#include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; } template bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #else #define dbg(x) {} #endif template struct ShortestPath { int V, E; int INVALID = -1; std::vector>> to; ShortestPath() = default; ShortestPath(int V) : V(V), E(0), to(V) {} void add_edge(int s, int t, T len) { assert(0 <= s and s < V); assert(0 <= t and t < V); to[s].emplace_back(t, len); E++; } std::vector dist; std::vector prev; // Dijkstra algorithm // Complexity: O(E log E) void Dijkstra(int s) { assert(0 <= s and s < V); dist.assign(V, std::numeric_limits::max()); dist[s] = 0; prev.assign(V, INVALID); using P = std::pair; std::priority_queue, std::greater

> pq; pq.emplace(0, s); while (!pq.empty()) { T d; int v; std::tie(d, v) = pq.top(); pq.pop(); if (dist[v] < d) continue; for (auto nx : to[v]) { T dnx = d + nx.second; if (dist[nx.first] > dnx) { dist[nx.first] = dnx, prev[nx.first] = v; pq.emplace(dnx, nx.first); } } } } // Bellman-Ford algorithm // Complexity: O(VE) bool BellmanFord(int s, int nb_loop) { assert(0 <= s and s < V); dist.assign(V, std::numeric_limits::max()); dist[s] = 0; prev.assign(V, INVALID); for (int l = 0; l < nb_loop; l++) { bool upd = false; for (int v = 0; v < V; v++) { if (dist[v] == std::numeric_limits::max()) continue; for (auto nx : to[v]) { T dnx = dist[v] + nx.second; if (dist[nx.first] > dnx) { dist[nx.first] = dnx, prev[nx.first] = v; upd = true; } } } if (!upd) return true; } return false; } void ZeroOneBFS(int s) { assert(0 <= s and s < V); dist.assign(V, std::numeric_limits::max()); dist[s] = 0; prev.assign(V, INVALID); std::deque que; que.push_back(s); while (!que.empty()) { int v = que.front(); que.pop_front(); for (auto nx : to[v]) { T dnx = dist[v] + nx.second; if (dist[nx.first] > dnx) { dist[nx.first] = dnx, prev[nx.first] = v; if (nx.second) { que.push_back(nx.first); } else { que.push_front(nx.first); } } } } } // Warshall-Floyd algorithm // Complexity: O(E + V^3) std::vector> dist2d; void WarshallFloyd() { dist2d.assign(V, std::vector(V, std::numeric_limits::max())); for (int i = 0; i < V; i++) { dist2d[i][i] = 0; for (auto p : to[i]) dist2d[i][p.first] = min(dist2d[i][p.first], p.second); } for (int k = 0; k < V; k++) { for (int i = 0; i < V; i++) { if (dist2d[i][k] = std::numeric_limits::max()) continue; for (int j = 0; j < V; j++) { if (dist2d[k][j] = std::numeric_limits::max()) continue; dist2d[i][j] = min(dist2d[i][j], dist2d[i][k] + dist2d[k][j]); } } } } }; // Shortest cycle detection of UNDIRECTED SIMPLE graphs // Assumption: only two types of edges are permitted: weight = 0 or W ( > 0) // Complexity: O(E) // Verified: struct ShortestCycle01 { int V, E; int INVALID = -1; std::vector>> to; // (nxt, weight) ShortestCycle01() = default; ShortestCycle01(int V) : V(V), E(0), to(V) {} void add_edge(int s, int t, int len) { assert(0 <= s and s < V); assert(0 <= t and t < V); assert(len >= 0); to[s].emplace_back(t, len); to[t].emplace_back(s, len); E++; } std::vector dist; std::vector prev; // Find minimum length simple cycle which passes vertex `v` // - return: (LEN, (a, b)) // - LEN: length of the shortest cycles if exists, numeric_limits::max() otherwise. // - the cycle consists of vertices [v, ..., prev[prev[a]], prev[a], a, b, prev[b], prev[prev[b]], ..., v] std::pair> Solve(int v) { assert(0 <= v and v < V); dist.assign(V, std::numeric_limits::max()); dist[v] = 0; prev.assign(V, -1); using P = pair; std::priority_queue, greater

> bfsq; std::vector, int>> add_edge; bfsq.emplace(0, pint(v, -1)); while (!bfsq.empty()) { auto [wnow, pp] = bfsq.top(); auto [now, prv] = pp; bfsq.pop(); for (auto nxt : to[now]) if (nxt.first != prv) { if (dist[nxt.first] == std::numeric_limits::max()) { dist[nxt.first] = dist[now] + nxt.second; prev[nxt.first] = now; bfsq.emplace(dist[nxt.first], pint(nxt.first, now)); } else { add_edge.emplace_back(std::make_pair(now, nxt.first), nxt.second); } } } lint minimum_cycle = std::numeric_limits::max(); int s = -1, t = -1; for (auto edge : add_edge) { int a = edge.first.first, b = edge.first.second; lint L = dist[a] + dist[b] + edge.second; if (L < minimum_cycle) minimum_cycle = L, s = a, t = b; } return std::make_pair(minimum_cycle, std::make_pair(s, t)); } }; // struct ShortestCycleOfUndirectedGraph { // int V, E; // std::vector>> to; // ShortestCycleOfUndirectedGraph(int N) : V(N), E(0), to(N) {} // void add_edge(int s, int t, int len) { // assert(0 <= s and s < V); // assert(0 <= t and t < V); // assert(len >= 0); // to[s].emplace_back(t, len); // to[t].emplace_back(s, len); // E++; // } // std::array, 2> dist; // std::array, 2> prev; // long long solve(int v) { // assert(0 <= v and v < V); // dist[0].assign(V, std::numeric_limits::max() / 2); // dist[1].assign(V, std::numeric_limits::max() / 2); // prev[0].assign(V, -1); // prev[1].assign(V, -1); // using P = std::pair; // std::priority_queue, std::greater

> pq; // while (!pq.empty()) { // long long wnow = pq.top().first; // int now = pq.top().second; // pq.pop(); // if (dist[1][now] < wnow) continue; // for (const auto nxtp : to[now]) { // int nxt = nxtp.first; // if (prev1[now] != nxt and chmin(dist1[nxt], dist1[now] + nxtp.second)) prev1[nxt] = // } // } // } // }; void solve_dir(int N, int M) { vector> to(N); while (M--) { int u, v, w; cin >> u >> v >> w; u--, v--; to[u].emplace_back(v, w); } lint ret = 1e18; REP(s, N) { ShortestPath graph(N + 1); REP(i, N) for (auto [j, w] : to[i]) { graph.add_edge(i, j, w); if (j == s) graph.add_edge(i, N, w); } graph.Dijkstra(s); if (graph.dist[N] < 1e18) chmin(ret, graph.dist[N]); } cout << (ret < 1e18 ? ret : -1) << '\n'; } int main() { int T, N, M; cin >> T >> N >> M; lint ret = 1e18; if (T == 1) solve_dir(N, M); else { ShortestCycle01 graph(N); while (M--) { int u, v, w; cin >> u >> v >> w; u--, v--; graph.add_edge(u, v, w); } REP(i, N) { chmin(ret, graph.Solve(i).first); dbg(ret); dbg(graph.dist); dbg(graph.prev); } cout << (ret < 1e18 ? ret : -1) << '\n'; } }