#include #include using namespace std; using namespace atcoder; #define overload4(_1, _2, _3, _4, name, ...) name #define rep1(n) for(int i = 0; i < (int)(n); ++i) #define rep2(i, n) for(int i = 0; i < (int)(n); ++i) #define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i) #define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i) #define ALL(a) (a).begin(), (a).end() #define Sort(a) (sort((a).begin(), (a).end())) #define RSort(a) (sort((a).rbegin(), (a).rend())) #define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end())) typedef long long int ll; typedef unsigned long long ul; typedef long double ld; typedef vector vi; typedef vector vll; typedef vector vc; typedef vector vst; typedef vector vd; typedef vector vld; typedef pair P; template long long sum(const T& a){ return accumulate(a.begin(), a.end(), 0LL); } template auto min(const T& a){ return *min_element(a.begin(), a.end()); } template auto max(const T& a){ return *max_element(a.begin(), a.end()); } const long long MINF = 0x7fffffffffff; const long long INF = 0x1fffffffffffffff; const long long MOD = 998244353; const long double EPS = 1e-9; const long double PI = acos(-1); template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } template istream &operator>>(istream &is, pair &p){ is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const pair &p){ os << "(" << p.first << ", " << p.second << ")"; return os; } template istream &operator>>(istream &is, vector &v){ for(T &in : v) is >> in; return is; } template ostream &operator<<(ostream &os, const vector &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; } template ostream &operator<<(ostream &os, const map &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; } template ostream &operator<<(ostream &os, const set &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, const multiset &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, queue q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; } template ostream &operator<<(ostream &os, deque q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; } template ostream &operator<<(ostream &os, stack st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; } template ostream &operator<<(ostream &os, priority_queue pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; } template inline T vin(T& vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; } template inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; } template void in(T&... a){ (cin >> ... >> a); } void out(){ cout << '\n'; } template void out(const T& a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; } template void inGraph(vector>& G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } } template struct DynamicLiChaoTree{ struct Line{ T a, b; Line(T _a, T _b) : a(_a), b(_b) {} inline T get(T x) const { return a * x + b; } }; struct Node{ Line x; Node *l, *r; Node(const Line &x) : x{x}, l{nullptr}, r{nullptr} {} }; Node *root = nullptr; DynamicLiChaoTree() {} private: Node *add_line_(Node *t, Line &x, const T &l, const T &r, const T &x_l, const T &x_r){ if(!t){ return new Node(x); } T t_l = t->x.get(l), t_r = t->x.get(r); if(t_l <= x_l && t_r <= x_r){ return t; } else if(t_l >= x_l && t_r >= x_r){ t->x = x; return t; } else{ T m = (l + r) / 2; if(m == r) --m; T t_m = t->x.get(m), x_m = x.get(m); if(t_m > x_m){ swap(t->x, x); if(t_l <= x_l){ t->l = add_line_(t->l, x, l, m, t_l, t_m); } else{ t->r = add_line_(t->r, x, m + 1, r, t_m + x.a, t_r); } } else{ if(x_l <= t_l){ t->l = add_line_(t->l, x, l, m, x_l, x_m); } else{ t->r = add_line_(t->r, x, m + 1, r, x_m + x.a, x_r); } } return t; } } Node *add_segment_(Node *t, Line &x, const T &a, const T &b, const T &l, const T &r, const T &x_l, const T &x_r){ if(r < a || b < l) return t; if(a <= l && r <= b){ Line y{x}; return add_line_(t, y, l, r, x_l, x_r); } if(t){ T t_l = t->x.get(l), t_r = t->x.get(r); if(t_l <= x_l && t_r <= x_r) return t; } else{ t = new Node(Line(0, id)); } T m = (l + r) / 2; if(m == r) --m; T x_m = x.get(m); t->l = add_segment_(t->l, x, a, b, l, m, x_l, x_m); t->r = add_segment_(t->r, x, a, b, m + 1, r, x_m + x.a, x_r); return t; } T query_(const Node *t, const T &l, const T &r, const T &x_c) const { if(!t) return id; if(l == r) return t->x.get(x_c); T m = (l + r) / 2; if(m == r) --m; if(x_c <= m){ return min(t->x.get(x_c), query_(t->l, l, m, x_c)); } else{ return min(t->x.get(x_c), query_(t->r, m + 1, r, x_c)); } } public: void add_line(const T &a, const T &b){ Line x(a, b); root = add_line_(root, x, x_low, x_high, x.get(x_low), x.get(x_high)); } void add_segment(const T &l, const T &r, const T &a, const T &b){ Line x(a, b); root = add_segment_(root, x, l, r - 1, x_low, x_high, x.get(x_low), x.get(x_high)); } T query(const T &x) const { return query_(root, x_low, x_high, x); } }; void input(){ } void solve(){ ll n, m; in(n, m); vll w; vin(w, n); vector>> G(n); rep(i, m){ ll u, v, t; in(u, v, t); u--, v--; G[u].push_back({v, t}); G[v].push_back({u, t}); } vector

p(n); rep(i, n) p[i] = {w[i], i}; Sort(p); DynamicLiChaoTree lct; vll cost(n, INF); cost[0] = 0; priority_queue, greater

> pq; pq.push({0, 0}); ll curr = 0; while(pq.size() || curr < n){ if(pq.empty()){ auto [wi, idx] = p[curr]; if(chmin(cost[idx], lct.query(wi))){ pq.emplace(cost[idx], idx); } curr++; continue; } auto [c, v] = pq.top(); ll ok = -1, ng = n; while(abs(ok - ng) > 1){ ll mid = (ok + ng) / 2; auto [wi, idx] = p[mid]; if(lct.query(wi) <= c){ ok = mid; } else{ ng = mid; } } rep(i, curr, ok + 1){ auto [wi, idx] = p[i]; if(chmin(cost[idx], lct.query(wi))){ pq.emplace(cost[idx], idx); } } if(curr < ok + 1){ curr = ok + 1; continue; } pq.pop(); lct.add_line(w[v], cost[v]); if(cost[v] < c) continue; for(auto [nv, t] : G[v]){ if(chmin(cost[nv], c + t)){ pq.push({cost[nv], nv}); } } } out(cost[n - 1]); } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(20); input(); solve(); }