Submission #1165762

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Source Code Expand

#include <iostream>
#include <algorithm>
#include <tuple>
#include <array>
#include <queue>
using namespace std;
using Weight = int;
using Flow = int;
 
constexpr Flow inf = 1234;
 
                            // N  E  S  W
constexpr array<int, 4> dr = {-1, 0, 1, 0},
                        dc = { 0, 1, 0,-1};
constexpr int dr_size = dr.size();
 
struct Edge {
  int dst, rev;
  Flow capa;
  Weight cost;
};
 
struct Graph {
  int size;
  vector<vector<Edge>> g;
  Graph(int size) : size(size) { g.resize(size); }
  void add_edge(int src, int dst, Flow capa);
  void add_edge(int src, int dst, Flow capa, Weight cost);
  Flow max_flow(int s, int t) { throw; }
  Flow min_cost_flow_ford(int s, int t, Flow f); // ベルマンフォード
  Flow min_cost_flow_dijk(int s, int t, Flow f); // ダイクストラ
};
 
struct FordFulkerson : Graph {
  vector<bool> used;
  FordFulkerson(int size) : Graph(size) {}
  Flow max_flow(int s, int t);
private:
  Flow dfs(int v, int t, Flow flow);
};
 
struct Dinic : Graph {
  vector<int> level, iter;
  Dinic(int size) : Graph(size) {}
  Flow max_flow(int s, int t);
private:
  void bfs(int s);
  Flow dfs(int v, int t, Flow flow);
};
 
void Graph::add_edge(int src, int dst, Flow capa) {
  add_edge(src, dst, capa, 0);
}
 
void Graph::add_edge(int src, int dst, Flow capa, Weight cost) {
  g[src].push_back(Edge({dst, int(g[dst].size()),   capa, cost}));
  g[dst].push_back(Edge({src, int(g[src].size())-1, 0,        -cost}));
}
 
Flow Graph::min_cost_flow_ford(int s, int t, Flow f) {
  Flow res = 0;
  vector<int> prev_v(size), prev_e(size);
  vector<Flow> dist;
  while(f > 0) {
    dist.assign(size, inf);
    dist[s] = 0;
    bool update = true;
    while(update) {
      update = false;
      for(int v=0; v<size; ++v) {
        if(dist[v] == inf) { continue; }
        for(int i=0; i<g[v].size(); ++i) {
          Edge& e = g[v][i];
          if(e.capa > 0 && dist[e.dst] > dist[v] + e.cost) {
            dist[e.dst] = dist[v] + e.cost;
            prev_v[e.dst] = v;
            prev_e[e.dst] = i;
            update = true;
          }
        }
      }
    }
    if(dist[t] == inf) { return inf; }
    Flow d = f;
    for(int v=t; v!=s; v=prev_v[v]) {
      d = min(d, g[prev_v[v]][prev_e[v]].capa);
    }
    f -= d;
    res += d * dist[t];
    for(int v=t; v!=s; v=prev_v[v]) {
      Edge& e = g[prev_v[v]][prev_e[v]];
      e.capa -= d;
      g[v][e.rev].capa += d;
    }
  }
  return res;
}
 
Flow Graph::min_cost_flow_dijk(int s, int t, Flow f) {
  Flow res = 0;
  vector<int> prev_v(size), prev_e(size);
  vector<int> h(size);
  while(f > 0) {
    vector<int> dist(size, inf);
    dist[s] = 0;
    queue<pair<int, int>> que;
    // 最短距離、番号
    que.emplace(0, s);
    while(!que.empty()) {
      int c, v; tie(c, v) = que.front(); que.pop();
      if(dist[v] < c) { continue; }
      for(int i=0; i<g[v].size(); ++i) {
        Edge& e = g[v][i];
        if(e.capa > 0 && dist[e.dst] > dist[v] + e.cost + h[v] - h[e.dst]) {
          dist[e.dst] = dist[v] + e.cost + h[v] - h[e.dst];
          prev_v[e.dst] = v;
          prev_e[e.dst] = i;
          que.emplace(dist[e.dst], e.dst);
        }
      }
    }
    if(dist[t] == inf) { return inf; }
    for(int v=0; v<size; ++v) { h[v] += dist[v]; }
    Flow d = f;
    for(int v=t; v!=s; v=prev_v[v]) {
      d = min(d, g[prev_v[v]][prev_e[v]].capa);
    }
    f -= d;
    res += d * h[t];
    for(int v=t; v!=s; v=prev_v[v]) {
      Edge& e = g[prev_v[v]][prev_e[v]];
      e.capa -= d;
      g[v][e.rev].capa += d;
    }
  }
  return res;
}
 
Flow FordFulkerson::max_flow(int s, int t) {
  Flow res = 0;
  while(true) {
    used.assign(size, false);
    Flow flow = dfs(s, t, inf);
    if(flow == 0) { return res; }
    res += flow;
    if(res >= inf) { return inf; }
  }
}
 
Flow FordFulkerson::dfs(int v, int t, Flow flow) {
  if(v == t) { return flow; }
  used[v] = true;
  for(Edge& e : g[v]) {
    if(used[e.dst] || e.capa <= 0) { continue; }
    int d = dfs(e.dst, t, min(flow, e.capa));
    if(d > 0) {
      e.capa -= d;
      g[e.dst][e.rev].capa += d;
      return d;
    }
  }
  return 0;
}
 
void Dinic::bfs(int s) {
  level.assign(size, -1);
  queue<int> que;
  level[s] = 0;
  que.push(s);
  while(!que.empty()) {
    int v = que.front(); que.pop();
    for(Edge& e : g[v]) {
      if(e.capa > 0 && level[e.dst] < 0) {
        level[e.dst] = level[v] + 1;
        que.push(e.dst);
      }
    }
  }
}
 
Flow Dinic::dfs(int v, int t, Flow flow) {
  if(v == t) { return flow; }
  for(int& i=iter[v]; i<g[v].size(); ++i) {
    Edge& e = g[v][i];
    if(e.capa <= 0 || level[v] >= level[e.dst]) { continue; }
    Flow d = dfs(e.dst, t, min(flow, e.capa));
    if(d > 0) {
      e.capa -= d;
      g[e.dst][e.rev].capa += d;
      return d;
    }
  }
  return 0;
}
 
Flow Dinic::max_flow(int s, int t) {
  Flow res = 0;
  while(true) {
    bfs(s);
    if(level[t] < 0) { return res; }
    iter.assign(size, 0);
    Flow flow;
    while((flow = dfs(s, t, inf)) > 0) {
      res += flow;
      if(res >= inf) { return inf; }
    }
  }
}
 
int main(void) {
  int R, C; cin >> R >> C;
  vector<string> G(R);
  for(int r=0; r<R; ++r) { cin >> G[r]; }
 
  Dinic graph(R*C*2 + 2);
 
  int s = R * C * 2,
      t = s + 1;
 
  for(int r=0; r<R; ++r) {
    for(int c=0; c<C; ++c) {
      int p = r * C + c,
          q = p + R * C;
      if(G[r][c] == 'X') {
        graph.add_edge(p, q, inf);
        graph.add_edge(s, p, inf);
      } else {
        graph.add_edge(p, q, 1);
      }
      for(int i=0; i<dr_size; ++i) {
        int nr = r + dr[i],
            nc = c + dc[i];
        if(0 <= nr && nr < R && 0 <= nc && nc < C) { // (r, c) は端ではない
          int np = nr * C + nc,
              nq = np + R * C;
          graph.add_edge(q, np, inf);
        } else { // (r, c) は端である
          graph.add_edge(q, t, inf);
        }
      }
    }
  }
 
  Flow res = graph.max_flow(s, t);
  if(res >= inf) { res = -1; }
  cout << res << endl;
 
  return 0;
}

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