test/assignment.test.cpp

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Last update: 2024-09-15 11:33:45+08:00
Problem: https://judge.yosupo.jp/problem/assignment

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Code

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

#include "../default/t.cpp"
#include "../graph/MCMF.cpp"

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  int n; cin >> n;
  vector a(n, vector<int>(n));
  for(auto &v : a)
    for(int &x : v)
      cin >> x;

  const int s = 2 * n, t = 2 * n + 1;
  MCMF<int, ll> mcmf(2 * n + 2);
  for(int v = 0; v < n; v++) {
    mcmf.addEdge(s, v, 1, 0);
    mcmf.addEdge(v + n, t, 1, 0);
  }
  for(int u = 0; u < n; u++)
    for(int v = 0; v < n; v++)
      mcmf.addEdge(u, v + n, 1, a[u][v]);

  mcmf.initPotential(s);
  cout << mcmf.runFlow(s, t, true).second << '\n';
  for(int v = 0; v < n; v++)
    for(auto e : mcmf.g[v])
      if (e.cap == 0 and e.to != s)
        cout << e.to - n << " \n"[v + 1 == n];

  return 0;
}

#line 1 "test/assignment.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/assignment"

#line 1 "default/t.cpp"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <variant>
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>

#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)

#define clock chrono::steady_clock::now().time_since_epoch().count()

using namespace std;

template<class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2> pr) {
  return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
  for(size_t i = 0; T x : arr) {
    os << x;
    if (++i != N) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
  for(size_t i = 0; T x : vec) {
    os << x;
    if (++i != size(vec)) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const set<T> &s) {
  for(size_t i = 0; T x : s) {
    os << x;
    if (++i != size(s)) os << ' ';
  }
  return os;
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2> &m) {
  for(size_t i = 0; pair<T1, T2> x : m) {
    os << x;
    if (++i != size(m)) os << ' ';
  }
  return os;
}

#ifdef DEBUG
#define dbg(...) cerr << '(', _do(#__VA_ARGS__), cerr << ") = ", _do2(__VA_ARGS__)
template<typename T> void _do(T &&x) { cerr << x; }
template<typename T, typename ...S> void _do(T &&x, S&&...y) { cerr << x << ", "; _do(y...); }
template<typename T> void _do2(T &&x) { cerr << x << endl; }
template<typename T, typename ...S> void _do2(T &&x, S&&...y) { cerr << x << ", "; _do2(y...); }
#else
#define dbg(...)
#endif

using ll = long long;
using ull = unsigned long long;
using ldb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

template<typename T> using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T> using max_heap = priority_queue<T>;

template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP = plus<T>>
void pSum(rng &v) {
  if (!v.empty())
    for(T p = v[0]; T &x : v | views::drop(1))
      x = p = OP()(p, x);
}
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP>
void pSum(rng &v, OP op) {
  if (!v.empty())
    for(T p = v[0]; T &x : v | views::drop(1))
      x = p = op(p, x);
}

template<ranges::forward_range rng>
void Unique(rng &v) {
  ranges::sort(v);
  v.resize(unique(v.begin(), v.end()) - v.begin());
}

template<ranges::random_access_range rng>
rng invPerm(rng p) {
  rng ret = p;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = i;
  return ret;
}

template<ranges::random_access_range rng, ranges::random_access_range rng2>
rng Permute(rng v, rng2 p) {
  rng ret = v;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = v[i];
  return ret;
}

template<bool directed>
vector<vector<int>> readGraph(int n, int m, int base) {
  vector<vector<int>> g(n);
  for(int i = 0; i < m; i++) {
    int u, v; cin >> u >> v;
    u -= base, v -= base;
    g[u].emplace_back(v);
    if constexpr (!directed)
      g[v].emplace_back(u);
  }
  return g;
}

template<class T>
void setBit(T &msk, int bit, bool x) {
  msk = (msk & ~(T(1) << bit)) | (T(x) << bit);
}
template<class T> void flipBit(T &msk, int bit) { msk ^= T(1) << bit; }
template<class T> bool getBit(T msk, int bit) { return msk >> bit & T(1); }

template<class T>
T floorDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? a / b : (a - b + 1) / b;
}
template<class T>
T ceilDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? (a + b - 1) / b : a / b;
}

template<class T> bool chmin(T &a, T b) { return a > b ? a = b, 1 : 0; }
template<class T> bool chmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
#line 1 "graph/MCMF.cpp"
template<class capT, class cosT>
struct MCMF {
  struct edge {
    int to, rev;
    capT cap;
    cosT cos;
    edge(int _to, capT _cap, cosT _cos, int _rev) :
        to(_to), rev(_rev), cap(_cap), cos(_cos) {}
  };

  int n;
  const capT CAP_MAX = numeric_limits<capT>::max();
  const cosT COS_MAX = numeric_limits<cosT>::max();
  vector<vector<edge>> g;
  vector<int> par, idx;
  vector<capT> f;
  vector<cosT> pot, dis;

  MCMF(int _n) : n(_n), g(n), par(n),
    idx(n), f(n), pot(n), dis(n) {}

  void addEdge(int from, int to, capT cap, cosT cos) {
    g[from].emplace_back(to, cap, cos, ssize(g[to]));
    g[to].emplace_back(from, 0, -cos, ssize(g[from]) - 1);
  }

  void initPotential(int s) {
    fill(dis.begin(), dis.end(), COS_MAX);
    dis[s] = 0;
    for(int i = 1; i < n; i++) {
      for(int v = 0; v < n; v++) {
        if (dis[v] == COS_MAX) continue;
        for(edge e : g[v])
          if (e.cap != 0 and dis[v] + e.cos < dis[e.to])
            dis[e.to] = dis[v] + e.cos;
      }
    }
    pot.swap(dis);
  }

  void initPotentialDAG(int s) {
    fill(dis.begin(), dis.end(), COS_MAX);
    dis[s] = 0;
    vector<int> topo = [&]() {
      vector<int> topo;
      vector<bool> vis(n, false);
      auto dfs = [&](int v, auto &&self) -> void {
        vis[v] = true;
        for(edge e : g[v])
          if (e.cap != 0 and !vis[e.to])
            self(e.to, self);
        topo.emplace_back(v);
      };
      for(int v = 0; v < n; v++)
        if (!vis[v])
          dfs(v, dfs);
      return topo;
    }();
    for(int v : topo | views::reverse)
      if (dis[v] != COS_MAX)
        for(edge e : g[v])
          if (e.cap != 0)
            chmin(dis[e.to], dis[v] + e.cos);
    pot.swap(dis);
  }

  pair<capT, cosT> runFlow(int s, int t, bool dense = false) {
    cosT cost = 0;
    capT flow = 0;
    while(true) {
      fill(dis.begin(), dis.end(), COS_MAX);
      dis[s] = 0, f[s] = CAP_MAX;
      if (dense) {
        vector<bool> vis(n, false);
        for(int i = 0; i < n; i++) {
          int v = -1;
          for(int j = 0; j < n; j++)
            if (!vis[j] and (v == -1 or dis[j] < dis[v]))
              v = j;
          if (v == -1 or dis[v] == COS_MAX) break;
          vis[v] = true;
          for(edge e : g[v]) {
            if (e.cap == 0) continue;
            if (cosT x = dis[v] + e.cos + pot[v] - pot[e.to]; x < dis[e.to]) {
              dis[e.to] = x, f[e.to] = min(f[v], e.cap);
              par[e.to] = v, idx[e.to] = g[e.to][e.rev].rev;
            }
          }
        }
      } else {
        using T = pair<cosT, int>;
        priority_queue<T, vector<T>, greater<T>> pq;
        pq.push(make_pair(dis[s], s));
        while(!pq.empty()) {
          auto [d, v] = pq.top(); pq.pop();
          if (dis[v] != d) continue;
          for(edge e : g[v]) {
            if (e.cap == 0) continue;
            if (cosT x = dis[v] + e.cos + pot[v] - pot[e.to]; x < dis[e.to]) {
              dis[e.to] = x, f[e.to] = min(f[v], e.cap);
              par[e.to] = v, idx[e.to] = g[e.to][e.rev].rev;
              pq.push(make_pair(dis[e.to], e.to));
            }
          }
        }
      }

      if (dis[t] == COS_MAX) break;

      int v = t;
      while(v != s) {
        edge &e = g[par[v]][idx[v]];
        e.cap -= f[t], g[v][e.rev].cap += f[t];
        v = par[v];
      }
      flow += f[t], cost += f[t] * (dis[t] - pot[s] + pot[t]);
      for(int i = 0; i < n; i++)
        if (dis[i] != COS_MAX)
          dis[i] += pot[i] - pot[s];
      pot.swap(dis);
    }

    return {flow, cost};
  }
};
#line 5 "test/assignment.test.cpp"

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  int n; cin >> n;
  vector a(n, vector<int>(n));
  for(auto &v : a)
    for(int &x : v)
      cin >> x;

  const int s = 2 * n, t = 2 * n + 1;
  MCMF<int, ll> mcmf(2 * n + 2);
  for(int v = 0; v < n; v++) {
    mcmf.addEdge(s, v, 1, 0);
    mcmf.addEdge(v + n, t, 1, 0);
  }
  for(int u = 0; u < n; u++)
    for(int v = 0; v < n; v++)
      mcmf.addEdge(u, v + n, 1, a[u][v]);

  mcmf.initPotential(s);
  cout << mcmf.runFlow(s, t, true).second << '\n';
  for(int v = 0; v < n; v++)
    for(auto e : mcmf.g[v])
      if (e.cap == 0 and e.to != s)
        cout << e.to - n << " \n"[v + 1 == n];

  return 0;
}