4 ms	4 MB
g++	testcase_12	AC	4 ms	4 MB
g++	testcase_13	AC	4 ms	4 MB
g++	testcase_14	AC	4 ms	4 MB
g++	testcase_15	AC	4 ms	4 MB
g++	testcase_16	AC	4 ms	4 MB
g++	testcase_17	AC	4 ms	4 MB
g++	testcase_18	AC	4 ms	4 MB
g++	testcase_19	AC	1285 ms	22 MB
g++	testcase_20	AC	1283 ms	22 MB
g++	testcase_21	AC	1282 ms	22 MB
g++	testcase_22	AC	1342 ms	26 MB
g++	testcase_23	AC	1352 ms	24 MB
g++	testcase_24	AC	1350 ms	24 MB
g++	testcase_25	AC	1385 ms	25 MB
g++	testcase_26	AC	1364 ms	27 MB
g++	testcase_27	AC	860 ms	28 MB
g++	testcase_28	AC	1122 ms	27 MB
g++	testcase_29	AC	1045 ms	25 MB
g++	testcase_30	AC	1129 ms	23 MB
clang++	testcase_00	AC	3 ms	4 MB
clang++	testcase_01	AC	2 ms	4 MB
clang++	testcase_02	AC	2 ms	4 MB
clang++	testcase_03	AC	2 ms	4 MB
clang++	testcase_04	AC	2 ms	4 MB
clang++	testcase_05	AC	2 ms	4 MB
clang++	testcase_06	AC	2 ms	4 MB
clang++	testcase_07	AC	2 ms	4 MB
clang++	testcase_08	AC	2 ms	4 MB
clang++	testcase_09	AC	2 ms	4 MB
clang++	testcase_10	AC	2 ms	4 MB
clang++	testcase_11	AC	4 ms	4 MB
clang++	testcase_12	AC	4 ms	4 MB
clang++	testcase_13	AC	4 ms	4 MB
clang++	testcase_14	AC	4 ms	4 MB
clang++	testcase_15	AC	4 ms	4 MB
clang++	testcase_16	AC	4 ms	4 MB
clang++	testcase_17	AC	4 ms	4 MB
clang++	testcase_18	AC	4 ms	4 MB
clang++	testcase_19	AC	1347 ms	22 MB
clang++	testcase_20	AC	1304 ms	22 MB
clang++	testcase_21	AC	1334 ms	22 MB
clang++	testcase_22	AC	1369 ms	26 MB
clang++	testcase_23	AC	1371 ms	24 MB
clang++	testcase_24	AC	1365 ms	23 MB
clang++	testcase_25	AC	1367 ms	25 MB
clang++	testcase_26	AC	1429 ms	27 MB
clang++	testcase_27	AC	868 ms	27 MB
clang++	testcase_28	AC	1127 ms	26 MB
clang++	testcase_29	AC	1069 ms	24 MB
clang++	testcase_30	AC	1134 ms	23 MB

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