#include using namespace std; using ll = long long; //min_ver class LiChaoTree{ struct Line{ long long a, b; long long get(long long x){return a * x + b; } Line(long long a, long long b) : a(a), b(b) {} }; struct Node { Node *left, *right; Line line; Node(Line line) : left(nullptr), right(nullptr), line(line) {} }; const long long inf = 1ll << 62; const Line inf_line = Line{0, inf}; Node *root; long long lx, rx; Node* _add_line(Node *nd, Line line, long long l, long long r){ if(l == r) return nullptr; if(nd == nullptr) return new Node(line); long long m = (l + r) >> 1; bool left = (line.get(l) <= nd->line.get(l)); bool mid = (line.get(m) <= nd->line.get(m)); bool right = (line.get(r) <= nd->line.get(r)); if(left && right)nd->line = line; if(left == right)return nd; if(mid) std::swap(nd->line, line); if(left != mid){ nd->left = _add_line(nd->left, line, l, m); }else{ nd->right = _add_line(nd->right, line, m, r); } return nd; } Node* _add_segment_line(long long a, long long b, Node *nd, Line line, long long l, long long r) { if(r <= a || b <= l) return nd; if(a <= l && r <= b) return _add_line(nd, line, l, r); if(nd == nullptr) nd = new Node(inf_line); long long m = (l + r) >> 1; nd->left = _add_segment_line(a, b, nd->left, line, l, m); nd->right = _add_segment_line(a, b, nd->right, line, m, r); return nd; } long long query(long long x, long long l, long long r){ Node *nd = root; long long res = inf; while(r > l && nd != nullptr) { long long m = (l + r) >> 1; res = std::min(res, nd->line.get(x)); if(x < m) { r = m; nd = nd->left; } else { l = m; nd = nd->right; } } return res; } public: // [xl, xr) LiChaoTree(long long lx, long long rx) : lx(lx), rx(rx), root(nullptr) {} void add_line(long long a, long long b) { Line line(a, b); root = _add_line(root, line, lx, rx); } void add_segment_line(long long a, long long b, long long l, long long r) { Line line = Line{a, b}; root = _add_segment_line(l, r, root, line, lx, rx); } long long get(long long x) { return query(x, lx, rx); } }; int main(){ ios::sync_with_stdio(false); cin.tie(0); int n, m; cin >> n >> m; LiChaoTree LCT(0, 1 << 30); vector a(n); priority_queue, vector>, greater>> pq, pq2; for(int i = 0; i < n; i++){ cin >> a[i]; pq2.emplace(a[i], i); } vector>> g(n); vector dp(n, 1ll << 62); for(int i = 0; i < m; i++){ int u, v; ll t; cin >> u >> v >> t; u--, v--; g[u].emplace_back(v, t); g[v].emplace_back(u, t); } dp[0] = 0; pq.emplace(0, 0); vector used(n); while(!pq.empty()){ while(!pq2.empty() && LCT.get(pq2.top().first) < pq.top().first){ auto [d2, v2] = pq2.top(); pq2.pop(); if(used[v2]) continue; dp[v2] = LCT.get(d2); pq.emplace(dp[v2], v2); } auto [d, v] = pq.top(); pq.pop(); if(d > dp[v]) continue; used[v] = true; LCT.add_line(a[v], d); for(auto &&[u, w] : g[v]){ if(d + w >= dp[u]) continue; dp[u] = d + w; pq.emplace(dp[u], u); } } cout << dp.back() << '\n'; }