#982488 (C++17) No.2764 Warp Drive Spacecraft

• 問題: No.2764 Warp Drive Spacecraft
• ユーザー: TKTYI
• 提出日時: 2024-05-17 23:09:19
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 530 ms / 3,000 ms
• コード長: 6,761 bytes
• コンパイル時間: 5,058 ms
• コンパイル使用メモリ: 293,180 KB
• 実行使用メモリ: 25,044 KB
• 最終ジャッジ日時: 2024-07-17 20:24:30
• 合計ジャッジ時間: 16,350 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,812 KB
testcase_01	AC	2 ms; 6,812 KB
testcase_02	AC	2 ms; 6,940 KB
testcase_03	AC	2 ms; 6,940 KB
testcase_04	AC	2 ms; 6,944 KB
testcase_05	AC	1 ms; 6,944 KB
testcase_06	AC	2 ms; 6,940 KB
testcase_07	AC	2 ms; 6,940 KB
testcase_08	AC	2 ms; 6,940 KB
testcase_09	AC	2 ms; 6,944 KB
testcase_10	AC	3 ms; 6,944 KB
testcase_11	AC	2 ms; 6,940 KB
testcase_12	AC	3 ms; 6,944 KB
testcase_13	AC	3 ms; 6,944 KB
testcase_14	AC	2 ms; 6,940 KB
testcase_15	AC	2 ms; 6,940 KB
testcase_16	AC	271 ms; 22,068 KB
testcase_17	AC	275 ms; 22,152 KB
testcase_18	AC	268 ms; 22,040 KB
testcase_19	AC	416 ms; 19,260 KB
testcase_20	AC	410 ms; 20,552 KB
testcase_21	AC	418 ms; 20,388 KB
testcase_22	AC	414 ms; 20,348 KB
testcase_23	AC	414 ms; 19,408 KB
testcase_24	AC	420 ms; 20,452 KB
testcase_25	AC	421 ms; 20,384 KB
testcase_26	AC	521 ms; 24,352 KB
testcase_27	AC	513 ms; 24,244 KB
testcase_28	AC	522 ms; 24,540 KB
testcase_29	AC	527 ms; 24,748 KB
testcase_30	AC	512 ms; 24,176 KB
testcase_31	AC	530 ms; 25,044 KB
testcase_32	AC	526 ms; 25,028 KB
testcase_33	AC	261 ms; 15,360 KB
testcase_34	AC	263 ms; 15,232 KB
testcase_35	AC	265 ms; 15,232 KB
testcase_36	AC	387 ms; 22,080 KB
testcase_37	AC	270 ms; 18,952 KB
testcase_38	AC	236 ms; 17,664 KB

ソースコード

#include<bits/stdc++.h>
#include<atcoder/all>
using namespace std;
using namespace atcoder;
typedef long long int ll;
typedef long double ld;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vvvi> vvvvi;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<vvb> vvvb;
typedef vector<vvvb> vvvvb;
typedef pair<ll,ll> pi;
typedef pair<ll,pi> ppi;
typedef pair<ll,ppi> pppi;
typedef pair<ll,pppi> ppppi;
#define FOR(i,l,r) for(ll i=l;i<r;i++)
#define REP(i,n) FOR(i,0,n)
#define RFOR(i,l,r) for(ll i=r-1;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<boost/multiprecision/cpp_int.hpp>
namespace mp=boost::multiprecision;
using Bint=mp::cpp_int;
*/
template<typename T>using min_priority_queue=priority_queue<T,vector<T>,greater<T>>;
template<typename T1,typename T2>ostream&operator<<(ostream&os,pair<T1,T2>p){os<<p.F<<" "<<p.S;return os;}
template<typename T1,typename T2>istream&operator>>(istream&is,pair<T1,T2>&p){is>>p.F>>p.S;return is;}
template<typename T>ostream&operator<<(ostream&os,vector<T>v){REP(i,sz(v))os<<v[i]<<(i+1!=sz(v)?" ":"");return os;}
template<typename T>istream&operator>>(istream&is,vector<T>&v){for(T&in:v)is>>in;return is;}
template<class T>bool chmax(T&a,T b){if(a<b){a=b;return 1;}return 0;}
template<class T>bool chmin(T&a,T b){if(b<a){a=b;return 1;}return 0;}
ld dist(ld x1,ld y1,ld x2,ld y2){return sqrtl((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));}
vi fast_mod_convolution(vi&a,vi&b,ll mod){
  const ll m1=167772161,m2=469762049,m3=1224736769;
  const ll m1_inv_m2=inv_mod(m1,m2);
  const ll m12_inv_m3=inv_mod(m1*m2,m3);
  const ll m12_mod=m1*m2%mod;
  auto x=convolution<m1>(a,b);
  auto y=convolution<m2>(a,b);
  auto z=convolution<m3>(a,b);
  vector<ll>ret(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<mint> vm;
typedef vector<vm> vvm;
typedef vector<vvm> vvvm;
typedef vector<vvvm> vvvvm;
ostream&operator<<(ostream&os,mint a){os<<a.val();return os;}
istream&operator>>(istream&is,mint&a){int x;is>>x;a=mint(x);return is;}
//*/
template<typename T=long double,class comp=less<T>>
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<pair<T,T>,pair<T,T>>>segments;
    set<pair<pair<T,T>,pair<T,T>>>lines;
    T intersection(pair<T,T>l1,pair<T,T>l2){
        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){
        pair<T,T>l=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<T,T>,pair<T,T>>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<pair<T,T>,pair<T,T>>>P;
            for(auto i=left;i!=right;i++)P.emplace_back(*i);
            for(pair<pair<T,T>,pair<T,T>>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<T,T>,pair<T,T>>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<T,T>,pair<T,T>>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<<line.first<<"x"<<(line.second>=0?"+":"")<<line.second<<"("<<seg.F<<","<<seg.S<<") ";}cout<<endl;
    }
};
int main(){
  ll N,M;cin>>N>>M;
  vi W(N);cin>>W;
  vector<vector<pi>>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_queue<pi>Q;
  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_dynamic<ld>CTD;
  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<<endl;
  return 0;
}