Problem p02561 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
using namespace std;
#define repex(i, a, b, c) for (int i = a; i < b; i += c)
#define repx(i, a, b) repex(i, a, b, 1)
#define rep(i, n) repx(i, 0, n)
#define repr(i, a, b) for (int i = a; i >= b; i--)
#define pb push_back
#define a first
#define b second
#define all(x) x.begin(), x.end()

// AtCoder Library(https://img.atcoder.jp/practice2/ac-library.zip)
// -> 一部改変(2020/09/13).
template <class T> struct simple_queue {
  vector<T> payload;
  int pos = 0;
  void reserve(int n) { payload.reserve(n); }
  int size() const { return int(payload.size()) - pos; }
  bool empty() const { return pos == int(payload.size()); }
  void push(const T &t) { payload.push_back(t); }
  T &front() { return payload[pos]; }
  void clear() {
    payload.clear();
    pos = 0;
  }
  void pop() { pos++; }
};

template <class Cap> struct mf_graph {
public:
  mf_graph() : _n(0) {}
  mf_graph(int n) : _n(n), g(n) {}
  int add_edge(int from, int to, Cap cap) {
    assert(0 <= from && from < _n);
    assert(0 <= to && to < _n);
    assert(0 <= cap);
    int m = int(pos.size());
    pos.pb({from, int(g[from].size())});
    g[from].pb(_edge{to, int(g[to].size()), cap});
    g[to].pb(_edge{from, int(g[from].size()) - 1, 0});
    return m;
  }
  struct edge {
    int from, to;
    Cap cap, flow;
  };
  edge get_edge(int i) {
    int m = int(pos.size());
    assert(0 <= i && i < m);
    auto _e = g[pos[i].a][pos[i].b];
    auto _re = g[_e.to][_e.rev];
    return edge{pos[i].a, _e.to, _e.cap + _re.cap, _re.cap};
  }
  vector<edge> edges() {
    int m = int(pos.size());
    vector<edge> result;
    rep(i, m) result.pb(get_edge(i));
    return result;
  }
  void change_edge(int i, Cap new_cap, Cap new_flow) {
    int m = int(pos.size());
    assert(0 <= i && i < m);
    assert(0 <= new_flow && new_flow <= new_cap);
    auto &_e = g[pos[i].a][pos[i].b];
    auto &_re = g[_e.to][_e.rev];
    _e.cap = new_cap - new_flow;
    _re.cap = new_flow;
  }
  Cap flow(int s, int t) { return flow(s, t, numeric_limits<Cap>::max()); }
  Cap flow(int s, int t, Cap flow_limit) {
    assert(0 <= s && s < _n);
    assert(0 <= t && t < _n);
    vector<int> level(_n), iter(_n);
    simple_queue<int> q;
    auto bfs = [&]() {
      fill(all(level), -1);
      level[s] = 0;
      q.clear();
      q.push(s);
      while (!q.empty()) {
        int v = q.front();
        q.pop();
        for (auto e : g[v]) {
          if (e.cap == 0 || level[e.to] >= 0)
            continue;
          level[e.to] = level[v] + 1;
          if (e.to == t)
            return;
          q.push(e.to);
        }
      }
    };
    auto dfs = [&](auto self, int v, Cap up) {
      if (v == s)
        return up;
      Cap res = 0;
      int level_v = level[v];
      for (int &i = iter[v]; i < int(g[v].size()); i++) {
        _edge &e = g[v][i];
        if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0)
          continue;
        Cap d = self(self, e.to, min(up - res, g[e.to][e.rev].cap));
        if (d <= 0)
          continue;
        g[v][i].cap += d;
        g[e.to][e.rev].cap -= d;
        res += d;
        if (res == up)
          break;
      }
      return res;
    };
    Cap flow = 0;
    while (flow < flow_limit) {
      bfs();
      if (level[t] == -1)
        break;
      fill(all(iter), 0);
      while (flow < flow_limit) {
        Cap f = dfs(dfs, t, flow_limit - flow);
        if (!f)
          break;
        flow += f;
      }
    }
    return flow;
  }
  vector<bool> min_cut(int s) {
    vector<bool> visited(_n);
    simple_queue<int> q;
    q.push(s);
    while (!q.empty()) {
      int p = q.front();
      q.pop();
      visited[p] = true;
      for (auto e : g[p]) {
        if (e.cap && !visited[e.to]) {
          visited[e.to] = true;
          q.push(e.to);
        }
      }
    }
    return visited;
  }

private:
  int _n;
  struct _edge {
    int to, rev;
    Cap cap;
  };
  vector<pair<int, int>> pos;
  vector<vector<_edge>> g;
};

// maxflow.html を 参照.
int main() {

  int n, m;
  scanf("%d %d", &n, &m);
  vector<string> grid;
  rep(i, n) {
    char c[111];
    scanf("%s", c);
    string s(c);
    grid.pb(c);
  }

  /**
   * generate (s -> even grid -> odd grid -> t) graph
   * grid(i, j) correspond to vertex (i * m + j)
   **/
  mf_graph<int> g(n * m + 2);
  int s = n * m, t = n * m + 1;
  // s -> even / odd -> t
  rep(i, n) {
    rep(j, m) {
      if (grid[i][j] == '#')
        continue;
      int v = i * m + j;
      if ((i + j) % 2 == 0)
        g.add_edge(s, v, 1);
      else
        g.add_edge(v, t, 1);
    }
  }
  // even -> odd
  rep(i, n) {
    rep(j, m) {
      if ((i + j) % 2 || grid[i][j] == '#')
        continue;
      int v0 = i * m + j;
      if (i && grid[i - 1][j] == '.') {
        int v1 = (i - 1) * m + j;
        g.add_edge(v0, v1, 1);
      }
      if (j && grid[i][j - 1] == '.') {
        int v1 = i * m + (j - 1);
        g.add_edge(v0, v1, 1);
      }
      if (i + 1 < n && grid[i + 1][j] == '.') {
        int v1 = (i + 1) * m + j;
        g.add_edge(v0, v1, 1);
      }
      if (j + 1 < m && grid[i][j + 1] == '.') {
        int v1 = i * m + (j + 1);
        g.add_edge(v0, v1, 1);
      }
    }
  }
  printf("%d\\n", g.flow(s, t));
  auto edges = g.edges();
  for (auto e : edges) {
    if (e.from == s || e.to == t || e.flow == 0)
      continue;
    int i0 = e.from / m, j0 = e.from % m;
    int i1 = e.to / m, j1 = e.to % m;
    if (i0 == i1 + 1) {
      grid[i1][j1] = 'v';
      grid[i0][j0] = '^';
    } else if (j0 == j1 + 1) {
      grid[i1][j1] = '>';
      grid[i0][j0] = '<';
    } else if (i0 == i1 - 1) {
      grid[i0][j0] = 'v';
      grid[i1][j1] = '^';
    } else {
      grid[i0][j0] = '>';
      grid[i1][j1] = '<';
    }
  }
  rep(i, n) printf("%s\\n", grid[i].c_str());
  return 0;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
#define repex(i, a, b, c) for (int i = a; i < b; i += c)
#define repx(i, a, b) repex(i, a, b, 1)
#define rep(i, n) repx(i, 0, n)
#define repr(i, a, b) for (int i = a; i >= b; i--)
#define pb push_back
#define a first
#define b second
#define all(x) x.begin(), x.end()

// AtCoder Library(https://img.atcoder.jp/practice2/ac-library.zip)
// -> 一部改変(2020/09/13).
template <class Cap> struct mf_graph {
public:
  mf_graph() : _n(0) {}
  mf_graph(int n) : _n(n), g(n) {}
  int add_edge(int from, int to, Cap cap) {
    assert(0 <= from && from < _n);
    assert(0 <= to && to < _n);
    assert(0 <= cap);
    int m = int(pos.size());
    pos.pb({from, int(g[from].size())});
    g[from].pb(_edge{to, int(g[to].size()), cap});
    g[to].pb(_edge{from, int(g[from].size()) - 1, 0});
    return m;
  }
  struct edge {
    int from, to;
    Cap cap, flow;
  };
  edge get_edge(int i) {
    int m = int(pos.size());
    assert(0 <= i && i < m);
    auto _e = g[pos[i].a][pos[i].b];
    auto _re = g[_e.to][_e.rev];
    return edge{pos[i].a, _e.to, _e.cap + _re.cap, _re.cap};
  }
  vector<edge> edges() {
    int m = int(pos.size());
    vector<edge> result;
    rep(i, m) result.pb(get_edge(i));
    return result;
  }
  void change_edge(int i, Cap new_cap, Cap new_flow) {
    int m = int(pos.size());
    assert(0 <= i && i < m);
    assert(0 <= new_flow && new_flow <= new_cap);
    auto &_e = g[pos[i].a][pos[i].b];
    auto &_re = g[_e.to][_e.rev];
    _e.cap = new_cap - new_flow;
    _re.cap = new_flow;
  }
  Cap flow(int s, int t) { return flow(s, t, numeric_limits<Cap>::max()); }
  Cap flow(int s, int t, Cap flow_limit) {
    assert(0 <= s && s < _n);
    assert(0 <= t && t < _n);
    vector<int> level(_n), iter(_n);
    queue<int> q;
    auto bfs = [&]() {
      fill(all(level), -1);
      level[s] = 0;
      q.push(s);
      while (!q.empty()) {
        int v = q.front();
        q.pop();
        for (auto e : g[v]) {
          if (e.cap == 0 || level[e.to] >= 0)
            continue;
          level[e.to] = level[v] + 1;
          if (e.to == t)
            return;
          q.push(e.to);
        }
      }
    };
    auto dfs = [&](auto self, int v, Cap up) {
      if (v == s)
        return up;
      Cap res = 0;
      int level_v = level[v];
      for (int &i = iter[v]; i < int(g[v].size()); i++) {
        _edge &e = g[v][i];
        if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0)
          continue;
        Cap d = self(self, e.to, min(up - res, g[e.to][e.rev].cap));
        if (d <= 0)
          continue;
        g[v][i].cap += d;
        g[e.to][e.rev].cap -= d;
        res += d;
        if (res == up)
          break;
      }
      return res;
    };
    Cap flow = 0;
    while (flow < flow_limit) {
      bfs();
      if (level[t] == -1)
        break;
      fill(all(iter), 0);
      while (flow < flow_limit) {
        Cap f = dfs(dfs, t, flow_limit - flow);
        if (!f)
          break;
        flow += f;
      }
    }
    return flow;
  }
  vector<bool> min_cut(int s) {
    vector<bool> visited(_n);
    queue<int> q;
    q.push(s);
    while (!q.empty()) {
      int p = q.front();
      q.pop();
      visited[p] = true;
      for (auto e : g[p]) {
        if (e.cap && !visited[e.to]) {
          visited[e.to] = true;
          q.push(e.to);
        }
      }
    }
    return visited;
  }

private:
  int _n;
  struct _edge {
    int to, rev;
    Cap cap;
  };
  vector<pair<int, int>> pos;
  vector<vector<_edge>> g;
};

// maxflow.html を 参照.
int main() {

  int n, m;
  scanf("%d %d", &n, &m);
  vector<string> grid;
  rep(i, n) {
    char c[111];
    scanf("%s", c);
    string s(c);
    grid.pb(c);
  }

  /**
   * generate (s -> even grid -> odd grid -> t) graph
   * grid(i, j) correspond to vertex (i * m + j)
   **/
  mf_graph<int> g(n * m + 2);
  int s = n * m, t = n * m + 1;
  // s -> even / odd -> t
  rep(i, n) {
    rep(j, m) {
      if (grid[i][j] == '#')
        continue;
      int v = i * m + j;
      if ((i + j) % 2 == 0)
        g.add_edge(s, v, 1);
      else
        g.add_edge(v, t, 1);
    }
  }
  // even -> odd
  rep(i, n) {
    rep(j, m) {
      if ((i + j) % 2 || grid[i][j] == '#')
        continue;
      int v0 = i * m + j;
      if (i && grid[i - 1][j] == '.') {
        int v1 = (i - 1) * m + j;
        g.add_edge(v0, v1, 1);
      }
      if (j && grid[i][j - 1] == '.') {
        int v1 = i * m + (j - 1);
        g.add_edge(v0, v1, 1);
      }
      if (i + 1 < n && grid[i + 1][j] == '.') {
        int v1 = (i + 1) * m + j;
        g.add_edge(v0, v1, 1);
      }
      if (j + 1 < m && grid[i][j + 1] == '.') {
        int v1 = i * m + (j + 1);
        g.add_edge(v0, v1, 1);
      }
    }
  }
  printf("%d\\n", g.flow(s, t));
  auto edges = g.edges();
  for (auto e : edges) {
    if (e.from == s || e.to == t || e.flow == 0)
      continue;
    int i0 = e.from / m, j0 = e.from % m;
    int i1 = e.to / m, j1 = e.to % m;
    if (i0 == i1 + 1) {
      grid[i1][j1] = 'v';
      grid[i0][j0] = '^';
    } else if (j0 == j1 + 1) {
      grid[i1][j1] = '>';
      grid[i0][j0] = '<';
    } else if (i0 == i1 - 1) {
      grid[i0][j0] = 'v';
      grid[i1][j1] = '^';
    } else {
      grid[i0][j0] = '>';
      grid[i1][j1] = '<';
    }
  }
  rep(i, n) printf("%s\\n", grid[i].c_str());
  return 0;
}