Problem p02561 (C++)

Buggy submission (status: Runtime Error):
#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
#include <unordered_map>

using namespace std;

typedef long long ll;

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.push_back({from, int(g[from].size())});
    g[from].push_back(_edge{to, int(g[to].size()), cap});
    g[to].push_back(_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].first][pos[i].second];
    auto _re = g[_e.to][_e.rev];
    return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap};
  }
  std::vector<edge> edges() {
    int m = int(pos.size());
    std::vector<edge> result;
    for (int i = 0; i < m; i++) {
      result.push_back(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].first][pos[i].second];
    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, std::numeric_limits<Cap>::max()); }
  Cap flow(int s, int t, Cap flow_limit) {
    assert(0 <= s && s < _n);
    assert(0 <= t && t < _n);

    std::vector<int> level(_n), iter(_n);
    queue<int> que;

    auto bfs = [&]() {
      std::fill(level.begin(), level.end(), -1);
      level[s] = 0;
      while (!que.empty())
        que.pop();
      que.push(s);
      while (!que.empty()) {
        int v = que.front();
        que.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;
          que.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, std::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;
      std::fill(iter.begin(), iter.end(), 0);
      while (flow < flow_limit) {
        Cap f = dfs(dfs, t, flow_limit - flow);
        if (!f)
          break;
        flow += f;
      }
    }
    return flow;
  }

  std::vector<bool> min_cut(int s) {
    std::vector<bool> visited(_n);
    queue<int> que;
    que.push(s);
    while (!que.empty()) {
      int p = que.front();
      que.pop();
      visited[p] = true;
      for (auto e : g[p]) {
        if (e.cap && !visited[e.to]) {
          visited[e.to] = true;
          que.push(e.to);
        }
      }
    }
    return visited;
  }

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

void solve() {
  int n, m;
  cin >> n >> m;
  vector<string> d(n);
  for (int i = 0; i < n; i++)
    cin >> d[i];
  mf_graph<int> g(n * m + 2);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      int from = m * i + j + 1 + 1;
      if (d[i][j] == '.' && j + 1 < m && d[i][j + 1] == '.') {
        int to = m * i + j + 2 + 1;
        if ((i + j) % 2 == 0)
          g.add_edge(from, to, 1);
        else
          g.add_edge(to, from, 1);
      }

      if (d[i][j] == '.' && i + 1 < n && d[i + 1][j] == '.') {
        int to = m * (i + 1) + j + 1 + 1;
        if ((i + j) % 2 == 0)
          g.add_edge(from, to, 1);
        else
          g.add_edge(to, from, 1);
      }

      if (d[i][j] == '.') {
        if ((i + j) % 2 == 0)
          g.add_edge(0, from, 1);
        else
          g.add_edge(from, 1, 1);
      }
    }
  }

  vector<string> ans = d;

  cout << g.flow(0, 1) << '\n';
  int num = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      int from = m * i + j + 1 + 1;
      if (d[i][j] == '.' && j + 1 < m && d[i][j + 1] == '.') {
        int to = m * i + j + 2 + 1;
        if (g.get_edge(num).flow == 1) {
          ans[i][j] = '>';
          ans[i][j + 1] = '<';
        }
        num++;
      }

      if (d[i][j] == '.' && i + 1 < n && d[i + 1][j] == '.') {
        int to = m * (i + 1) + j + 1 + 1;
        if (g.get_edge(num).flow == 1) {
          ans[i][j] = 'v';
          ans[i + 1][j] = '^';
        }
        num++;
      }

      if (d[i][j] == '.') {
        num++;
      }
    }
  }

  for (int i = 0; i < n; i++)
    cout << ans[i] << '\n';
}

int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
#if defined(_DEBUG)
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
#endif
  int q = 1;
  // cin >> q;
  for (; q > 0; q--) {
    solve();
    // cout << endl;
  }
}

Fixed submission:
#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
#include <unordered_map>

using namespace std;

typedef long long ll;

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.push_back({from, int(g[from].size())});
    g[from].push_back(_edge{to, int(g[to].size()), cap});
    g[to].push_back(_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].first][pos[i].second];
    auto _re = g[_e.to][_e.rev];
    return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap};
  }
  std::vector<edge> edges() {
    int m = int(pos.size());
    std::vector<edge> result;
    for (int i = 0; i < m; i++) {
      result.push_back(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].first][pos[i].second];
    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, std::numeric_limits<Cap>::max()); }
  Cap flow(int s, int t, Cap flow_limit) {
    assert(0 <= s && s < _n);
    assert(0 <= t && t < _n);

    std::vector<int> level(_n), iter(_n);
    queue<int> que;

    auto bfs = [&]() {
      std::fill(level.begin(), level.end(), -1);
      level[s] = 0;
      while (!que.empty())
        que.pop();
      que.push(s);
      while (!que.empty()) {
        int v = que.front();
        que.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;
          que.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, std::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;
      std::fill(iter.begin(), iter.end(), 0);
      while (flow < flow_limit) {
        Cap f = dfs(dfs, t, flow_limit - flow);
        if (!f)
          break;
        flow += f;
      }
    }
    return flow;
  }

  std::vector<bool> min_cut(int s) {
    std::vector<bool> visited(_n);
    queue<int> que;
    que.push(s);
    while (!que.empty()) {
      int p = que.front();
      que.pop();
      visited[p] = true;
      for (auto e : g[p]) {
        if (e.cap && !visited[e.to]) {
          visited[e.to] = true;
          que.push(e.to);
        }
      }
    }
    return visited;
  }

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

void solve() {
  int n, m;
  cin >> n >> m;
  vector<string> d(n);
  for (int i = 0; i < n; i++)
    cin >> d[i];
  mf_graph<int> g(n * m + 2);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      int from = m * i + j + 1 + 1;
      if (d[i][j] == '.' && j + 1 < m && d[i][j + 1] == '.') {
        int to = m * i + j + 2 + 1;
        if ((i + j) % 2 == 0)
          g.add_edge(from, to, 1);
        else
          g.add_edge(to, from, 1);
      }

      if (d[i][j] == '.' && i + 1 < n && d[i + 1][j] == '.') {
        int to = m * (i + 1) + j + 1 + 1;
        if ((i + j) % 2 == 0)
          g.add_edge(from, to, 1);
        else
          g.add_edge(to, from, 1);
      }

      if (d[i][j] == '.') {
        if ((i + j) % 2 == 0)
          g.add_edge(0, from, 1);
        else
          g.add_edge(from, 1, 1);
      }
    }
  }

  vector<string> ans = d;

  cout << g.flow(0, 1) << '\n';
  int num = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      int from = m * i + j + 1 + 1;
      if (d[i][j] == '.' && j + 1 < m && d[i][j + 1] == '.') {
        int to = m * i + j + 2 + 1;
        if (g.get_edge(num).flow == 1) {
          ans[i][j] = '>';
          ans[i][j + 1] = '<';
        }
        num++;
      }

      if (d[i][j] == '.' && i + 1 < n && d[i + 1][j] == '.') {
        int to = m * (i + 1) + j + 1 + 1;
        if (g.get_edge(num).flow == 1) {
          ans[i][j] = 'v';
          ans[i + 1][j] = '^';
        }
        num++;
      }

      if (d[i][j] == '.') {
        num++;
      }
    }
  }

  for (int i = 0; i < n; i++)
    cout << ans[i] << '\n';
}

int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
#if defined(_DEBUG)
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
#endif
  int q = 1;
  // cin >> q;
  for (; q > 0; q--) {
    solve();
    // cout << endl;
  }
}