Problem p02884 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
#define LLI long long int
#define FOR(v, a, b) for (LLI v = (a); v < (b); ++v)
#define FORE(v, a, b) for (LLI v = (a); v <= (b); ++v)
#define REP(v, n) FOR(v, 0, n)
#define REPE(v, n) FORE(v, 0, n)
#define REV(v, a, b) for (LLI v = (a); v >= (b); --v)
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define ITR(it, c) for (auto it = (c).begin(); it != (c).end(); ++it)
#define RITR(it, c) for (auto it = (c).rbegin(); it != (c).rend(); ++it)
#define EXIST(c, x) ((c).find(x) != (c).end())
#define fst first
#define snd second
#define popcount __builtin_popcount
#define UNIQ(v) (v).erase(unique(ALL(v)), (v).end())
#define bit(i) (1LL << (i))

#ifdef DEBUG
#include <misc/C++/Debug.cpp>
#else
#define dump(...) ((void)0)
#endif

#define gcd __gcd

using namespace std;
template <class T> constexpr T lcm(T m, T n) { return m / gcd(m, n) * n; }

template <typename I> void join(ostream &ost, I s, I t, string d = " ") {
  for (auto i = s; i != t; ++i) {
    if (i != s)
      ost << d;
    ost << *i;
  }
  ost << endl;
}
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &a : v)
    is >> a;
  return is;
}

template <typename T, typename U> bool chmin(T &a, const U &b) {
  return (a > b ? a = b, true : false);
}
template <typename T, typename U> bool chmax(T &a, const U &b) {
  return (a < b ? a = b, true : false);
}
template <typename T, size_t N, typename U>
void fill_array(T (&a)[N], const U &v) {
  fill((U *)a, (U *)(a + N), v);
}

struct Init {
  Init() {
    cin.tie(0);
    ios::sync_with_stdio(false);
  }
} init;

template <typename Cost = int> class Edge {
public:
  int from, to;
  Cost cost;
  Edge() {}
  Edge(int to, Cost cost) : to(to), cost(cost) {}
  Edge(int from, int to, Cost cost) : from(from), to(to), cost(cost) {}

  Edge rev() const { return Edge(to, from, cost); }

  friend ostream &operator<<(ostream &os, const Edge &e) {
    os << "(FROM: " << e.from << ","
       << "TO: " << e.to << ","
       << "COST: " << e.cost << ")";
    return os;
  }
};

template <typename T> using Graph = vector<vector<Edge<T>>>;
template <typename T> using Tree = vector<vector<Edge<T>>>;

template <typename C, typename T> void add_edge(C &g, int from, int to, T w) {
  g[from].push_back(Edge<T>(from, to, w));
}

template <typename C, typename T> void add_undirected(C &g, int a, int b, T w) {
  g[a].push_back(Edge<T>(a, b, w));
  g[b].push_back(Edge<T>(b, a, w));
}

double solve(int cur, const Graph<int> &g, vector<double> &dp, int proh) {
  if (dp[cur] >= 0)
    return dp[cur];
  double ret = 0;

  if (cur == proh) {
    int n = g[cur].size();
    n -= 1;

    if (n == 0) {
      return dp[cur] = INT_MAX;
    }

    vector<double> temp;
    for (auto &e : g[cur]) {
      temp.push_back(solve(e.to, g, dp, proh));
    }

    ret = accumulate(ALL(temp), 0.0) - *max_element(ALL(temp));

    ret /= n;

    ret += 1;

  } else {
    int n = g[cur].size();

    for (auto &e : g[cur]) {
      ret += solve(e.to, g, dp, proh) / n;
    }

    ret += 1;
  }

  return dp[cur] = ret;
}

int main() {
  int N, M;
  while (cin >> N >> M) {
    Graph<int> g(N);
    vector<pair<int, int>> edges;
    REP(i, M) {
      int s, t;
      cin >> s >> t;
      --s, --t;
      add_edge(g, s, t, 1);
      edges.emplace_back(s, t);
    }

    dump(g);

    double ans = M;

    {
      vector<double> dp(N, -1);
      dp[N - 1] = 0;
      auto res = solve(0, g, dp, -1);
      chmin(ans, res);
    }

    REP(i, M) {
      vector<double> dp(N, -1);
      dp[N - 1] = 0;
      auto res = solve(0, g, dp, i);
      chmin(ans, res);
    }

    cout << fixed << setprecision(12) << ans << endl;
  }

  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
#define LLI long long int
#define FOR(v, a, b) for (LLI v = (a); v < (b); ++v)
#define FORE(v, a, b) for (LLI v = (a); v <= (b); ++v)
#define REP(v, n) FOR(v, 0, n)
#define REPE(v, n) FORE(v, 0, n)
#define REV(v, a, b) for (LLI v = (a); v >= (b); --v)
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define ITR(it, c) for (auto it = (c).begin(); it != (c).end(); ++it)
#define RITR(it, c) for (auto it = (c).rbegin(); it != (c).rend(); ++it)
#define EXIST(c, x) ((c).find(x) != (c).end())
#define fst first
#define snd second
#define popcount __builtin_popcount
#define UNIQ(v) (v).erase(unique(ALL(v)), (v).end())
#define bit(i) (1LL << (i))

#ifdef DEBUG
#include <misc/C++/Debug.cpp>
#else
#define dump(...) ((void)0)
#endif

#define gcd __gcd

using namespace std;
template <class T> constexpr T lcm(T m, T n) { return m / gcd(m, n) * n; }

template <typename I> void join(ostream &ost, I s, I t, string d = " ") {
  for (auto i = s; i != t; ++i) {
    if (i != s)
      ost << d;
    ost << *i;
  }
  ost << endl;
}
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &a : v)
    is >> a;
  return is;
}

template <typename T, typename U> bool chmin(T &a, const U &b) {
  return (a > b ? a = b, true : false);
}
template <typename T, typename U> bool chmax(T &a, const U &b) {
  return (a < b ? a = b, true : false);
}
template <typename T, size_t N, typename U>
void fill_array(T (&a)[N], const U &v) {
  fill((U *)a, (U *)(a + N), v);
}

struct Init {
  Init() {
    cin.tie(0);
    ios::sync_with_stdio(false);
  }
} init;

template <typename Cost = int> class Edge {
public:
  int from, to;
  Cost cost;
  Edge() {}
  Edge(int to, Cost cost) : to(to), cost(cost) {}
  Edge(int from, int to, Cost cost) : from(from), to(to), cost(cost) {}

  Edge rev() const { return Edge(to, from, cost); }

  friend ostream &operator<<(ostream &os, const Edge &e) {
    os << "(FROM: " << e.from << ","
       << "TO: " << e.to << ","
       << "COST: " << e.cost << ")";
    return os;
  }
};

template <typename T> using Graph = vector<vector<Edge<T>>>;
template <typename T> using Tree = vector<vector<Edge<T>>>;

template <typename C, typename T> void add_edge(C &g, int from, int to, T w) {
  g[from].push_back(Edge<T>(from, to, w));
}

template <typename C, typename T> void add_undirected(C &g, int a, int b, T w) {
  g[a].push_back(Edge<T>(a, b, w));
  g[b].push_back(Edge<T>(b, a, w));
}

double solve(int cur, const Graph<int> &g, vector<double> &dp, int proh) {
  if (dp[cur] >= 0)
    return dp[cur];
  double ret = 0;

  if (cur == proh) {
    int n = g[cur].size();
    n -= 1;

    if (n == 0) {
      return dp[cur] = INT_MAX;
    }

    vector<double> temp;
    for (auto &e : g[cur]) {
      temp.push_back(solve(e.to, g, dp, proh));
    }

    ret = accumulate(ALL(temp), 0.0) - *max_element(ALL(temp));

    ret /= n;

    ret += 1;

  } else {
    int n = g[cur].size();

    for (auto &e : g[cur]) {
      ret += solve(e.to, g, dp, proh) / n;
    }

    ret += 1;
  }

  return dp[cur] = ret;
}

int main() {
  int N, M;
  while (cin >> N >> M) {
    Graph<int> g(N);
    vector<pair<int, int>> edges;
    REP(i, M) {
      int s, t;
      cin >> s >> t;
      --s, --t;
      add_edge(g, s, t, 1);
      edges.emplace_back(s, t);
    }

    dump(g);

    double ans = M;

    {
      vector<double> dp(N, -1);
      dp[N - 1] = 0;
      auto res = solve(0, g, dp, -1);
      chmin(ans, res);
    }

    REP(i, N) {
      vector<double> dp(N, -1);
      dp[N - 1] = 0;
      auto res = solve(0, g, dp, i);
      chmin(ans, res);
    }

    cout << fixed << setprecision(12) << ans << endl;
  }

  return 0;
}