結果

問題 No.703 ゴミ拾い Easy
コンテスト
ユーザー Haar
提出日時 2019-03-20 17:56:33
言語 C++14
(gcc 13.3.0 + boost 1.89.0)
結果
AC  
実行時間 119 ms / 1,500 ms
コード長 4,047 bytes
記録
コンパイル時間 1,957 ms
コンパイル使用メモリ 182,692 KB
実行使用メモリ 15,056 KB
最終ジャッジ日時 2025-01-02 14:07:47
合計ジャッジ時間 6,394 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 46
権限があれば一括ダウンロードができます

ソースコード

diff #
raw source code 

#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 <misc/C++/Debug.cpp>
#else
#define dump(x)
#endif

#define gcd __gcd

using namespace std;
template <class T> constexpr T lcm(T m, T n){return m/gcd(m,n)*n;}

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 T, typename U> T& chmin(T &a, const U &b){return a = (a<=b?a:b);}
template <typename T, typename U> T& chmax(T &a, const U &b){return a = (a>=b?a:b);}
template <typename T, size_t N, typename U> void fill_array(T (&a)[N], const U &v){fill((U*)a, (U*)(a+N), v);}


template <typename T> class LiChaoSegmentTree{
  using line = pair<T,T>;

  struct node{
    line l;
    node *left, *right;
    node(const line &l): l(l), left(nullptr), right(nullptr){}
  };

  vector<T> xs;
  int n;
  node *root;
  T e;
  function<bool(T,T)> cmp;
  function<T(T,T)> chm;

public:
  LiChaoSegmentTree(const vector<T> &xs, const bool min_mode, const T &e): xs(xs), n(xs.size()), root(nullptr), e(e){
    if(min_mode){
      cmp = [](const T &a, const T &b){return a < b;};
      chm = [](const T &a, const T &b){return min(a,b);};
    }else{
      cmp = [](const T &a, const T &b){return a > b;};
      chm = [](const T &a, const T &b){return max(a,b);};
    }
  }

  T apply(const line &l, const T &x) const{
    return l.fst*x + l.snd;
  }

protected:
  node* add(node *t, const int left, const int right, line l){ // [l,r]
    if(!t) return new node(l);

    if(cmp(apply(t->l, xs[left]), apply(l, xs[left])) and cmp(apply(t->l, xs[right]), apply(l, xs[right]))){
      return t;
    }
    if(!cmp(apply(t->l, xs[left]), apply(l, xs[left])) and !cmp(apply(t->l, xs[right]), apply(l, xs[right]))){
      t->l = l;
      return t;
    }

    int mid = (left + right) / 2;

    if(!cmp(apply(t->l, xs[mid]), apply(l, xs[mid]))) swap(t->l, l);
    if(!cmp(apply(t->l, xs[left]), apply(l, xs[left]))){
      t->left = add(t->left, left, mid, l);
    }else{
      t->right = add(t->right, mid+1, right, l);
    }

    return t;
  }

public:
  void add_line(T a, T b){
    root = add(root, 0, n-1, make_pair(a,b));
  }

  

protected:
  T query(node *t, const int left, const int right, const int i) const{
    if(!t) return e;
    if(right == left) return apply(t->l, xs[i]);
    int mid = (left + right) / 2;
    if(i <= mid) return chm(apply(t->l, xs[i]), query(t->left, left, mid, i));
    else return chm(apply(t->l, xs[i]), query(t->right, mid+1, right, i));
  }
  
public:
  T query(const T &x) const{
    return query(root, 0, n-1, lower_bound(ALL(xs), x) - xs.begin());
  }
};


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

  int n;
  while(cin >> n){
    vector<LLI> a(n), x(n), y(n); cin >> a >> x >> y;

    LiChaoSegmentTree<LLI> cht(a,true,LLONG_MAX);

    vector<LLI> dp(n);
    
    dp[0] = y[0]*y[0] + (x[0]-a[0])*(x[0]-a[0]);
    cht.add_line(-2*x[1], dp[0]+y[1]*y[1]+x[1]*x[1]);

    FOR(i,1,n){
      dp[i] = y[0]*y[0] + (a[i]-x[0])*(a[i]-x[0]);

      chmin(dp[i], cht.query(a[i]) + a[i]*a[i]);

      if(i<n-1) cht.add_line(-2*x[i+1], dp[i]+y[i+1]*y[i+1]+x[i+1]*x[i+1]);
    }
    cout << dp[n-1] << endl;
  }
  
  return 0;
}
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