#include #include using namespace std; using namespace atcoder; typedef long long int ll; typedef long double ld; typedef vector vi; typedef vector vvi; typedef vector vvvi; typedef vector vvvvi; typedef vector vb; typedef vector vvb; typedef vector vvvb; typedef vector vvvvb; typedef pair pi; typedef pair ppi; typedef pair pppi; typedef pair ppppi; #define FOR(i,l,r) for(ll i=l;i=l;i--) #define RREP(i,n) RFOR(i,0,n) #define ALL(x) x.begin(),x.end() #define F first #define S second #define BS(A,x) binary_search(ALL(A),x) #define LB(A,x) (ll)(lower_bound(ALL(A),x)-A.begin()) #define UB(A,x) (ll)(upper_bound(ALL(A),x)-A.begin()) #define COU(A,x) (UB(A,x)-LB(A,x)) #define sz(c) ((ll)(c).size()) /* #include namespace mp=boost::multiprecision; using Bint=mp::cpp_int; */ templateusing min_priority_queue=priority_queue,greater>; templateostream&operator<<(ostream&os,pairp){os<istream&operator>>(istream&is,pair&p){is>>p.F>>p.S;return is;} templateostream&operator<<(ostream&os,vectorv){REP(i,sz(v))os<istream&operator>>(istream&is,vector&v){for(T&in:v)is>>in;return is;} templatebool chmax(T&a,T b){if(abool chmin(T&a,T b){if(b(a,b); auto y=convolution(a,b); auto z=convolution(a,b); vectorret(sz(a)+sz(b)-1); REP(i,sz(ret)){ ll v1=(y[i]-x[i])*m1_inv_m2%m2;if(v1<0)v1+=m2; ll v2=(z[i]-(x[i]+m1*v1)%m3)*m12_inv_m3%m3;if(v2<0)v2+=m3; ret[i]=(x[i]+m1*v1+m12_mod*v2)%mod; } return ret; } const ld EPS=1e-8; //* using mint=modint998244353; const ll mod=998244353; //*/ /* using mint=modint1000000007; const ll mod=1000000007; //*/ //using mint=modint; //* typedef vector vm; typedef vector vvm; typedef vector vvvm; typedef vector vvvvm; ostream&operator<<(ostream&os,mint a){os<>(istream&is,mint&a){int x;is>>x;a=mint(x);return is;} //*/ template> struct convex_hull_trick_dynamic{ //maxを求めるよ! //compは機能しないよ! private: const T INF=1e18; set,pair>>segments; set,pair>>lines; T intersection(pairl1,pairl2){ return (l2.second-l1.second)/(l1.first-l2.first); } public: T get(T x){ auto it=prev(segments.lower_bound(make_pair(make_pair(x,INF),make_pair(INF,INF)))); return (*it).second.first*x+(*it).second.second; } void add(T a,T b){ pairl=make_pair(a,b); if(lines.size()==0){ lines.insert(make_pair(l,make_pair(-INF,INF))); segments.insert(make_pair(make_pair(-INF,INF),l)); return; } auto it=lines.lower_bound(make_pair(l,make_pair(-INF,-INF))); if(it!=lines.end()&&(*it).first.first==a)return; if(it!=lines.begin()&&(*prev(it)).first.first==a){ pair,pair>p=*prev(it); lines.erase(prev(it)); segments.erase(make_pair(p.second,p.first)); it=lines.lower_bound(make_pair(l,make_pair(-INF,-INF))); } if(it!=lines.end()){ T x=(*it).second.first; if(comp()(a*x+b,(*it).first.first*x+(*it).first.second))return; } { auto left=it,right=it; while(left!=lines.begin()){ T x=(*prev(left)).second.first; if(comp()(a*x+b,(*prev(left)).first.first*x+(*prev(left)).first.second))break; left--; } while(right!=lines.end()){ T x=(*right).second.second; if(comp()(a*x+b,(*right).first.first*x+(*right).first.second))break; right++; } vector,pair>>P; for(auto i=left;i!=right;i++)P.emplace_back(*i); for(pair,pair>p:P){ lines.erase(p); segments.erase(make_pair(p.second,p.first)); } } it=lines.lower_bound(make_pair(l,make_pair(-INF,-INF))); T left=-INF,right=INF; if(it!=lines.begin()){ it--; left=intersection(l,(*it).first); pair,pair>ls=*it; lines.erase(it); segments.erase(make_pair(ls.second,ls.first)); ls.second.second=left; lines.insert(ls); segments.insert(make_pair(ls.second,ls.first)); it=lines.lower_bound(make_pair(l,make_pair(-INF,-INF))); } if(it!=lines.end()){ right=intersection(l,(*it).first); pair,pair>ls=*it; lines.erase(it); segments.erase(make_pair(ls.second,ls.first)); ls.second.first=right; lines.insert(ls); segments.insert(make_pair(ls.second,ls.first)); it=lines.lower_bound(make_pair(l,make_pair(-INF,-INF))); } lines.insert(make_pair(l,make_pair(left,right))); segments.insert(make_pair(make_pair(left,right),l)); } void print(){ for(auto[line,seg]:lines){cout<=0?"+":"")<>N>>M; vi W(N);cin>>W; vector>E(N); REP(i,M){ ll u,v,c;cin>>u>>v>>c;u--;v--; E[u].emplace_back(pi(v,c)); E[v].emplace_back(pi(u,c)); } vi D1(N,1e18),D2(N,1e18); D1[0]=D2[N-1]=0; min_priority_queueQ; Q.emplace(pi(0,0)); while(sz(Q)){ ll d=Q.top().F,v=Q.top().S;Q.pop(); if(d!=D1[v])continue; for(auto[u,c]:E[v])if(chmin(D1[u],D1[v]+c))Q.emplace(pi(D1[u],u)); } Q.emplace(pi(0,N-1)); while(sz(Q)){ ll d=Q.top().F,v=Q.top().S;Q.pop(); if(d!=D2[v])continue; for(auto[u,c]:E[v])if(chmin(D2[u],D2[v]+c))Q.emplace(pi(D2[u],u)); } convex_hull_trick_dynamicCTD; REP(i,N)CTD.add(-W[i],-D2[i]); ld ans=D1[N-1]; REP(i,N)chmin(ans,D1[i]-CTD.get(W[i])); ll _ans=ans; cout<<_ans<