Luzhiled's Library

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:x: test/verify/aoj-3139.test.cpp

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Code

// clang-format off
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3139
// clang-format on

#include <algorithm>
#include <functional>
#include <iostream>
#include <vector>

#include "../../graph/others/block-cut-tree.hpp"
#include "../../graph/tree/centroid-decomposition.hpp"
#include "../../structure/union-find/union-find.hpp"

using namespace std;

int main() {
  int N, M;
  cin >> N >> M;
  BlockCutTree<int> g(N);
  Graph<> h(N);
  UnionFind uf(N);
  vector<int> A(M), B(M), C(M);
  for (int i = 0; i < M; i++) {
    cin >> A[i] >> B[i] >> C[i];
    --A[i], --B[i];
    g.add_edge(A[i], B[i], C[i]);
    if (uf.unite(A[i], B[i])) h.add_edge(A[i], B[i], C[i]);
  }
  g.build();

  vector<int> sum(N);
  function<void(int, int)> build_sum = [&](int idx, int par) {
    for (auto& to : h.g[idx]) {
      if (to != par) {
        sum[to] = sum[idx] ^ to.cost;
        build_sum(to, idx);
      }
    }
  };
  build_sum(0, -1);

  auto& t = g.tree;
  vector<int> weight(t.size());

  Graph<int> tree(t);
  CentroidDecomposition<int> cpd(tree);
  int root = cpd.build();
  auto& ushitapunichia = cpd.tree;

  {
    for (int i = 0; i < g.bc.size(); i++) {
      for (auto& e : g.bc[i]) weight[i] ^= e.cost;
    }
    for (int i = 0; i < t.size(); i++) {
      if (i < g.bc.size() && g.bc[i].size() >= 2) continue;
      weight[i] = 0;
    }
  }

  using vi = vector<int>;

  auto f = [](vi& a, int b) {
    for (int y : a) b = min(b, b ^ y);
    if (b) a.emplace_back(b);
  };

  int Q;
  cin >> Q;
  vector<int> X(Q), Y(Q), K(Q), Z(Q);
  for (int i = 0; i < Q; i++) {
    cin >> X[i] >> Y[i] >> K[i];
    --X[i], --Y[i], --K[i];
    Z[i] = sum[X[i]] ^ sum[Y[i]];
    X[i] = g[X[i]];
    Y[i] = g[Y[i]];
  }

  vector<vector<int> > ev(t.size());
  for (int i = 0; i < Q; i++) {
    ev[X[i]].emplace_back(i);
    ev[Y[i]].emplace_back(i);
  }
  vector<int> used(t.size());
  vector<vector<int> > cash(t.size());
  vector<int> last(Q);
  int ptr = 1;
  vector<int> ans(Q);

  auto calc_ans = [&](const vector<int>& a, vector<int> b, int k, int base) {
    for (int x : a) {
      if (b.size() >= 30) break;
      for (int y : b) x = min(x, x ^ y);
      if (x) b.emplace_back(x);
    }
    auto& tap = b;
    if (1 << tap.size() <= k) {
      return -1;
    } else {
      sort(tap.begin(), tap.end());
      for (int j = (int)tap.size() - 1; j >= 0; j--) {
        if (k < (1 << j)) {
          base = min(base, base ^ tap[j]);
        } else {
          k -= 1 << j;
          base = max(base, base ^ tap[j]);
        }
      }
      return base;
    }
  };

  function<void(int, int, vector<int>, int, int)> add_dfs =
      [&](int idx, int par, vector<int> base, int Left, int id) {
        if (weight[idx]) f(base, weight[idx]);
        cash[idx] = base;

        for (auto& q : ev[idx]) {
          if (Left <= last[q] && last[q] < id)
            ans[q] = calc_ans(cash[X[q]], cash[Y[q]], K[q], Z[q]);
          last[q] = id;
        }

        for (auto& to : t.g[idx]) {
          if (to == par) continue;
          if (used[to]) continue;
          add_dfs(to, idx, base, Left, id);
        }
      };

  function<void(int)> dfs = [&](int centroid) {
    used[centroid] = true;

    vector<int> base;
    int Left = ptr;
    if (weight[centroid]) base.emplace_back(weight[centroid]);
    for (auto& q : ev[centroid]) {
      if (last[q] == ptr) ans[q] = calc_ans(base, base, K[q], Z[q]);
      last[q] = ptr;
    }
    cash[centroid] = base;
    ++ptr;

    for (auto& to : t.g[centroid]) {
      if (used[to]) continue;
      add_dfs(to, centroid, base, Left, ptr++);
    }

    for (auto& to : ushitapunichia.g[centroid]) {
      dfs(to);
    }
    used[centroid] = false;
  };
  dfs(root);

  for (auto& p : ans) cout << p << "\n";
}

#line 1 "test/verify/aoj-3139.test.cpp"
// clang-format off
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3139
// clang-format on

#include <algorithm>
#include <functional>
#include <iostream>
#include <vector>

#line 2 "graph/others/block-cut-tree.hpp"

#include <utility>
#line 5 "graph/others/block-cut-tree.hpp"

#line 2 "graph/connected-components/bi-connected-components.hpp"

#line 4 "graph/connected-components/bi-connected-components.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/others/low-link.hpp"

#line 6 "graph/others/low-link.hpp"

#line 8 "graph/others/low-link.hpp"

/**
 * @brief Low Link(橋/関節点)
 * @see http://kagamiz.hatenablog.com/entry/2013/10/05/005213
 *
 */
template <typename T = int>
struct LowLink : Graph<T> {
 public:
  using Graph<T>::Graph;
  std::vector<int> ord, low, articulation;
  std::vector<Edge<T> > bridge;
  using Graph<T>::g;

  virtual void build() {
    used.assign(g.size(), 0);
    ord.assign(g.size(), 0);
    low.assign(g.size(), 0);
    int k = 0;
    for (int i = 0; i < (int)g.size(); i++) {
      if (!used[i]) k = dfs(i, k, -1);
    }
  }

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

 private:
  std::vector<int> used;

  int dfs(int idx, int k, int par) {
    used[idx] = true;
    ord[idx] = k++;
    low[idx] = ord[idx];
    bool is_articulation = false, beet = false;
    int cnt = 0;
    for (auto& to : g[idx]) {
      if (to == par && !std::exchange(beet, true)) {
        continue;
      }
      if (!used[to]) {
        ++cnt;
        k = dfs(to, k, idx);
        low[idx] = std::min(low[idx], low[to]);
        is_articulation |= par >= 0 && low[to] >= ord[idx];
        if (ord[idx] < low[to]) bridge.emplace_back(to);
      } else {
        low[idx] = std::min(low[idx], ord[to]);
      }
    }
    is_articulation |= par == -1 && cnt > 1;
    if (is_articulation) articulation.push_back(idx);
    return k;
  }
};
#line 7 "graph/connected-components/bi-connected-components.hpp"

template <typename T = int>
struct BiConnectedComponents : LowLink<T> {
 public:
  using LowLink<T>::LowLink;
  using LowLink<T>::g;
  using LowLink<T>::ord;
  using LowLink<T>::low;

  std::vector<std::vector<Edge<T> > > bc;

  void build() override {
    LowLink<T>::build();
    used.assign(g.size(), 0);
    for (int i = 0; i < (int)used.size(); i++) {
      if (!used[i]) dfs(i, -1);
    }
  }

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

 private:
  std::vector<int> used;
  std::vector<Edge<T> > tmp;

  void dfs(int idx, int par) {
    used[idx] = true;
    bool beet = false;
    for (auto& to : g[idx]) {
      if (to == par && !std::exchange(beet, true)) continue;
      if (!used[to] || ord[to] < ord[idx]) {
        tmp.emplace_back(to);
      }
      if (!used[to]) {
        dfs(to, idx);
        if (low[to] >= ord[idx]) {
          bc.emplace_back();
          for (;;) {
            auto e = tmp.back();
            bc.back().emplace_back(e);
            tmp.pop_back();
            if (e.idx == to.idx) break;
          }
        }
      }
    }
  }
};
#line 8 "graph/others/block-cut-tree.hpp"

/**
 * @brief Block Cut Tree
 * @see https://ei1333.hateblo.jp/entry/2020/03/25/010057
 */
template <typename T = int>
struct BlockCutTree : BiConnectedComponents<T> {
 public:
  using BiConnectedComponents<T>::BiConnectedComponents;
  using BiConnectedComponents<T>::g;
  using BiConnectedComponents<T>::articulation;
  using BiConnectedComponents<T>::bc;

  std::vector<int> rev;
  std::vector<std::vector<int> > group;
  Graph<T> tree;

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

  int operator[](const int& k) const { return rev[k]; }

  void build() override {
    BiConnectedComponents<T>::build();
    rev.assign(g.size(), -1);
    int ptr = (int)bc.size();
    for (auto& idx : articulation) {
      rev[idx] = ptr++;
    }
    std::vector<int> last(ptr, -1);
    tree = Graph<T>(ptr);
    for (int i = 0; i < (int)bc.size(); i++) {
      for (auto& e : bc[i]) {
        for (auto& ver : {e.from, e.to}) {
          if (rev[ver] >= (int)bc.size()) {
            if (std::exchange(last[rev[ver]], i) != i) {
              tree.add_edge(rev[ver], i, e.cost);
            }
          } else {
            rev[ver] = i;
          }
        }
      }
    }
    group.resize(ptr);
    for (int i = 0; i < (int)g.size(); i++) {
      group[rev[i]].emplace_back(i);
    }
  }
};
#line 2 "graph/tree/centroid-decomposition.hpp"

#line 4 "graph/tree/centroid-decomposition.hpp"

#line 6 "graph/tree/centroid-decomposition.hpp"

/**
 * @brief Centroid-Decomposition(重心分解)
 */
template <typename T>
struct CentroidDecomposition : Graph<T> {
 public:
  using Graph<T>::Graph;
  using Graph<T>::g;
  Graph<int> tree;

  int build(int t = 0) {
    sub.assign(g.size(), 0);
    v.assign(g.size(), 0);
    tree = Graph<int>(g.size());
    return build_dfs(0);
  }

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

 private:
  std::vector<int> sub;
  std::vector<int> v;

  inline int build_dfs(int idx, int par) {
    sub[idx] = 1;
    for (auto& to : g[idx]) {
      if (to == par || v[to]) continue;
      sub[idx] += build_dfs(to, idx);
    }
    return sub[idx];
  }

  inline int search_centroid(int idx, int par, const int mid) {
    for (auto& to : g[idx]) {
      if (to == par || v[to]) continue;
      if (sub[to] > mid) return search_centroid(to, idx, mid);
    }
    return idx;
  }

  inline int build_dfs(int idx) {
    int centroid = search_centroid(idx, -1, build_dfs(idx, -1) / 2);
    v[centroid] = true;
    for (auto& to : g[centroid]) {
      if (!v[to]) tree.add_directed_edge(centroid, build_dfs(to));
    }
    v[centroid] = false;
    return centroid;
  }
};
#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 13 "test/verify/aoj-3139.test.cpp"

using namespace std;

int main() {
  int N, M;
  cin >> N >> M;
  BlockCutTree<int> g(N);
  Graph<> h(N);
  UnionFind uf(N);
  vector<int> A(M), B(M), C(M);
  for (int i = 0; i < M; i++) {
    cin >> A[i] >> B[i] >> C[i];
    --A[i], --B[i];
    g.add_edge(A[i], B[i], C[i]);
    if (uf.unite(A[i], B[i])) h.add_edge(A[i], B[i], C[i]);
  }
  g.build();

  vector<int> sum(N);
  function<void(int, int)> build_sum = [&](int idx, int par) {
    for (auto& to : h.g[idx]) {
      if (to != par) {
        sum[to] = sum[idx] ^ to.cost;
        build_sum(to, idx);
      }
    }
  };
  build_sum(0, -1);

  auto& t = g.tree;
  vector<int> weight(t.size());

  Graph<int> tree(t);
  CentroidDecomposition<int> cpd(tree);
  int root = cpd.build();
  auto& ushitapunichia = cpd.tree;

  {
    for (int i = 0; i < g.bc.size(); i++) {
      for (auto& e : g.bc[i]) weight[i] ^= e.cost;
    }
    for (int i = 0; i < t.size(); i++) {
      if (i < g.bc.size() && g.bc[i].size() >= 2) continue;
      weight[i] = 0;
    }
  }

  using vi = vector<int>;

  auto f = [](vi& a, int b) {
    for (int y : a) b = min(b, b ^ y);
    if (b) a.emplace_back(b);
  };

  int Q;
  cin >> Q;
  vector<int> X(Q), Y(Q), K(Q), Z(Q);
  for (int i = 0; i < Q; i++) {
    cin >> X[i] >> Y[i] >> K[i];
    --X[i], --Y[i], --K[i];
    Z[i] = sum[X[i]] ^ sum[Y[i]];
    X[i] = g[X[i]];
    Y[i] = g[Y[i]];
  }

  vector<vector<int> > ev(t.size());
  for (int i = 0; i < Q; i++) {
    ev[X[i]].emplace_back(i);
    ev[Y[i]].emplace_back(i);
  }
  vector<int> used(t.size());
  vector<vector<int> > cash(t.size());
  vector<int> last(Q);
  int ptr = 1;
  vector<int> ans(Q);

  auto calc_ans = [&](const vector<int>& a, vector<int> b, int k, int base) {
    for (int x : a) {
      if (b.size() >= 30) break;
      for (int y : b) x = min(x, x ^ y);
      if (x) b.emplace_back(x);
    }
    auto& tap = b;
    if (1 << tap.size() <= k) {
      return -1;
    } else {
      sort(tap.begin(), tap.end());
      for (int j = (int)tap.size() - 1; j >= 0; j--) {
        if (k < (1 << j)) {
          base = min(base, base ^ tap[j]);
        } else {
          k -= 1 << j;
          base = max(base, base ^ tap[j]);
        }
      }
      return base;
    }
  };

  function<void(int, int, vector<int>, int, int)> add_dfs =
      [&](int idx, int par, vector<int> base, int Left, int id) {
        if (weight[idx]) f(base, weight[idx]);
        cash[idx] = base;

        for (auto& q : ev[idx]) {
          if (Left <= last[q] && last[q] < id)
            ans[q] = calc_ans(cash[X[q]], cash[Y[q]], K[q], Z[q]);
          last[q] = id;
        }

        for (auto& to : t.g[idx]) {
          if (to == par) continue;
          if (used[to]) continue;
          add_dfs(to, idx, base, Left, id);
        }
      };

  function<void(int)> dfs = [&](int centroid) {
    used[centroid] = true;

    vector<int> base;
    int Left = ptr;
    if (weight[centroid]) base.emplace_back(weight[centroid]);
    for (auto& q : ev[centroid]) {
      if (last[q] == ptr) ans[q] = calc_ans(base, base, K[q], Z[q]);
      last[q] = ptr;
    }
    cash[centroid] = base;
    ++ptr;

    for (auto& to : t.g[centroid]) {
      if (used[to]) continue;
      add_dfs(to, centroid, base, Left, ptr++);
    }

    for (auto& to : ushitapunichia.g[centroid]) {
      dfs(to);
    }
    used[centroid] = false;
  };
  dfs(root);

  for (auto& p : ans) cout << p << "\n";
}
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