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// #define Many_SubTask #include <bits/stdc++.h> using namespace std; #define int long long #define all(a) begin(a), end(a) #define pb push_back #define pii pair<int, int> #define F first #define S second #define mp make_pair const int mod = 998244353; const int inf = 1e18; const int MAXN = 100005; int n, m; vector<pii> Map[MAXN]; int dis[MAXN][2], length[MAXN][2]; struct node { int idx, val, len, cp; bool operator<(node a) const { if(val == a.val) return len > a.len; return val < a.val; } }; priority_queue<node> pq; void Dijkstra(int s, int e) { for (int i = 1; i <= n; i++) dis[i][0] = dis[i][1] = 1e9; dis[s][0] = 0; pq.push({s, dis[s][0], length[s][0], 0}); while (!pq.empty()) { auto [src, val, len, cp] = pq.top(); pq.pop(); if (dis[src][cp] < val) continue; else if(dis[src][cp] == val && length[src][cp] > len) continue; for (auto [des, val] : Map[src]) { // use coupon if(!cp){ if (dis[src][0] + 0 < dis[des][1]) { dis[des][1] = dis[src][0]; length[des][1] = length[src][0] + 1; pq.push({des, dis[des][1], length[des][1], 1}); } else if (dis[src][0] + 0 == dis[des][1] && length[src][0] + 1 > length[des][1]) { length[des][1] = length[src][0] + 1; pq.push({des, dis[des][1], length[des][1], 1}); } } // use coupon if (dis[src][cp] + val < dis[des][cp]) { dis[des][cp] = dis[src][cp] + val; length[des][cp] = length[src][cp] + 1; pq.push({des, dis[des][cp], length[des][cp], cp}); } else if (dis[src][cp] + val == dis[des][cp] && length[src][cp] + 1 > length[des][cp]) { length[des][cp] = length[src][cp] + 1; pq.push({des, dis[des][cp], length[des][cp], cp}); } } } } // 8 2 3 9 // 6 2 4 9 void solve() { cin >> n >> m; while (m--) { int u, v, w; cin >> u >> v >> w; Map[u].pb({v, w}); Map[v].pb({u, w}); } Dijkstra(1, n); cout << dis[n][1] << ' ' << length[n][1] - 1 << '\n'; } signed main() { cin.sync_with_stdio(0), cin.tie(0); int N = 1; #ifdef Many_SubTask cin >> N; #endif for (int i = 1; i <= N; i++) { solve(); } }
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