#include #include #include #include #include #include #include #include #define rep(i, a, b) for (int i = int(a); i < int(b); i++) using namespace std; using ll = long long int; // NOLINT using P = pair; // clang-format off #ifdef _DEBUG_ #define dump(...) do{ cerr << __LINE__ << ":\t" << #__VA_ARGS__ << " = "; debug_print(__VA_ARGS__); } while(false) template void debug_print(const T &t, const Ts &...ts) { cerr << t; ((cerr << ", " << ts), ...); cerr << endl; } #else #define dump(...) do{ } while(false) #endif template vector make_v(size_t a, T b) { return vector(a, b); } template auto make_v(size_t a, Ts... ts) { return vector(a, make_v(ts...)); } template bool chmin(T &a, const T& b) { if (a > b) {a = b; return true; } return false; } template bool chmax(T &a, const T& b) { if (a < b) {a = b; return true; } return false; } template void print(const T& t, const Ts&... ts) { cout << t; ((cout << ' ' << ts), ...); cout << '\n'; } constexpr static struct PositiveInfinity { template constexpr operator T() const { return numeric_limits::max() / 2; } constexpr auto operator-() const; } inf; // NOLINT constexpr static struct NegativeInfinity { template constexpr operator T() const { return numeric_limits::lowest() / 2; } constexpr auto operator-() const; } NegativeInfinityVal; constexpr auto PositiveInfinity::operator-() const { return NegativeInfinityVal; } constexpr auto NegativeInfinity::operator-() const { return inf; } // clang-format on #include #include #include #include enum class CostType { NoEdge, One, ZeroOne, Plus, PlusMinus, }; template class Graph { using Edge = pair; using ShortestInfo = pair, vector>; vector> g; CostType cost_type; ShortestInfo no_edge(Vertex s) { auto costs = vector(g.size(), Inf); auto prev = vector(g.size(), None); costs[s] = 0; return make_pair(std::move(costs), std::move(prev)); } ShortestInfo bfs01(Vertex s) { auto [costs, prev] = no_edge(s); deque deq; deq.emplace_back(0, s); while (deq.size()) { auto [c, v] = deq.front(); deq.pop_front(); if (costs[v] < c) continue; for (auto &&[nc, nv] : adjacent(v)) { if (costs[nv] > c + nc) { costs[nv] = c + nc; if (nc == 0) { deq.emplace_front(c, nv); } else { deq.emplace_back(c + 1, nv); } prev[nv] = v; } } } return make_pair(std::move(costs), std::move(prev)); } ShortestInfo bfs(Vertex s) { auto [costs, prev] = no_edge(s); queue que; que.emplace(0, s); while (que.size()) { auto [c, v] = que.front(); que.pop(); if (costs[v] < c) continue; for (auto &&[nc, nv] : adjacent(v)) { if (costs[nv] > c + nc) { costs[nv] = c + nc; que.emplace(c + nc, nv); prev[nv] = v; } } } return make_pair(std::move(costs), std::move(prev)); } ShortestInfo dijkstra(Vertex s) { auto [costs, prev] = no_edge(s); priority_queue, greater> pq; pq.emplace(0, s); while (pq.size()) { auto [c, v] = pq.top(); pq.pop(); if (costs[v] < c) continue; for (auto &&[nc, nv] : adjacent(v)) { if (costs[nv] > c + nc) { costs[nv] = c + nc; pq.emplace(c + nc, nv); prev[nv] = v; } } } return make_pair(std::move(costs), std::move(prev)); } ShortestInfo bellman_ford(Vertex s) { auto [costs, prev] = no_edge(s); for (size_t i = 0, n = g.size(); i < 2 * n; i++) { for (Vertex v = 0; v < static_cast(n); v++) { if (costs[v] == Inf) continue; for (auto &&[cost, nv] : adjacent(v)) { if (costs[v] == -Inf || costs[v] + cost < costs[nv]) { if (i >= n) { costs[nv] = -Inf; } else { costs[nv] = costs[v] + cost; } prev[nv] = v; } } } } return make_pair(std::move(costs), std::move(prev)); } void update_cost_type(Cost cost) { CostType ct = CostType::NoEdge; if (signbit(cost)) { ct = CostType::PlusMinus; } else if (cost != 0 && cost != 1) { ct = CostType::Plus; } else if (cost == 0) { ct = CostType::ZeroOne; } else if (cost == 1) { ct = CostType::One; } cost_type = static_cast(max(static_cast(ct), static_cast(cost_type))); } public: Graph(size_t n) : g(n), cost_type(CostType::NoEdge) {} void add_edge(Vertex s, Vertex t, Cost cost) { update_cost_type(cost); g[s].emplace_back(cost, t); } const vector &adjacent(Vertex v) const { return g[v]; } size_t size() const { return g.size(); } CostType get_cost_type() const { return cost_type; } ShortestInfo shortest(Vertex s) { switch (cost_type) { case CostType::ZeroOne: return bfs01(s); case CostType::One: return bfs(s); case CostType::Plus: return dijkstra(s); case CostType::PlusMinus: return bellman_ford(s); case CostType::NoEdge: return no_edge(s); } __builtin_unreachable(); } constexpr static Cost Inf = numeric_limits::max(); constexpr static Vertex None = -1; }; int main() { cin.tie(nullptr); ios::sync_with_stdio(false); int n, m; cin >> n >> m; vector tm(n); rep(i, 0, n) { cin >> tm[i]; } Graph g(n); rep(i, 0, m) { int a, b, c; cin >> a >> b >> c; a--; b--; g.add_edge(a, b, c - tm[b]); } auto [cost, prev] = g.shortest(0); ll ans = cost[n - 1]; if (ans == -g.Inf) { print("inf"); } else { print(-ans + tm[0]); } return 0; }