#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #ifdef LOCAL # include "debug_print.hpp" # define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else # define debug(...) (static_cast(0)) #endif using namespace std; #define rep1(a) for(int i = 0; i < a; i++) #define rep2(i, a) for(int i = 0; i < a; i++) #define rep3(i, a, b) for(int i = a; i < b; i++) #define rep4(i, a, b, c) for(int i = a; i < b; i += c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(a) for(int i = (a)-1; i >= 0; i--) #define rrep2(i, a) for(int i = (a)-1; i >= 0; i--) #define rrep3(i, a, b) for(int i = (b)-1; i >= a; i--) #define rrep4(i, a, b, c) for(int i = (b)-1; i >= a; i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() #define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() ); #define pb push_back using ll = long long; using D = double; using LD = long double; using P = pair; using vi = vector; using vl = vector; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) template using PQ = priority_queue>; template using minPQ = priority_queue, greater>; templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &...u) { cout << t; outr(u...); } #line 1 "structure/convex-hull-trick/dynamic-li-chao-tree.hpp" /** * @brief Dynamic-Li-Chao-Tree * */ 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; DynamicLiChaoTree() : root{nullptr} {} 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 (x_l >= t_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 (t_l >= x_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; } } 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)); } 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; } 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 Node *t, const T &l, const T &r, const T &x) const { if (!t) return id; if (l == r) return t->x.get(x); T m = (l + r) / 2; if (m == r) --m; if (x <= m) return min(t->x.get(x), query(t->l, l, m, x)); else return min(t->x.get(x), query(t->r, m + 1, r, x)); } T query(const T &x) const { return query(root, x_low, x_high, x); } }; int main(){ ios_base::sync_with_stdio(false); cin.tie(nullptr); int n,m; in(n,m); vector w(n); in(w); vector>> g(n); rep(i,m){ int u,v; ll t; in(u,v,t); u--; v--; g[u].pb({v,t}); g[v].pb({u,t}); } const ll INF = 4e18; vector d(n,INF),e(n,INF); d[0] = e[n-1] = 0; minPQ> pq; pq.push({0,0}); while(pq.size()){ auto [cd,cv] = pq.top(); pq.pop(); if(d[cv] > cd) continue; for(auto [nv, w] : g[cv]){ if(d[nv] > w+cd){ d[nv]=w+cd; pq.push({d[nv],nv}); } } } pq.push({0,n-1}); while(pq.size()){ auto [cd,cv] = pq.top(); pq.pop(); if(e[cv] > cd) continue; for(auto [nv, w] : g[cv]){ if(e[nv] > w+cd){ e[nv]=w+cd; pq.push({e[nv],nv}); } } } DynamicLiChaoTree t; rep(i,n)if(e[i]!=INF) t.add_line(w[i],e[i]); ll ans = min(w[0]*w[n-1],d[n-1]); rep(i,n)if(d[i]!=INF){ chmin(ans, t.query(w[i])+d[i]); } out(ans); }