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QOJ

IDSubmission IDProblemHackerOwnerResultSubmit timeJudge time
#758#114688#6508. This is not an Abnormal Team!edxmaspyFailed.2024-07-30 12:02:392024-07-30 12:02:39

Details

Extra Test:

Invalid Input

input:

6 4 7
3 1
3 2
2 2
4 1
4 1
5 2
1 4

output:


result:

FAIL duplicated edges (4, 1)

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#114688#6508. This is not an Abnormal Team!maspyAC ✓495ms79676kbC++2318.8kb2023-06-22 22:30:242023-06-22 22:30:27

answer

#line 1 "library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T, typename U>
T ceil(T x, U y) {
  return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
  return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sum = 0;
  for (auto &&a: A) sum += a;
  return sum;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  assert(!que.empty());
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  assert(!que.empty());
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}
#endif
#line 1 "library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>

namespace fastio {
#define FASTIO
// クラスが read(), print() を持っているかを判定するメタ関数
struct has_write_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.write(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_write : public decltype(has_write_impl::check<T>(std::declval<T>())) {
};

struct has_read_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.read(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_read : public decltype(has_read_impl::check<T>(std::declval<T>())) {};

struct Scanner {
  FILE *fp;
  char line[(1 << 15) + 1];
  size_t st = 0, ed = 0;
  void reread() {
    memmove(line, line + st, ed - st);
    ed -= st;
    st = 0;
    ed += fread(line + ed, 1, (1 << 15) - ed, fp);
    line[ed] = '\0';
  }
  bool succ() {
    while (true) {
      if (st == ed) {
        reread();
        if (st == ed) return false;
      }
      while (st != ed && isspace(line[st])) st++;
      if (st != ed) break;
    }
    if (ed - st <= 50) {
      bool sep = false;
      for (size_t i = st; i < ed; i++) {
        if (isspace(line[i])) {
          sep = true;
          break;
        }
      }
      if (!sep) reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    while (true) {
      size_t sz = 0;
      while (st + sz < ed && !isspace(line[st + sz])) sz++;
      ref.append(line + st, sz);
      st += sz;
      if (!sz || st != ed) break;
      reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    bool neg = false;
    if (line[st] == '-') {
      neg = true;
      st++;
    }
    ref = T(0);
    while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
    if (neg) ref = -ref;
    return true;
  }
  template <typename T,
            typename enable_if<has_read<T>::value>::type * = nullptr>
  inline bool read_single(T &x) {
    x.read();
    return true;
  }
  bool read_single(double &ref) {
    string s;
    if (!read_single(s)) return false;
    ref = std::stod(s);
    return true;
  }
  bool read_single(char &ref) {
    string s;
    if (!read_single(s) || s.size() != 1) return false;
    ref = s[0];
    return true;
  }
  template <class T>
  bool read_single(vector<T> &ref) {
    for (auto &d: ref) {
      if (!read_single(d)) return false;
    }
    return true;
  }
  template <class T, class U>
  bool read_single(pair<T, U> &p) {
    return (read_single(p.first) && read_single(p.second));
  }
  template <size_t N = 0, typename T>
  void read_single_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
      auto &x = std::get<N>(t);
      read_single(x);
      read_single_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool read_single(tuple<T...> &tpl) {
    read_single_tuple(tpl);
    return true;
  }
  void read() {}
  template <class H, class... T>
  void read(H &h, T &... t) {
    bool f = read_single(h);
    assert(f);
    read(t...);
  }
  Scanner(FILE *fp) : fp(fp) {}
};

struct Printer {
  Printer(FILE *_fp) : fp(_fp) {}
  ~Printer() { flush(); }

  static constexpr size_t SIZE = 1 << 15;
  FILE *fp;
  char line[SIZE], small[50];
  size_t pos = 0;
  void flush() {
    fwrite(line, 1, pos, fp);
    pos = 0;
  }
  void write(const char val) {
    if (pos == SIZE) flush();
    line[pos++] = val;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  void write(T val) {
    if (pos > (1 << 15) - 50) flush();
    if (val == 0) {
      write('0');
      return;
    }
    if (val < 0) {
      write('-');
      val = -val; // todo min
    }
    size_t len = 0;
    while (val) {
      small[len++] = char(0x30 | (val % 10));
      val /= 10;
    }
    for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
    pos += len;
  }
  void write(const string s) {
    for (char c: s) write(c);
  }
  void write(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++) write(s[i]);
  }
  void write(const double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  template <typename T,
            typename enable_if<has_write<T>::value>::type * = nullptr>
  inline void write(T x) {
    x.write();
  }
  template <class T>
  void write(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  template <class T, class U>
  void write(const pair<T, U> val) {
    write(val.first);
    write(' ');
    write(val.second);
  }
  template <size_t N = 0, typename T>
  void write_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
      if constexpr (N > 0) { write(' '); }
      const auto x = std::get<N>(t);
      write(x);
      write_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool write(tuple<T...> tpl) {
    write_tuple(tpl);
    return true;
  }
  template <class T, size_t S>
  void write(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  void write(i128 val) {
    string s;
    bool negative = 0;
    if (val < 0) {
      negative = 1;
      val = -val;
    }
    while (val) {
      s += '0' + int(val % 10);
      val /= 10;
    }
    if (negative) s += "-";
    reverse(all(s));
    if (len(s) == 0) s = "0";
    write(s);
  }
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  printer.write(head);
  if (sizeof...(Tail)) printer.write(' ');
  print(forward<Tail>(tail)...);
}

void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
  scanner.read(head);
  read(tail...);
}
} // namespace fastio
using fastio::print;
using fastio::flush;
using fastio::read;

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 3 "main.cpp"

#line 1 "library/flow/maxflow.hpp"
template <typename Cap>
struct MaxFlowGraph {
  struct Edge {
    int to, rev;
    Cap cap;
    Cap flow = 0;
  };

  int N;
  vc<tuple<int, int, Cap, Cap>> dat;
  vc<int> prog, level;
  vc<int> que;
  vc<Edge> edges;
  vc<int> indptr;
  Cap flow_ans;
  bool calculated;
  bool is_prepared;

  MaxFlowGraph(int N) : N(N), calculated(0), is_prepared(0) {}

  void add(int frm, int to, Cap cap, Cap rev_cap = 0) {
    assert(0 <= frm && frm < N);
    assert(0 <= to && to < N);
    assert(Cap(0) <= cap);
    if (frm == to) return;
    dat.eb(frm, to, cap, rev_cap);
  }

  void build() {
    assert(!is_prepared);
    int M = len(dat);
    is_prepared = 1;
    indptr.assign(N, 0);
    for (auto&& [a, b, c, d]: dat) indptr[a]++, indptr[b]++;
    indptr = cumsum<int>(indptr);
    vc<int> nxt_idx = indptr;
    edges.resize(2 * M);
    for (auto&& [a, b, c, d]: dat) {
      int p = nxt_idx[a]++;
      int q = nxt_idx[b]++;
      edges[p] = Edge{b, q, c};
      edges[q] = Edge{a, p, d};
    }
  }

  vc<tuple<int, int, Cap>> get_flow_edges() {
    vc<tuple<int, int, Cap>> res;
    FOR(frm, N) {
      FOR(k, indptr[frm], indptr[frm + 1]) {
        auto& e = edges[k];
        if (e.flow <= 0) continue;
        res.eb(frm, e.to, e.flow);
      }
    }
    return res;
  }

  Cap flow(int source, int sink) {
    assert(is_prepared);
    if (calculated) return flow_ans;
    calculated = true;
    flow_ans = 0;
    while (set_level(source, sink)) {
      prog = indptr;
      while (1) {
        Cap x = flow_dfs(source, sink, infty<Cap>);
        if (x == 0) break;
        flow_ans += x;
        chmin(flow_ans, infty<Cap>);
        if (flow_ans == infty<Cap>) return flow_ans;
      }
    }
    return flow_ans;
  }

  // 最小カットの値および、カットを表す 01 列を返す
  pair<Cap, vc<int>> cut(int source, int sink) {
    Cap f = flow(source, sink);
    vc<int> res(N);
    FOR(v, N) res[v] = (level[v] >= 0 ? 0 : 1);
    return {f, res};
  }

private:
  bool set_level(int source, int sink) {
    que.resize(N);
    level.assign(N, -1);
    level[source] = 0;
    int l = 0, r = 0;
    que[r++] = source;
    while (l < r) {
      int v = que[l++];
      FOR(k, indptr[v], indptr[v + 1]) {
        auto& e = edges[k];
        if (e.cap > 0 && level[e.to] == -1) {
          level[e.to] = level[v] + 1;
          if (e.to == sink) return true;
          que[r++] = e.to;
        }
      }
    }
    return false;
  }

  Cap flow_dfs(int v, int sink, Cap lim) {
    if (v == sink) return lim;
    Cap res = 0;
    for (int& i = prog[v]; i < indptr[v + 1]; ++i) {
      auto& e = edges[i];
      if (e.cap > 0 && level[e.to] == level[v] + 1) {
        Cap a = flow_dfs(e.to, sink, min(lim, e.cap));
        if (a > 0) {
          e.cap -= a, e.flow += a;
          edges[e.rev].cap += a, edges[e.rev].flow -= a;
          res += a;
          lim -= a;
          if (lim == 0) break;
        }
      }
    }
    return res;
  }
};
#line 5 "main.cpp"

void solve() {
  INT(N1, N2, M);
  int source = 0;
  auto left = [&](int i) -> int { return 1 + i; };
  auto right = [&](int i) -> int { return 1 + N1 + i; };
  int sink = 1 + N1 + N2;

  map<pi, int> MP;

  MaxFlowGraph<int> G(sink + 1);
  FOR(v, N1) G.add(source, left(v), 1);
  FOR(v, N2) G.add(right(v), sink, 1);
  FOR(M) {
    LL(a, b);
    --a, --b;
    MP[pi{a, b}]++;
    G.add(left(a), right(b), 1);
  }
  G.build();
  int F0 = G.flow(source, sink);

  vc<int> deg1(N1), deg2(N2);

  for (auto [a, b, c]: G.get_flow_edges()) {
    if (a == source) deg1[b - 1] += c;
    elif (b == sink) deg2[a - 1 - N1] += c;
    else {
      a -= 1, b -= 1 + N1;
      MP[pi{a, b}] -= c;
    }
  }

  MaxFlowGraph<int> G1(sink + 1);
  FOR(i, N1) if (deg1[i] == 0) { G1.add(source, left(i), 1); }
  FOR(i, N2) if (deg2[i] == 1) { G1.add(right(i), sink, 1); }
  for (auto&& [p, x]: MP) {
    auto [a, b] = p;
    if (x == 0) { G1.add(right(b), left(a), 1); }
    if (x == 1) { G1.add(left(a), right(b), 1); }
  }
  G1.build();
  int F1 = G1.flow(source, sink);
  for (auto [a, b, c]: G1.get_flow_edges()) {
    if (a == source) deg1[b - 1] += c;
    elif (b == sink) deg2[a - 1 - N1] += c;
    else {
      if (a < b) {
        a -= 1, b -= 1 + N1;
        MP[pi{a, b}] -= c;
      } else {
        a -= 1 + N1, b -= 1;
        MP[pi{b, a}] += c;
      }
    }
  }

  MaxFlowGraph<int> G2(sink + 1);
  FOR(i, N1) if (deg1[i] == 1) { G2.add(source, left(i), 1); }
  FOR(i, N2) if (deg2[i] == 0) { G2.add(right(i), sink, 1); }
  for (auto&& [p, x]: MP) {
    auto [a, b] = p;
    if (x == 0) { G2.add(right(b), left(a), 1); }
    if (x == 1) { G2.add(left(a), right(b), 1); }
  }
  G2.build();
  int F2 = G2.flow(source, sink);
  for (auto [a, b, c]: G2.get_flow_edges()) {
    if (a == source) deg1[b - 1] += c;
    elif (b == sink) deg2[a - 1 - N1] += c;
    else {
      if (a < b) {
        a -= 1, b -= 1 + N1;
        MP[pi{a, b}] -= c;
      } else {
        a -= 1 + N1, b -= 1;
        MP[pi{b, a}] += c;
      }
    }
  }

  pi ANS = {0, 0};
  FOR(i, N1) if (deg1[i] == 0)++ ANS.fi;
  FOR(i, N2) if (deg2[i] == 0)++ ANS.fi;
  FOR(i, N1) if (deg1[i] == 2)++ ANS.se;
  FOR(i, N2) if (deg2[i] == 2)++ ANS.se;
  print(ANS);
}

signed main() {
  solve();
  return 0;
}