Luzhiled's Library

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

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Code

#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3139"

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

#include "../../structure/union-find/union-find.hpp"

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

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);
  MFP([&](auto rec, int idx, int par) -> void {
    for(auto &to : h.g[idx]) {
      if(to != par) {
        sum[to] = sum[idx] ^ to.cost;
        rec(to, idx);
      }
    }
  })(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) chmin(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) chmin(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)) {
          chmin(base, base ^ tap[j]);
        } else {
          k -= 1 << j;
          chmax(base, base ^ tap[j]);
        }
      }
      return base;
    }
  };

  auto add_dfs = MFP([&](auto add_dfs, int idx, int par, vector< int > base, int Left, int id) -> void {
    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);
    }
  });


  MFP([&](auto dfs, int centroid) -> void {
    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;
  })(root);


  for(auto &p : ans) cout << p << "\n";
}
#line 1 "test/verify/aoj-3139.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3139"

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

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;

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-3139.test.cpp"

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

struct UnionFind {
  vector< int > data;

  UnionFind() = default;

  explicit UnionFind(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]) 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);
  }

  vector< vector< int > > groups() {
    int n = (int) data.size();
    vector< vector< int > > ret(n);
    for(int i = 0; i < n; i++) {
      ret[find(i)].emplace_back(i);
    }
    ret.erase(remove_if(begin(ret), end(ret), [&](const vector< int > &v) {
      return v.empty();
    }), end(ret));
    return ret;
  }
};
#line 6 "test/verify/aoj-3139.test.cpp"

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

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

/**
 * @brief Low Link(橋/関節点)
 * @see http://kagamiz.hatenablog.com/entry/2013/10/05/005213
 * @docs docs/low-link.md
 */
template< typename T = int >
struct LowLink : Graph< T > {
public:
  using Graph< T >::Graph;
  vector< int > ord, low, articulation;
  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:
  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 && !exchange(beet, true)) {
        continue;
      }
      if(!used[to]) {
        ++cnt;
        k = dfs(to, k, idx);
        low[idx] = 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] = min(low[idx], ord[to]);
      }
    }
    is_articulation |= par == -1 && cnt > 1;
    if(is_articulation) articulation.push_back(idx);
    return k;
  }
};
#line 3 "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;

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

  void dfs(int idx, int par) {
    used[idx] = true;
    bool beet = false;
    for(auto &to : g[idx]) {
      if(to == par && !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 5 "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;

  vector< int > rev;
  vector< 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++;
    }
    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(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"

/**
 * @brief Centroid-Decomosition(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:
  vector< int > sub;
  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 9 "test/verify/aoj-3139.test.cpp"

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);
  MFP([&](auto rec, int idx, int par) -> void {
    for(auto &to : h.g[idx]) {
      if(to != par) {
        sum[to] = sum[idx] ^ to.cost;
        rec(to, idx);
      }
    }
  })(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) chmin(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) chmin(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)) {
          chmin(base, base ^ tap[j]);
        } else {
          k -= 1 << j;
          chmax(base, base ^ tap[j]);
        }
      }
      return base;
    }
  };

  auto add_dfs = MFP([&](auto add_dfs, int idx, int par, vector< int > base, int Left, int id) -> void {
    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);
    }
  });


  MFP([&](auto dfs, int centroid) -> void {
    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;
  })(root);


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