test/verify/yosupo-assignment.test.cpp

• View this file on GitHub
• Last update: 2022-09-11 00:53:50+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

#define 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"
#define PROBLEM "https://judge.yosupo.jp/problem/assignment"

#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/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)
 * @docs docs/hungarian.md
 */
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";
}

Back to top page