#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define rep(i, n) for (int i = 0; i < n; i++) #define rep1(i, n) for (int i = 1; i < n + 1; i++) #define rev(i, n) for (int i = n - 1; i >= 0; i--) #define all(A) A.begin(), A.end() #define itr(A, l, r) A.begin() + l, A.begin() + r #define debug(var) cout << #var << " = " << var << endl; typedef long long ll; template ostream &operator<<(ostream &os, const pair &p) { os << "(" << p.first << "," << p.second << ")"; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 != (int)v.size() ? " " : ""); } return os; } template ostream &operator<<(ostream &os, const vector> &v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << endl; } return os; } template ostream &operator<<(ostream &os, const vector>> &v) { int n = v.size(); int m = v[0].size(); int p = v[0][0].size(); rep(k, p) { os << "k = " << k << endl; rep(i, n) { rep(j, m) { os << v[i][j][k]; if (j < m - 1) { os << " "; } else { os << endl; } } } } return os; } template istream &operator>>(istream &is, vector &v) { for (T &in : v) is >> in; return is; } template ostream &operator<<(ostream &os, map &mp) { for (auto &[key, val] : mp) { os << key << ":" << val << " "; } cout << endl; return os; } template ostream &operator<<(ostream &os, set st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, multiset st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, queue q) { while (q.size()) { os << q.front() << " "; q.pop(); } return os; } template ostream &operator<<(ostream &os, deque q) { while (q.size()) { os << q.front() << " "; q.pop_front(); } return os; } template ostream &operator<<(ostream &os, stack st) { while (st.size()) { os << st.top() << " "; st.pop(); } return os; } template ostream &operator<<(ostream &os, priority_queue pq) { while (pq.size()) { os << pq.top() << " "; pq.pop(); } return os; } template ostream &operator<<(ostream &os, priority_queue, greater> mpq) { while (mpq.size()) { os << mpq.top() << " "; mpq.pop(); } return os; } int main(){ int n,m; cin >> n >> m; vector>> to(n); vector>> from(n); rep(i,m){ int a,b,c; cin >> a >> b >> c; to[a].push_back({b,c}); from[b].push_back({a,c}); } // debug(to); vector dp(n,-1); // queue> q; priority_queue> q; q.push({0,0}); while(q.size()){ // debug(q.top()); auto [now_cost,now_pos] = q.top(); q.pop(); if(now_cost <= dp[now_pos]){ continue; } dp[now_pos] = now_cost; for(auto [next_pos,weight] : to[now_pos]){ int next_cost = now_cost + weight; if(next_cost <= dp[next_pos]){ continue; } q.push({next_cost,next_pos}); } } using S = pair; priority_queue, greater> mq; mq.push({dp[n-1],n-1}); vector ep(n,1e9); while(mq.size()){ auto [now_cost,now_pos] = mq.top(); mq.pop(); if(now_cost >= ep[now_pos]){ continue; } ep[now_pos]= now_cost; for(auto [next_pos, weight] : from[now_pos]){ int next_cost = now_cost - weight; if(next_cost >= ep[now_pos]){ continue; } mq.push({next_cost,next_pos}); } } int ans = 0; rep(i,n){ ans += dp[i] < ep[i]; } // debug(dp); // debug(ans); cout << dp[n-1] << " " << ans << "/" << n << endl; }