Problem p02561 (C++)

Buggy submission (status: Runtime Error):
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;

// template
#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define ALL(v) (v).begin(), (v).end()
typedef long long int ll;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;
const double eps = 1e-12;
template <typename T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
// end

#include <algorithm>

#include <vector>

namespace atcoder {

namespace internal {

template <class T> struct simple_queue {
  std::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++; }
};

} // namespace internal

} // namespace atcoder

#include <cassert>
#include <limits>
#include <queue>
#include <vector>

namespace atcoder {

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);
    internal::simple_queue<int> que;

    auto bfs = [&]() {
      std::fill(level.begin(), level.end(), -1);
      level[s] = 0;
      que.clear();
      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);
    internal::simple_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;
};

} // namespace atcoder

// python3 ac-library/expander.py sol.cpp

int dx[] = {1, -1, 0, 0}, dy[] = {0, 0, 1, -1};

int main() {
  int n, m;
  cin >> n >> m;
  vector<string> g(n), res(n);
  rep(i, 0, n) {
    cin >> g[i];
    res[i] = g[i];
  }
  atcoder::mf_graph<int> flow(n * m + 2);
  int s = n * m, t = n * m + 1;
  rep(i, 0, n) rep(j, 0, m) if (g[i][j] == '.' and (i + j) % 2 == 0) {
    rep(k, 0, 4) {
      int tx = i + dx[k], ty = j + dy[k];
      if (tx < 0 or tx >= n or ty < 0 or ty >= m or g[tx][ty] == '#')
        continue;
      flow.add_edge(i * m + j, tx * m + ty, 1);
    }
  }
  rep(i, 0, n) rep(j, 0, n) if (g[i][j] == '.') {
    if ((i + j) % 2 == 0)
      flow.add_edge(s, i * m + j, 1);
    else
      flow.add_edge(i * m + j, t, 1);
  }
  int val = flow.flow(s, t);
  cout << val << endl;
  for (auto &e : flow.edges()) {
    if (e.from == s or e.to == t)
      continue;
    if (e.flow != 1)
      continue;
    int x1 = e.from / m, y1 = e.from % m;
    int x2 = e.to / m, y2 = e.to % m;
    if (x1 == x2) {
      if (y1 > y2)
        swap(y1, y2);
      res[x1][y1] = '>';
      res[x2][y2] = '<';
    } else {
      if (x1 > x2)
        swap(x1, x2);
      res[x1][y1] = 'v';
      res[x2][y2] = '^';
    }
  }
  rep(i, 0, n) cout << res[i] << endl;
  return 0;
}


Fixed submission:
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;

// template
#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define ALL(v) (v).begin(), (v).end()
typedef long long int ll;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;
const double eps = 1e-12;
template <typename T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
// end

#include <algorithm>

#include <vector>

namespace atcoder {

namespace internal {

template <class T> struct simple_queue {
  std::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++; }
};

} // namespace internal

} // namespace atcoder

#include <cassert>
#include <limits>
#include <queue>
#include <vector>

namespace atcoder {

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);
    internal::simple_queue<int> que;

    auto bfs = [&]() {
      std::fill(level.begin(), level.end(), -1);
      level[s] = 0;
      que.clear();
      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);
    internal::simple_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;
};

} // namespace atcoder

// python3 ac-library/expander.py sol.cpp

int dx[] = {1, -1, 0, 0}, dy[] = {0, 0, 1, -1};

int main() {
  int n, m;
  cin >> n >> m;
  vector<string> g(n), res(n);
  rep(i, 0, n) {
    cin >> g[i];
    res[i] = g[i];
  }
  atcoder::mf_graph<int> flow(n * m + 2);
  int s = n * m, t = n * m + 1;
  rep(i, 0, n) rep(j, 0, m) if (g[i][j] == '.' and (i + j) % 2 == 0) {
    rep(k, 0, 4) {
      int tx = i + dx[k], ty = j + dy[k];
      if (tx < 0 or tx >= n or ty < 0 or ty >= m or g[tx][ty] == '#')
        continue;
      flow.add_edge(i * m + j, tx * m + ty, 1);
    }
  }
  rep(i, 0, n) rep(j, 0, m) {
    if ((i + j) % 2 == 0)
      flow.add_edge(s, i * m + j, 1);
    else
      flow.add_edge(i * m + j, t, 1);
  }
  int val = flow.flow(s, t);
  cout << val << endl;
  for (auto &e : flow.edges()) {
    if (e.from == s or e.to == t)
      continue;
    if (e.flow != 1)
      continue;
    int x1 = e.from / m, y1 = e.from % m;
    int x2 = e.to / m, y2 = e.to % m;
    if (x1 == x2) {
      if (y1 > y2)
        swap(y1, y2);
      res[x1][y1] = '>';
      res[x2][y2] = '<';
    } else {
      if (x1 > x2)
        swap(x1, x2);
      res[x1][y1] = 'v';
      res[x2][y2] = '^';
    }
  }
  rep(i, 0, n) cout << res[i] << endl;
  return 0;
}