#729890 (C++17) No.705 ゴミ拾い Hard

• 問題: No.705 ゴミ拾い Hard
• ユーザー: tute7627
• 提出日時: 2022-01-12 02:11:11
• 言語: C++17 (gcc 13.3.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 148 ms / 1,500 ms
• コード長: 10,086 bytes
• コンパイル時間: 2,389 ms
• コンパイル使用メモリ: 212,376 KB
• 最終ジャッジ日時: 2025-01-27 10:34:40
• ジャッジサーバーID （参考情報）: judge3 / judge1

ファイルパターン	結果
sample	AC * 4
other	AC * 40

ソースコード

//#define _GLIBCXX_DEBUG

#include<bits/stdc++.h>
using namespace std;

#define endl '\n'
#define lfs cout<<fixed<<setprecision(10)
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()
#define UNIQUE(a) (a).erase(unique((a).begin(),(a).end()),(a).end())
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9+7;
const ll MOD9 = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template<typename T> using PQ = priority_queue<T>;
template<typename T> using QP = priority_queue<T,vector<T>,greater<T>>;
template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});}
void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}  
template<typename T1,typename T2,typename T3>void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);};  
template<typename T>void debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout<<sv<<v[i][j];cout<<endl;}};
template<typename T>void debug(const T &v,ll n,string sv=" "){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout<<sv<<v[i];cout<<endl;};
template<typename T>void debug(const vector<T>&v){debug(v,v.size());}
template<typename T>void debug(const vector<vector<T>>&v){for(auto &vv:v)debug(vv,vv.size());}
template<typename T>void debug(stack<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(queue<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(deque<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop_front();}cout<<endl;}
template<typename T>void debug(PQ<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(QP<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(const set<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T>void debug(const multiset<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T,size_t size>void debug(const array<T, size> &a){for(auto z:a)cout<<z<<" ";cout<<endl;}
template<typename T,typename V>void debug(const map<T,V>&v){for(auto z:v)cout<<"["<<z.first<<"]="<<z.second<<",";cout<<endl;}
template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}
ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;}
vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};
template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}
template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << p.first << " " << p.second;}
template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;}
template<typename T>void rearrange(vector<int>&ord, vector<T>&v){
  auto tmp = v;
  for(int i=0;i<tmp.size();i++)v[i] = tmp[ord[i]];
}
template<typename Head, typename... Tail>void rearrange(vector<int>&ord,Head&& head, Tail&&... tail){
  rearrange(ord, head);
  rearrange(ord, tail...);
}
template<typename T> vector<int> ascend(const vector<T>&v){
  vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
  sort(ord.begin(),ord.end(),[&](int i,int j){return v[i]<v[j];});
  return ord;
}
template<typename T> vector<int> descend(const vector<T>&v){
  vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
  sort(ord.begin(),ord.end(),[&](int i,int j){return v[i]>v[j];});
  return ord;
}
template<typename T> vector<T> inv_perm(const vector<T>&ord){
  vector<T>inv(ord.size());
  for(int i=0;i<ord.size();i++)inv[ord[i]] = i;
  return inv;
}
ll FLOOR(ll n,ll div){assert(div>0);return n>=0?n/div:(n-div+1)/div;}
ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;}
ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;}
ll modulo(ll n,ll d){return (n%d+d)%d;};
template<typename T>T min(const vector<T>&v){return *min_element(v.begin(),v.end());}
template<typename T>T max(const vector<T>&v){return *max_element(v.begin(),v.end());}
template<typename T>T acc(const vector<T>&v){return accumulate(v.begin(),v.end(),T(0));};
template<typename T>T reverse(const T &v){return T(v.rbegin(),v.rend());};
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
int popcount(ll x){return __builtin_popcountll(x);};
int poplow(ll x){return __builtin_ctzll(x);};
int pophigh(ll x){return 63 - __builtin_clzll(x);};
template<typename T>T poll(queue<T> &q){auto ret=q.front();q.pop();return ret;};
template<typename T>T poll(priority_queue<T> &q){auto ret=q.top();q.pop();return ret;};
template<typename T>T poll(QP<T> &q){auto ret=q.top();q.pop();return ret;};
template<typename T>T poll(stack<T> &s){auto ret=s.top();s.pop();return ret;};
ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;}
ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;}
ll POW(ll x, ll k){ll ret=1;for(int i=0;i<k;i++){if(LLONG_MAX/x<=ret)return LLONG_MAX;ret*=x;}return ret;}
template< typename T = int >
struct edge {
  int to;
  T cost;
  int id;
  edge():id(-1){};
  edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){}
  operator int() const { return to; }
};

template<typename T>
using Graph = vector<vector<edge<T>>>;
template<typename T>
Graph<T>revgraph(const Graph<T> &g){
  Graph<T>ret(g.size());
  for(int i=0;i<g.size();i++){
    for(auto e:g[i]){
      int to = e.to;
      e.to = i;
      ret[to].push_back(e);
    }
  }
  return ret;
}
template<typename T>
Graph<T> readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){
  Graph<T> ret(n);
  for(int es = 0; es < m; es++){
    int u,v;
    T w=1;
    cin>>u>>v;u-=indexed,v-=indexed;
    if(weighted)cin>>w;
    ret[u].emplace_back(v,w,es);
    if(!directed)ret[v].emplace_back(u,w,es);
  }
  return ret;
}
template<typename T>
Graph<T> readParent(int n,int indexed=1,bool directed=true){
  Graph<T>ret(n);
  for(int i=1;i<n;i++){
    int p;cin>>p;
    p-=indexed;
    ret[p].emplace_back(i);
    if(!directed)ret[i].emplace_back(p);
  }
  return ret;
}
#include <functional>
#include <memory>
#include <vector>

template <class T> class larsch {
  struct reduce_row;
  struct reduce_col;

  struct reduce_row {
    int n;
    std::function<T(int, int)> f;
    int cur_row;
    int state;
    std::unique_ptr<reduce_col> rec;

    reduce_row(int n_) : n(n_), f(), cur_row(0), state(0), rec() {
      const int m = n / 2;
      if (m != 0) {
        rec = std::make_unique<reduce_col>(m);
      }
    }

    void set_f(std::function<T(int, int)> f_) {
      f = f_;
      if (rec) {
        rec->set_f([&](int i, int j) -> T { return f(2 * i + 1, j); });
      }
    }

    int get_argmin() {
      const int cur_row_ = cur_row;
      cur_row += 1;
      if (cur_row_ % 2 == 0) {
        const int prev_argmin = state;
        const int next_argmin = [&]() {
          if (cur_row_ + 1 == n) {
            return n - 1;
          } else {
            return rec->get_argmin();
          }
        }();
        state = next_argmin;
        int ret = prev_argmin;
        for (int j = prev_argmin + 1; j <= next_argmin; j += 1) {
          if (f(cur_row_, ret) > f(cur_row_, j)) {
            ret = j;
          }
        }
        return ret;
      } else {
        if (f(cur_row_, state) <= f(cur_row_, cur_row_)) {
          return state;
        } else {
          return cur_row_;
        }
      }
    }
  };

  struct reduce_col {
    int n;
    std::function<T(int, int)> f;
    int cur_row;
    std::vector<int> cols;
    reduce_row rec;

    reduce_col(int n_) : n(n_), f(), cur_row(0), cols(), rec(n) {}

    void set_f(std::function<T(int, int)> f_) {
      f = f_;
      rec.set_f([&](int i, int j) -> T { return f(i, cols[j]); });
    }

    int get_argmin() {
      const int cur_row_ = cur_row;
      cur_row += 1;
      const auto cs = [&]() -> std::vector<int> {
        if (cur_row_ == 0) {
          return {{0}};
        } else {
          return {{2 * cur_row_ - 1, 2 * cur_row_}};
        }
      }();
      for (const int j : cs) {
        while ([&]() {
          const int size = cols.size();
          return size != cur_row_ && f(size - 1, cols.back()) > f(size - 1, j);
        }()) {
          cols.pop_back();
        }
        if (cols.size() != n) {
          cols.push_back(j);
        }
      }
      return cols[rec.get_argmin()];
    }
  };

  std::unique_ptr<reduce_row> base;

public:
  larsch(int n, std::function<T(int, int)> f)
      : base(std::make_unique<reduce_row>(n)) {
    base->set_f(f);
  }

  int get_argmin() { return base->get_argmin(); }
};

/**
 * @brief LARSCH Algorithm
 * @docs docs/larsch.md
 */
int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
  ll n;cin>>n;
  vector<ll>a(n),x(n),y(n);
  rep(i,0,n)cin>>a[i];
  rep(i,0,n)cin>>x[i];
  rep(i,0,n)cin>>y[i];
  auto th=[](ll x){
    return x*x*x;
  };
  vector<ll>dp(n+1,0);
  dp[0]=0;
  auto f=[&](int to,int from)->ll{
    to++;
    if(to<=from)return INF;
    else{
      return dp[from]+th(abs(a[to-1]-x[from]))+th(y[from]);
    }
  };
  larsch<ll>solve(n,f);
  rep(i,0,n){
    dp[i+1]=f(i,solve.get_argmin());
  }
  cout<<dp[n]<<endl;
  return 0;
}