// compile: make data // run: ./data < data.in #include <bits/stdc++.h> using namespace std; #pragma GCC optimize("O3,unroll-loops") #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt") #ifdef LOCAL #include <debug/codeforces.h> #define debug(x...) _debug_print(#x, x); #define Debug(x...) _debug_print_format(#x, x); #else #define debug(x...) #define Debug(x...) #endif template<typename...Args> void print_(Args...args){((cout<<args<<" "),...)<<endl;} #define rep(i,a,b) for(int i=(a);i<(int)(b);++i) #define sz(v) ((int)(v).size()) #define print(...) print_(__VA_ARGS__); #define FIND(a, x) ((find(a.begin(),a.end(),(x))!=a.end())?1:0) #define cmin(x,...) x=min({(x), __VA_ARGS__}) #define cmax(x,...) x=max({(x), __VA_ARGS__}) #define INTMAX (int)(9223372036854775807) #define INF (int)(1152921504606846976) #define double long double #define int long long #define MAXN 200010 #define P 1000000007 struct graph { struct node { int v, w; bool operator<(const node &other) const { return w < other.w; } bool operator==(const node &other) const { return v == other.v && w == other.w; } }; vector<vector<node>> e; int n; bool directed; graph(int V, bool D = 0) { n = V; e.resize(n); directed = D; } void add_edge(int u, int v, int w = 1) { e[u].push_back(node{v, w}); } void dijkstra(int s, vector<int> &dis, vector<int> &nmin, vector<int> &nmax, vector<int> &nsum) { dis.resize(n, INF); nmin.resize(n, INF); nmax.resize(n, -INF); nsum.resize(n, 0); vector<bool> vis(n, 0); struct temp { int d, u, num; bool operator<(const temp &other) const { return d < other.d; } bool operator>(const temp &other) const { return d > other.d; } }; priority_queue<temp, vector<temp>, greater<temp>> pq; dis[s] = 0, nsum[s] = 1, nmin[s] = nmax[s] = 0, pq.push({0, s, 0}); while (!pq.empty()) { auto [d, u, num] = pq.top(); pq.pop(); if (vis[u]) continue; vis[u] = 1; for (auto [v, w]: e[u]) { if (dis[v] > dis[u] + w) { dis[v] = dis[u] + w; nmin[v] = nmin[u] + 1; nmax[v] = nmax[u] + 1; nsum[v] = nsum[u]; pq.push({dis[v], v, num + 1}); } else if (dis[v] == dis[u] + w) { cmin(nmin[v], nmin[u] + 1); cmax(nmax[v], nmax[u] + 1); nsum[v] = (nsum[v] + nsum[u]) % P; pq.push({dis[v], v, num + 1}); } } } } void graphviz_dump(string filename = "graph.dot") { ofstream gf; gf.open(filename); gf << (directed ? "digraph" : "graph") << " {\n"; gf << " "; rep(i, 0, n) gf << i << " ;"[i==n-1]; gf << endl; string notation = directed ? " -> " : " -- "; bool weighted = 0; for (auto es: e) for (auto edge: es) if (edge.w != 1) weighted = 1; rep(u, 0, n) { for (auto [v, w]: e[u]) { if (!directed && u > v) continue; gf << " " << u << notation << v << (weighted ? " ;\n" : ";\n"); } } gf << "}\n"; } }; int32_t main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); int n, m; cin >> n >> m; graph g(n, 1); rep(i, 0, m) { int u, v, w; cin >> u >> v >> w; g.add_edge(u-1, v-1, w); } g.graphviz_dump(); vector<int> dis, nmin, nmax, nsum; g.dijkstra(0, dis, nmin, nmax, nsum); cout << dis[n-1] << " " << nsum[n-1] << " " << nmin[n-1] << " " << nmax[n-1] << endl; return 0; }
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