#312652 (C++14) No.409 ダイエット

• 問題: No.409 ダイエット
• ユーザー: Haar
• 提出日時: 2019-01-25 14:49:21
• 言語: C++14 (gcc 13.3.0 + boost 1.89.0)
• 結果: WA
• 実行時間: -
• コード長: 6,304 bytes
• コンパイル時間: 1,827 ms
• コンパイル使用メモリ: 180,400 KB
• 実行使用メモリ: 12,288 KB
• 最終ジャッジ日時: 2024-09-16 04:47:45
• 合計ジャッジ時間: 16,853 ms
• ジャッジサーバーID （参考情報）: judge1 / judge6

ファイルパターン	結果
other	AC * 86 WA * 6

ソースコード

#include <bits/stdc++.h>
#define FOR(v, a, b) for(int v = (a); v < (b); ++v)
#define FORE(v, a, b) for(int v = (a); v <= (b); ++v)
#define REP(v, n) FOR(v, 0, n)
#define REPE(v, n) FORE(v, 0, n)
#define REV(v, a, b) for(int v = (a); v >= (b); --v)
#define ALL(x) (x).begin(), (x).end()
#define ITR(it, c) for(auto it = (c).begin(); it != (c).end(); ++it)
#define RITR(it, c) for(auto it = (c).rbegin(); it != (c).rend(); ++it)
#define EXIST(c,x) ((c).find(x) != (c).end())
#define LLI long long int
#define fst first
#define snd second
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
#ifndef M_E
#define M_E 2.71828182845904523536
#endif
#ifdef DEBUG
#include <boost/core/demangle.hpp>
#define dump(x) cerr << "L" << __LINE__ << ": in " << __PRETTY_FUNCTION__ << " \e[32;1m" << boost::core::demangle(typeid(x).name()) << "\e[37m" << " " << (#x) << " = " << (x) << "\e[m" << endl;
#else
#define dump(x)
#endif
using namespace std;
#define gcd __gcd
template <class T> constexpr T lcm(T m, T n){return m*n/gcd(m,n);}

template <typename T> using V = vector<T>;
template <typename T, typename U> using P = pair<T,U>;
template <typename I> void join(ostream &ost, I s, I t, string d=" "){for(auto i=s; i!=t; ++i){if(i!=s)ost<<d; ost<<*i;}ost<<endl;}
template <typename T> istream& operator>>(istream &is, vector<T> &v){for(auto &a : v) is >> a; return is;}
template <typename T, typename U> istream& operator>>(istream &is, pair<T,U> &p){is >> p.first >> p.second; return is;}

template <typename Iter> ostream& out_container(ostream &os, Iter first, Iter last){
  os << "{"; auto itr = first; while(itr != last){if(itr != first) os << ","; os << *itr; ++itr;} os << "}"; return os;
}

template <typename T> ostream& operator<<(ostream &os, const vector<T> &c){return out_container(os,ALL(c));}
template <typename T> ostream& operator<<(ostream &os, const deque<T> &c){return out_container(os,ALL(c));}
template <typename T> ostream& operator<<(ostream &os, const set<T> &c){return out_container(os,ALL(c));}
template <typename T> ostream& operator<<(ostream &os, const unordered_set<T> &c){return out_container(os,ALL(c));}
template <typename T, typename U> ostream& operator<<(ostream &os, const map<T,U> &c){return out_container(os,ALL(c));}
template <typename T, typename U> ostream& operator<<(ostream &os, const unordered_map<T,U> &c){return out_container(os,ALL(c));}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T,U> &p){os << "(" << p.first << "," << p.second << ")"; return os;}

template <typename T> T& chmin(T &a, const T &b){return a = min(a,b);}
template <typename T> T& chmax(T &a, const T &b){return a = max(a,b);}


// 追加直線の傾きが単調減少、minクエリの値が単調増加
template <typename T> class ConvexHullTrick{
public:
  deque<pair<T,T>> lines;

  bool is_needless(pair<T,T> a, pair<T,T> b, pair<T,T> c){
    return (a.snd-b.snd)*(a.fst-c.fst) >= (a.snd-c.snd)*(a.fst-b.fst);
  }
  
  void add(T a, T b){
    if(!lines.empty()){
      auto l = lines.back();
      if(l.fst == a){
	if(l.snd < b) return;
	else lines.pop_back();
      }
    }
    while(lines.size()>=2 && is_needless(make_pair(a,b), lines.back(), *(lines.end()-2))){
      lines.pop_back();
    }
    lines.push_back(make_pair(a,b));
  }

  T apply(pair<T,T> f, T x){
    return f.fst*x + f.snd;
  }

  T query(T x){
    while(lines.size()>=2 && apply(lines[0],x)>apply(lines[1],x)){
      lines.pop_front();
    }
    return apply(lines[0],x);
  }
};

class Rational{
public:
  int64_t nume, deno;
  Rational(): nume(0), deno(1){}
  Rational(int64_t num): nume(num), deno(1){} 
  Rational(int64_t num, int64_t den){
    int64_t g = gcd(num,den);
    nume = num/g;
    deno = den/g;
  }
  Rational& operator+=(const Rational &a);
  Rational& operator-=(const Rational &a);
  Rational& operator*=(const Rational &a);
  Rational& operator/=(const Rational &a);
};

ostream& operator<<(ostream &os, const Rational &r){os << r.nume << "/" << r.deno; return os;}
istream& operator>>(istream &is, Rational &r){is >> r.nume; r.deno = 1; return is;}

Rational operator-(const Rational &a){return Rational(-a.nume, a.deno);}

Rational operator+(const Rational &a, const Rational &b){int64_t l = lcm(a.deno,b.deno); return Rational(a.nume*l/a.deno + b.nume*l/b.deno, l);}
Rational operator-(const Rational &a, const Rational &b){int64_t l = lcm(a.deno,b.deno); return Rational(a.nume*l/a.deno - b.nume*l/b.deno, l);}
Rational operator*(const Rational &a, const Rational &b){return Rational(a.nume*b.nume, a.deno*b.deno);}
Rational operator/(const Rational &a, const Rational &b){return Rational(a.nume*b.deno, a.deno*b.nume);}

bool operator==(const Rational &a, const Rational &b){return a.nume == b.nume && a.deno == b.deno;}
bool operator!=(const Rational &a, const Rational &b){return !(a==b);}
bool operator<(const Rational &a, const Rational &b){return a.nume*b.deno < b.nume*a.deno;}
bool operator<=(const Rational &a, const Rational &b){return a.nume*b.deno <= b.nume*a.deno;}
bool operator>(const Rational &a, const Rational &b){return !(a<=b);}
bool operator>=(const Rational &a, const Rational &b){return !(a<b);}

double to_double(const Rational &a){return (double)a.nume/a.deno;}

Rational& Rational::operator+=(const Rational &a){*this = *this+a; return *this;}
Rational& Rational::operator-=(const Rational &a){*this = *this-a; return *this;}
Rational& Rational::operator*=(const Rational &a){*this = *this*a; return *this;}
Rational& Rational::operator/=(const Rational &a){*this = *this/a; return *this;}

Rational abs(const Rational &a){return Rational(abs(a.nume), abs(a.deno));}



int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);

  LLI N;
  Rational A,B,W;
  while(cin >> N >> A >> B >> W){
    vector<Rational> D(N); cin >> D;

    vector<Rational> dp(N);

    ConvexHullTrick<Rational> cht;
    dp[0] = W+D[0];
    cht.add(-B/2,dp[0]+A*0+B*0*(0+1)/2);
    
    FOR(i,1,N){
      Rational t = cht.query(Rational(i));
      //dump(t);
      dp[i] = D[i]-A*(i-1)+B*i*i/2+t;
      chmin(dp[i], D[i]+W-A*i+B*i*(i+1)/2);

      cht.add(-B*(2*i+1)/2,dp[i]+A*i+B*i*(i+1)/2);
    }
    
    //dump(dp);

    Rational ans = -A*(N-1)+B*N*N/2+cht.query(N);
    chmin(ans, W-A*N+B*N*(N+1)/2);
    
    cout << ans.nume << endl;
  }
  
  return 0;
}