Problem p01670 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define rrep(i, n) for (int i = (int)(n)-1; i >= 0; --i)
#define srep(i, s, t) for (int i = (int)(s); i < (int)(t); ++i)
#define each(a, b) for (auto &(a) : (b))
#define all(v) (v).begin(), (v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)), v.erase(unique(all(v)), v.end())
#define cmx(x, y) x = max(x, y)
#define cmn(x, y) x = min(x, y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout << #x << " = " << (x) << endl
#define spair(p) cout << #p << ": " << p.fi << " " << p.se << endl
#define sar(a, n)                                                              \\
  cout << #a << ":";                                                           \\
  rep(pachico, n) cout << " " << a[pachico];                                   \\
  cout << endl
#define svec(v)                                                                \\
  cout << #v << ":";                                                           \\
  rep(pachico, v.size()) cout << " " << v[pachico];                            \\
  cout << endl
#define svecp(v)                                                               \\
  cout << #v << ":";                                                           \\
  each(pachico, v) cout << " {" << pachico.first << ":" << pachico.second      \\
                        << "}";                                                \\
  cout << endl
#define sset(s)                                                                \\
  cout << #s << ":";                                                           \\
  each(pachico, s) cout << " " << pachico;                                     \\
  cout << endl
#define smap(m)                                                                \\
  cout << #m << ":";                                                           \\
  each(pachico, m) cout << " {" << pachico.first << ":" << pachico.second      \\
                        << "}";                                                \\
  cout << endl

using namespace std;

typedef pair<int, int> P;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<P> vp;
typedef vector<string> vs;

const int MAX_N = 100005;

template <typename T> class ListIterator;

// 常に不変なイテレーターが欲しい場合に別のコンテナにこれをかぶせる形で使うとよい
template <typename T> class List {
public:
  using iterator = ListIterator<T>;

private:
  int N, sz;
  vector<int> prev, next;
  vector<T> container;
  friend ListIterator<T>;

public:
  // 添字 next_index の要素の前に添字 now_index の要素の iterator を挿入
  iterator insert(int next_index, int now_index) {
    sz++;
    prev[now_index] = prev[next_index], next[now_index] = next_index;
    next[prev[next_index]] = now_index, prev[next_index] = now_index;
    return iterator(this, now_index);
  }
  // 添字 index の値を削除 → 次の要素の iterator を返す
  iterator erase(int index) {
    sz--;
    next[prev[index]] = next[index], prev[next[index]] = prev[index];
    return iterator(this, next[index]);
  }

public:
  friend ostream &operator<<(ostream &os, List &ls) {
    for (auto &val : ls) {
      os << val << ' ';
    }
    return os;
  }
  const T &operator[](size_t index) const { return container[index]; }
  T &operator[](size_t index) { return container[index]; }
  size_t size() { return sz; }
  bool empty() { return size() == 0; }
  T &front() { return container[next[N]]; }
  T &back() { return container[prev[N]]; }
  iterator begin() { return iterator(this, next[N]); }
  iterator end() { return iterator(this, N); }
  iterator insert(const iterator &itr, int index) {
    return insert(itr.index, index);
  }
  iterator erase(const iterator &itr) { return erase(itr.index); }
  iterator push_back() { return insert(N, prev[N] + 1); }
  void pop_back() { erase(prev[N]); }
  void clear() {
    N = sz = 0;
    prev = next = {0};
    container.clear();
  }

public:
  List() : N(0), sz(0), prev({0}), next({0}) {}
  List(int _N) : container(_N) { build(); }
  List(int _N, T val) : container(_N, val) { build(); }
  List(const List &ls)
      : N(ls.N), sz(ls.sz), prev(ls.prev), next(ls.next),
        container(ls.container) {}
  List(const vector<T> &vec) : container(vec) { build(); }
  List &operator=(const List &ls) {
    container = ls.container;
    build();
    return *this;
  }
  List &operator=(const vector<T> &vec) {
    container = vec;
    build();
    return *this;
  }
  List &operator=(const List &&ls) noexcept {
    container = ls.container;
    build();
    return *this;
  }
  List(initializer_list<T> vals) : container(vals.begin(), vals.end()) {
    build();
  }
  iterator push_back(T val) {
    N++, sz++;
    prev.push_back(N - 1), prev[0] = N;
    next.back() = N, next.push_back(0);
    container.push_back(val);
    return iterator(this, N - 1);
  }
  void build() {
    N = sz = (int)container.size();
    prev.resize(N + 1), next.resize(N + 1);
    iota(prev.begin(), prev.end(), -1), iota(next.begin(), next.end(), 1);
    prev[0] = N, next[N] = 0;
  }
};

template <typename T>
class ListIterator
    : public std::iterator<bidirectional_iterator_tag, T, ptrdiff_t, T *, T &> {
private:
  friend List<T>;
  List<T> *ls_ptr;
  int index;

private:
  ListIterator(List<T> *ls, int _index) : ls_ptr(ls), index(_index) {}

public:
  ListIterator() {}
  ListIterator(const ListIterator &itr) {
    ls_ptr = itr.ls_ptr, index = itr.index;
  }
  operator int() const noexcept { return index; }
  ListIterator &operator=(const ListIterator &itr) & {
    ls_ptr = itr.ls_ptr, index = itr.index;
    return *this;
  }
  ListIterator &operator=(ListIterator &&itr) &noexcept {
    ls_ptr = itr.ls_ptr, index = itr.index;
    return *this;
  }
  T &operator*() const { return ls_ptr->container[index]; }
  T *operator->() const { return &ls_ptr->container[index]; }
  ListIterator &operator++() {
    index = ls_ptr->next[index];
    return *this;
  }
  ListIterator operator++(int) {
    ListIterator res = *this;
    index = ls_ptr->next[index];
    return res;
  }
  ListIterator &operator--() {
    index = ls_ptr->prev[index];
    return *this;
  };
  ListIterator operator--(int) {
    ListIterator res = *this;
    index = ls_ptr->prev[index];
    return res;
  };
  bool operator==(const ListIterator &itr) const { return !(*this != itr); };
  bool operator!=(const ListIterator &itr) const {
    return this->ls_ptr != itr.ls_ptr || this->index != itr.index;
  }
  friend void swap(const ListIterator<T> &itr1, const ListIterator<T> &itr2) {
    ListIterator<T> tmp = itr1;
    itr1 = itr2, itr2 = itr1;
  };
};

// 多重辺はなし
class MVC {
private:
  struct edge {
    int to, rev;
  };
  struct info {
    // from から to 番目に出ている辺が(を) next の前から消えた(に入れる)
    int from, to, next;
    info(int ag1, int ag2, int ag3) : from(ag1), to(ag2), next(ag3) {}
  };
  int V, rem_edge_size, fp_size;
  vector<List<edge>> G;
  List<int> rem_ver;
  vector<int> cand, deg;
  vector<vector<info>> edge_info;
  set<int> small_deg_ver, use_ver;

  bool push_cand(int u, int add_size) {
    add_size++, cand.push_back(u);
    return (int)cand.size() < ans_size;
  }

  bool erase(int u, bool use, bool alr_use, int add_size,
             vector<pair<int, int>> &erase_ver) {
    if (use && !alr_use) {
      if (!push_cand(u, add_size))
        return false;
    }
    erase_ver.emplace_back(u, rem_ver.erase(u));
    for (auto &e : G[u]) {
      edge_info[u].emplace_back(e.to, e.rev, G[e.to].erase(e.rev));
      deg[e.to]--, rem_edge_size--;
      if (deg[e.to] == 0)
        erase_ver.emplace_back(e.to, rem_ver.erase(e.to));
      if (!use) {
        if (use_ver.count(e.to) == 1)
          continue;
        if (!push_cand(e.to, add_size))
          return false;
        if (deg[e.to] > 0)
          use_ver.insert(e.to);
      } else {
        if (deg[e.to] == 1 && use_ver.count(e.to) == 0)
          small_deg_ver.insert(e.to);
      }
    }
    return true;
  }
  bool erase_rec_set(set<int> &st, bool flag, int add_size,
                     vector<pair<int, int>> &erase_ver) {
    while (!st.empty()) {
      int v = *st.begin();
      st.erase(v);
      if (deg[v] == 0)
        continue;
      if (!erase(v, flag, flag, add_size, erase_ver))
        return false;
    }
    return true;
  }
  bool erase_rec(int u, bool use, int add_size,
                 vector<pair<int, int>> &erase_ver) {
    if (!erase(u, use, false, add_size, erase_ver))
      return false;
    while (!small_deg_ver.empty() || !use_ver.empty()) {
      if (!erase_rec_set(small_deg_ver, false, add_size, erase_ver))
        return false;
      if (!erase_rec_set(use_ver, true, add_size, erase_ver))
        return false;
    }
    return true;
  }
  bool preprocessing(int K, int add_size, vector<pair<int, int>> &erase_ver) {
    for (int u : rem_ver) {
      if (deg[u] > K) {
        if (!erase_rec(u, true, add_size, erase_ver))
          return false;
      }
    }
    return true;
  }
  void postprocessing(int K, int add_size, vector<pair<int, int>> &erase_ver) {
    // 最初の層で行われた前処理による変更は特に後処理する必要がない
    if (K == fp_size)
      return;
    for (int i = 0; i < add_size; i++) {
      cand.pop_back();
    }
    for (int i = (int)erase_ver.size() - 1; i >= 0; i--) {
      auto &p = erase_ver[i];
      while (!edge_info[p.first].empty()) {
        auto &dat = edge_info[p.first].back();
        G[dat.from].insert(dat.next, dat.to), deg[dat.from]++, rem_edge_size++;
        edge_info[p.first].pop_back();
      }
      rem_ver.insert(p.second, p.first);
    }
  }
  bool check() {
    if (rem_edge_size == 0) {
      if ((int)cand.size() < ans_size) {
        ans_size = (int)cand.size(), ans_set = cand;
      }
      return false;
    }
    return (int)rem_ver.size() > 0;
  }
  void transition(int K, int next_ver, bool use) {
    int pl_add_size = 0;
    vector<pair<int, int>> pl_erase_ver;
    if (!erase_rec(next_ver, use, pl_add_size, pl_erase_ver)) {
      return postprocessing(K - 1, pl_add_size, pl_erase_ver);
    }
    if (check())
      judge(K - 1);
    return postprocessing(K - 1, pl_add_size, pl_erase_ver);
  }
  int find_max_degree_ver() {
    // 次数の高い頂点から探索する
    int max_deg = -1, next_ver = -1;
    for (int v : rem_ver) {
      if (deg[v] > max_deg)
        max_deg = deg[v], next_ver = v;
    }
    if (2 * rem_edge_size > (long long)max_deg * (int)rem_ver.size())
      return -1;
    return next_ver;
  }
  void judge(int K) {
    int add_size = 0;
    vector<pair<int, int>> erase_ver;
    if (!preprocessing(K, add_size, erase_ver))
      return postprocessing(K, add_size, erase_ver);
    if (!check())
      return postprocessing(K, add_size, erase_ver);
    int next_ver = find_max_degree_ver();
    if (next_ver < 0)
      return postprocessing(K, add_size, erase_ver);
    // 使う場合
    transition(K, next_ver, true);
    // 使わない場合
    if ((int)cand.size() + (int)G[next_ver].size() >= ans_size) {
      transition(K, next_ver, false);
    }
    return postprocessing(K, add_size, erase_ver);
  }

public:
  vector<int> ans_set;
  int ans_size;

  MVC(int node_size)
      : V(node_size), rem_edge_size(0), G(V), rem_ver(V), deg(V, 0),
        edge_info(V) {
    for (int i = 0; i < V; i++)
      rem_ver[i] = i;
  }
  void add_edge(int u, int v) {
    G[u].push_back((edge){v, (int)G[v].size()});
    G[v].push_back((edge){u, (int)G[u].size() - 1});
    deg[u]++, deg[v]++, rem_edge_size++;
  }
  bool solve(int K) {
    fp_size = K, ans_size = fp_size + 1;
    judge(fp_size);
    return ans_size <= fp_size;
  }
};

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n, m, K;
  cin >> n >> m >> K;
  MVC mvc(n);
  rep(i, m) {
    int a, b;
    cin >> a >> b;
    mvc.add_edge(a - 1, b - 1);
  }
  if (mvc.solve(K)) {
    cout << mvc.ans_size << "\\n";
  } else {
    cout << "Impossible\\n";
  }
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define rrep(i, n) for (int i = (int)(n)-1; i >= 0; --i)
#define srep(i, s, t) for (int i = (int)(s); i < (int)(t); ++i)
#define each(a, b) for (auto &(a) : (b))
#define all(v) (v).begin(), (v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)), v.erase(unique(all(v)), v.end())
#define cmx(x, y) x = max(x, y)
#define cmn(x, y) x = min(x, y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout << #x << " = " << (x) << endl
#define spair(p) cout << #p << ": " << p.fi << " " << p.se << endl
#define sar(a, n)                                                              \\
  cout << #a << ":";                                                           \\
  rep(pachico, n) cout << " " << a[pachico];                                   \\
  cout << endl
#define svec(v)                                                                \\
  cout << #v << ":";                                                           \\
  rep(pachico, v.size()) cout << " " << v[pachico];                            \\
  cout << endl
#define svecp(v)                                                               \\
  cout << #v << ":";                                                           \\
  each(pachico, v) cout << " {" << pachico.first << ":" << pachico.second      \\
                        << "}";                                                \\
  cout << endl
#define sset(s)                                                                \\
  cout << #s << ":";                                                           \\
  each(pachico, s) cout << " " << pachico;                                     \\
  cout << endl
#define smap(m)                                                                \\
  cout << #m << ":";                                                           \\
  each(pachico, m) cout << " {" << pachico.first << ":" << pachico.second      \\
                        << "}";                                                \\
  cout << endl

using namespace std;

typedef pair<int, int> P;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<P> vp;
typedef vector<string> vs;

const int MAX_N = 100005;

template <typename T> class ListIterator;

// 常に不変なイテレーターが欲しい場合に別のコンテナにこれをかぶせる形で使うとよい
template <typename T> class List {
public:
  using iterator = ListIterator<T>;

private:
  int N, sz;
  vector<int> prev, next;
  vector<T> container;
  friend ListIterator<T>;

public:
  // 添字 next_index の要素の前に添字 now_index の要素の iterator を挿入
  iterator insert(int next_index, int now_index) {
    sz++;
    prev[now_index] = prev[next_index], next[now_index] = next_index;
    next[prev[next_index]] = now_index, prev[next_index] = now_index;
    return iterator(this, now_index);
  }
  // 添字 index の値を削除 → 次の要素の iterator を返す
  iterator erase(int index) {
    sz--;
    next[prev[index]] = next[index], prev[next[index]] = prev[index];
    return iterator(this, next[index]);
  }

public:
  friend ostream &operator<<(ostream &os, List &ls) {
    for (auto &val : ls) {
      os << val << ' ';
    }
    return os;
  }
  const T &operator[](size_t index) const { return container[index]; }
  T &operator[](size_t index) { return container[index]; }
  size_t size() { return sz; }
  bool empty() { return size() == 0; }
  T &front() { return container[next[N]]; }
  T &back() { return container[prev[N]]; }
  iterator begin() { return iterator(this, next[N]); }
  iterator end() { return iterator(this, N); }
  iterator insert(const iterator &itr, int index) {
    return insert(itr.index, index);
  }
  iterator erase(const iterator &itr) { return erase(itr.index); }
  iterator push_back() { return insert(N, prev[N] + 1); }
  void pop_back() { erase(prev[N]); }
  void clear() {
    N = sz = 0;
    prev = next = {0};
    container.clear();
  }

public:
  List() : N(0), sz(0), prev({0}), next({0}) {}
  List(int _N) : container(_N) { build(); }
  List(int _N, T val) : container(_N, val) { build(); }
  List(const List &ls)
      : N(ls.N), sz(ls.sz), prev(ls.prev), next(ls.next),
        container(ls.container) {}
  List(const vector<T> &vec) : container(vec) { build(); }
  List &operator=(const List &ls) {
    container = ls.container;
    build();
    return *this;
  }
  List &operator=(const vector<T> &vec) {
    container = vec;
    build();
    return *this;
  }
  List &operator=(const List &&ls) noexcept {
    container = ls.container;
    build();
    return *this;
  }
  List(initializer_list<T> vals) : container(vals.begin(), vals.end()) {
    build();
  }
  iterator push_back(T val) {
    N++, sz++;
    prev.push_back(N - 1), prev[0] = N;
    next.back() = N, next.push_back(0);
    container.push_back(val);
    return iterator(this, N - 1);
  }
  void build() {
    N = sz = (int)container.size();
    prev.resize(N + 1), next.resize(N + 1);
    iota(prev.begin(), prev.end(), -1), iota(next.begin(), next.end(), 1);
    prev[0] = N, next[N] = 0;
  }
};

template <typename T>
class ListIterator
    : public std::iterator<bidirectional_iterator_tag, T, ptrdiff_t, T *, T &> {
private:
  friend List<T>;
  List<T> *ls_ptr;
  int index;

private:
  ListIterator(List<T> *ls, int _index) : ls_ptr(ls), index(_index) {}

public:
  ListIterator() {}
  ListIterator(const ListIterator &itr) {
    ls_ptr = itr.ls_ptr, index = itr.index;
  }
  operator int() const noexcept { return index; }
  ListIterator &operator=(const ListIterator &itr) & {
    ls_ptr = itr.ls_ptr, index = itr.index;
    return *this;
  }
  ListIterator &operator=(ListIterator &&itr) &noexcept {
    ls_ptr = itr.ls_ptr, index = itr.index;
    return *this;
  }
  T &operator*() const { return ls_ptr->container[index]; }
  T *operator->() const { return &ls_ptr->container[index]; }
  ListIterator &operator++() {
    index = ls_ptr->next[index];
    return *this;
  }
  ListIterator operator++(int) {
    ListIterator res = *this;
    index = ls_ptr->next[index];
    return res;
  }
  ListIterator &operator--() {
    index = ls_ptr->prev[index];
    return *this;
  };
  ListIterator operator--(int) {
    ListIterator res = *this;
    index = ls_ptr->prev[index];
    return res;
  };
  bool operator==(const ListIterator &itr) const { return !(*this != itr); };
  bool operator!=(const ListIterator &itr) const {
    return this->ls_ptr != itr.ls_ptr || this->index != itr.index;
  }
  friend void swap(const ListIterator<T> &itr1, const ListIterator<T> &itr2) {
    ListIterator<T> tmp = itr1;
    itr1 = itr2, itr2 = itr1;
  };
};

// 多重辺はなし
class MVC {
private:
  struct edge {
    int to, rev;
  };
  struct info {
    // from から to 番目に出ている辺が(を) next の前から消えた(に入れる)
    int from, to, next;
    info(int ag1, int ag2, int ag3) : from(ag1), to(ag2), next(ag3) {}
  };
  int V, rem_edge_size, fp_size;
  vector<List<edge>> G;
  List<int> rem_ver;
  vector<int> cand, deg;
  vector<vector<info>> edge_info;
  set<int> small_deg_ver, use_ver;

  bool push_cand(int u, int add_size) {
    add_size++, cand.push_back(u);
    return (int)cand.size() < ans_size;
  }

  bool erase(int u, bool use, bool alr_use, int add_size,
             vector<pair<int, int>> &erase_ver) {
    if (use && !alr_use) {
      if (!push_cand(u, add_size))
        return false;
    }
    erase_ver.emplace_back(u, rem_ver.erase(u));
    for (auto &e : G[u]) {
      edge_info[u].emplace_back(e.to, e.rev, G[e.to].erase(e.rev));
      deg[e.to]--, rem_edge_size--;
      if (deg[e.to] == 0)
        erase_ver.emplace_back(e.to, rem_ver.erase(e.to));
      if (!use) {
        if (use_ver.count(e.to) == 1)
          continue;
        if (!push_cand(e.to, add_size))
          return false;
        if (deg[e.to] > 0)
          use_ver.insert(e.to);
      } else {
        if (deg[e.to] == 1 && use_ver.count(e.to) == 0)
          small_deg_ver.insert(e.to);
      }
    }
    return true;
  }
  bool erase_rec_set(set<int> &st, bool flag, int add_size,
                     vector<pair<int, int>> &erase_ver) {
    while (!st.empty()) {
      int v = *st.begin();
      st.erase(v);
      if (deg[v] == 0)
        continue;
      if (!erase(v, flag, flag, add_size, erase_ver))
        return false;
    }
    return true;
  }
  bool erase_rec(int u, bool use, int add_size,
                 vector<pair<int, int>> &erase_ver) {
    if (!erase(u, use, false, add_size, erase_ver))
      return false;
    while (!small_deg_ver.empty() || !use_ver.empty()) {
      if (!erase_rec_set(small_deg_ver, false, add_size, erase_ver))
        return false;
      if (!erase_rec_set(use_ver, true, add_size, erase_ver))
        return false;
    }
    return true;
  }
  bool preprocessing(int K, int add_size, vector<pair<int, int>> &erase_ver) {
    for (int u : rem_ver) {
      if (deg[u] > K) {
        if (!erase_rec(u, true, add_size, erase_ver))
          return false;
      }
    }
    return true;
  }
  void postprocessing(int K, int add_size, vector<pair<int, int>> &erase_ver) {
    // 最初の層で行われた前処理による変更は特に後処理する必要がない
    if (K == fp_size)
      return;
    for (int i = 0; i < add_size; i++) {
      cand.pop_back();
    }
    for (int i = (int)erase_ver.size() - 1; i >= 0; i--) {
      auto &p = erase_ver[i];
      while (!edge_info[p.first].empty()) {
        auto &dat = edge_info[p.first].back();
        G[dat.from].insert(dat.next, dat.to), deg[dat.from]++, rem_edge_size++;
      }
      rem_ver.insert(p.second, p.first);
    }
  }
  bool check() {
    if (rem_edge_size == 0) {
      if ((int)cand.size() < ans_size) {
        ans_size = (int)cand.size(), ans_set = cand;
      }
      return false;
    }
    return (int)rem_ver.size() > 0;
  }
  void transition(int K, int next_ver, bool use) {
    int pl_add_size = 0;
    vector<pair<int, int>> pl_erase_ver;
    if (!erase_rec(next_ver, use, pl_add_size, pl_erase_ver)) {
      return postprocessing(K - 1, pl_add_size, pl_erase_ver);
    }
    if (check())
      judge(K - 1);
    return postprocessing(K - 1, pl_add_size, pl_erase_ver);
  }
  int find_max_degree_ver() {
    // 次数の高い頂点から探索する
    int max_deg = -1, next_ver = -1;
    for (int v : rem_ver) {
      if (deg[v] > max_deg)
        max_deg = deg[v], next_ver = v;
    }
    if (2 * rem_edge_size > (long long)max_deg * (int)rem_ver.size())
      return -1;
    return next_ver;
  }
  void judge(int K) {
    int add_size = 0;
    vector<pair<int, int>> erase_ver;
    if (!preprocessing(K, add_size, erase_ver))
      return postprocessing(K, add_size, erase_ver);
    if (!check())
      return postprocessing(K, add_size, erase_ver);
    int next_ver = find_max_degree_ver();
    if (next_ver < 0)
      return postprocessing(K, add_size, erase_ver);
    // 使う場合
    transition(K, next_ver, true);
    // 使わない場合
    if ((int)cand.size() + (int)G[next_ver].size() >= ans_size) {
      transition(K, next_ver, false);
    }
    return postprocessing(K, add_size, erase_ver);
  }

public:
  vector<int> ans_set;
  int ans_size;

  MVC(int node_size)
      : V(node_size), rem_edge_size(0), G(V), rem_ver(V), deg(V, 0),
        edge_info(V) {
    for (int i = 0; i < V; i++)
      rem_ver[i] = i;
  }
  void add_edge(int u, int v) {
    G[u].push_back((edge){v, (int)G[v].size()});
    G[v].push_back((edge){u, (int)G[u].size() - 1});
    deg[u]++, deg[v]++, rem_edge_size++;
  }
  bool solve(int K) {
    fp_size = K, ans_size = fp_size + 1;
    judge(fp_size);
    return ans_size <= fp_size;
  }
};

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n, m, K;
  cin >> n >> m >> K;
  MVC mvc(n);
  rep(i, m) {
    int a, b;
    cin >> a >> b;
    mvc.add_edge(a - 1, b - 1);
  }
  if (mvc.solve(K)) {
    cout << mvc.ans_size << "\\n";
  } else {
    cout << "Impossible\\n";
  }
  return 0;
}