test/verify/yosupo-assignment.test.cpp

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• Last update: 2024-07-28 19:56:12+09:00
• Problem: https://judge.yosupo.jp/problem/assignment

Depends on

• Hungarian(二部グラフの最小重み最大マッチング) (graph/flow/hungarian.hpp)
• math/matrix/matrix.hpp
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/assignment

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

#include "../../graph/flow/hungarian.hpp"

int main() {
  int N;
  cin >> N;
  Matrix< int64_t > X(N + 1, N + 1);
  for(int i = 1; i <= N; i++) {
    for(int j = 1; j <= N; j++) {
      cin >> X[j][i];
    }
  }
  auto ret = hungarian(X);
  cout << ret.first << "\n";
  ret.second.erase(begin(ret.second));
  for(auto& p : ret.second) --p;
  cout << ret.second << "\n";
}

#line 1 "test/verify/yosupo-assignment.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/assignment

#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif

using namespace std;

using int64 = long long;

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(std::forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{std::forward<F>(f)};
}
#line 4 "test/verify/yosupo-assignment.test.cpp"

#line 1 "math/matrix/matrix.hpp"
template <class T>
struct Matrix {
  vector<vector<T> > A;

  Matrix() {}

  Matrix(size_t n, size_t m) : A(n, vector<T>(m, 0)) {}

  Matrix(size_t n) : A(n, vector<T>(n, 0)) {};

  size_t size() const {
    if (A.empty()) return 0;
    assert(A.size() == A[0].size());
    return A.size();
  }

  size_t height() const { return (A.size()); }

  size_t width() const { return (A[0].size()); }

  inline const vector<T> &operator[](int k) const { return (A.at(k)); }

  inline vector<T> &operator[](int k) { return (A.at(k)); }

  static Matrix I(size_t n) {
    Matrix mat(n);
    for (int i = 0; i < n; i++) mat[i][i] = 1;
    return (mat);
  }

  Matrix &operator+=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j];
    return (*this);
  }

  Matrix &operator-=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j];
    return (*this);
  }

  Matrix &operator*=(const Matrix &B) {
    size_t n = height(), m = B.width(), p = width();
    assert(p == B.height());
    vector<vector<T> > C(n, vector<T>(m, 0));
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++)
        for (int k = 0; k < p; k++)
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
    A.swap(C);
    return (*this);
  }

  Matrix &operator^=(long long k) {
    Matrix B = Matrix::I(height());
    while (k > 0) {
      if (k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return (*this);
  }

  Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }

  Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }

  Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }

  Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }

  friend ostream &operator<<(ostream &os, Matrix &p) {
    size_t n = p.height(), m = p.width();
    for (int i = 0; i < n; i++) {
      os << "[";
      for (int j = 0; j < m; j++) {
        os << p[i][j] << (j + 1 == m ? "]\n" : ",");
      }
    }
    return (os);
  }

  T determinant() {
    Matrix B(*this);
    assert(width() == height());
    T ret = 1;
    for (int i = 0; i < width(); i++) {
      int idx = -1;
      for (int j = i; j < width(); j++) {
        if (B[j][i] != 0) idx = j;
      }
      if (idx == -1) return (0);
      if (i != idx) {
        ret *= -1;
        swap(B[i], B[idx]);
      }
      ret *= B[i][i];
      T vv = B[i][i];
      for (int j = 0; j < width(); j++) {
        B[i][j] /= vv;
      }
      for (int j = i + 1; j < width(); j++) {
        T a = B[j][i];
        for (int k = 0; k < width(); k++) {
          B[j][k] -= B[i][k] * a;
        }
      }
    }
    return (ret);
  }
};
#line 2 "graph/flow/hungarian.hpp"

/**
 * @brief Hungarian(二部グラフの最小重み最大マッチング)
 *
 */
template <typename T>
pair<T, vector<int> > hungarian(Matrix<T> &A) {
  const T infty = numeric_limits<T>::max();
  const int N = (int)A.height();
  const int M = (int)A.width();
  vector<int> P(M), way(M);
  vector<T> U(N, 0), V(M, 0), minV;
  vector<bool> used;

  for (int i = 1; i < N; i++) {
    P[0] = i;
    minV.assign(M, infty);
    used.assign(M, false);
    int j0 = 0;
    while (P[j0] != 0) {
      int i0 = P[j0], j1 = 0;
      used[j0] = true;
      T delta = infty;
      for (int j = 1; j < M; j++) {
        if (used[j]) continue;
        T curr = A[i0][j] - U[i0] - V[j];
        if (curr < minV[j]) minV[j] = curr, way[j] = j0;
        if (minV[j] < delta) delta = minV[j], j1 = j;
      }
      for (int j = 0; j < M; j++) {
        if (used[j])
          U[P[j]] += delta, V[j] -= delta;
        else
          minV[j] -= delta;
      }
      j0 = j1;
    }
    do {
      P[j0] = P[way[j0]];
      j0 = way[j0];
    } while (j0 != 0);
  }
  return {-V[0], P};
}
#line 6 "test/verify/yosupo-assignment.test.cpp"

int main() {
  int N;
  cin >> N;
  Matrix< int64_t > X(N + 1, N + 1);
  for(int i = 1; i <= N; i++) {
    for(int j = 1; j <= N; j++) {
      cin >> X[j][i];
    }
  }
  auto ret = hungarian(X);
  cout << ret.first << "\n";
  ret.second.erase(begin(ret.second));
  for(auto& p : ret.second) --p;
  cout << ret.second << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	6 ms	3 MB
g++	hand_minus_00	AC	151 ms	5 MB
g++	hand_plus_00	AC	149 ms	5 MB
g++	max_random_00	AC	36 ms	5 MB
g++	max_random_01	AC	37 ms	5 MB
g++	max_random_02	AC	35 ms	5 MB
g++	max_random_03	AC	36 ms	5 MB
g++	max_random_04	AC	37 ms	5 MB
g++	multiplication_table_00	AC	167 ms	5 MB
g++	random_00	AC	9 ms	4 MB
g++	random_01	AC	9 ms	4 MB
g++	random_02	AC	6 ms	4 MB
g++	random_03	AC	9 ms	4 MB
g++	random_04	AC	5 ms	3 MB
clang++	example_00	AC	6 ms	3 MB
clang++	hand_minus_00	AC	137 ms	5 MB
clang++	hand_plus_00	AC	136 ms	5 MB
clang++	max_random_00	AC	34 ms	5 MB
clang++	max_random_01	AC	35 ms	5 MB
clang++	max_random_02	AC	33 ms	5 MB
clang++	max_random_03	AC	35 ms	5 MB
clang++	max_random_04	AC	36 ms	5 MB
clang++	multiplication_table_00	AC	147 ms	5 MB
clang++	random_00	AC	9 ms	4 MB
clang++	random_01	AC	9 ms	4 MB
clang++	random_02	AC	6 ms	4 MB
clang++	random_03	AC	9 ms	4 MB
clang++	random_04	AC	5 ms	3 MB

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