結果

問題 No.2988 Min-Plus Convolution Query
ユーザー 👑 tute7627
提出日時 2024-12-13 01:31:57
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,896 ms / 2,000 ms
コード長 14,032 bytes
コンパイル時間 16,340 ms
コンパイル使用メモリ 326,344 KB
最終ジャッジ日時 2025-02-26 12:50:51
ジャッジサーバーID
（参考情報） 		judge5 / 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 * 2
other AC * 40
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ソースコード

diff #
プレゼンテーションモードにする

//#define _GLIBCXX_DEBUG
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include <debug_print.hpp>
#define OUT(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define OUT(...) (static_cast<void>(0))
#endif
#define endl '\n'
#define lfs cout<<fixed<<setprecision(15)
#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--)
namespace template_tute{
  using ll = long long;
  using ld = long double;
  const ll MOD1 = 1e9+7;
  const ll MOD9 = 998244353;
  const ll INF = 4.1e18;
  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<ll>({a,b,c})-min<ll>({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;}
  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){os<<"[";for(auto &z:v)os << z << ",";os<<"]"; 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 make_pair(v[i],i)<make_pair(v[j],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 make_pair(v[i],-i)>make_pair(v[j],-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;}
  std::ostream &operator<<(std::ostream &dest, __int128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
      __uint128_t tmp = value < 0 ? -value : value;
      char buffer[128];
      char *d = std::end(buffer);
      do {
        --d;
        *d = "0123456789"[tmp % 10];
        tmp /= 10;
      } while (tmp != 0);
      if (value < 0) {
        --d;
        *d = '-';
      }
      int len = std::end(buffer) - d;
      if (dest.rdbuf()->sputn(d, len) != len) {
        dest.setstate(std::ios_base::badbit);
      }
    }
    return dest;
  }
  namespace converter{
    int dict[500];
    const string lower="abcdefghijklmnopqrstuvwxyz";
    const string upper="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
    const string digit="0123456789";
    const string digit1="123456789";
    void regi_str(const string &t){
      for(int i=0;i<t.size();i++){
        dict[t[i]]=i;
      }
    }
    void regi_int(const string &t){
      for(int i=0;i<t.size();i++){
        dict[i]=t[i];
      }
    }
    vector<int>to_int(const string &s,const string &t){
      regi_str(t);
      vector<int>ret(s.size());
      for(int i=0;i<s.size();i++){
        ret[i]=dict[s[i]];
      }
      return ret;
    }
    vector<int>to_int(const string &s){
      auto t=s;
      sort(t.begin(),t.end());
      t.erase(unique(t.begin(),t.end()),t.end());
      return to_int(s,t);
    }
    
    vector<vector<int>>to_int(const vector<string>&s,const string &t){
      regi_str(t);
      vector<vector<int>>ret(s.size(),vector<int>(s[0].size()));
      for(int i=0;i<s.size();i++){
        for(int j=0;j<s[0].size();j++){
          ret[i][j]=dict[s[i][j]];
        }
      }
      return ret;
    }
    vector<vector<int>>to_int(const vector<string>&s){
      string t;
      for(int i=0;i<s.size();i++){
        t+=s[i];
      }
      sort(t.begin(),t.end());t.erase(unique(t.begin(),t.end()),t.end());
      return to_int(s,t);
    }
    string to_str(const vector<int>&s,const string &t){
      regi_int(t);
      string ret;
      for(auto z:s)ret+=dict[z];
      return ret;
    }
    vector<string> to_str(const vector<vector<int>>&s,const string &t){
      regi_int(t);
      vector<string>ret(s.size());
      for(int i=0;i<s.size();i++){
        for(auto z:s[i])ret[i]+=dict[z];
      }
      return ret;
    }
  }
  template< typename T = int >
  struct edge {
    int to;
    T cost;
    int id;
    edge():to(-1),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;
  }
}
using namespace template_tute;
namespace nachia {
template<class Elem>
struct SmawkAlgorithm {
template<class Gen, class Cmp = std::less<Elem>>
std::vector<std::pair<Elem, int>> Solve(
    int height, int width,
    Gen gen,
    Cmp cmp = Cmp()
){
    if(height == 0) return std::vector<std::pair<Elem, int>>(0);
    auto reduce = [&](int yst, const std::vector<int>& cols)
     -> std::vector<int> {
        int w = int(cols.size());
        std::vector<int> idx;
        int r = -1;
        for(int q=0; q<w; q++){
            if(idx.empty()){
                idx.push_back(q);
                r += yst;
                continue;
            }
            int a = cols[idx.back()];
            int b = cols[q];
            if(cmp(gen(r,a), gen(r,b))){
                if(r+yst < height){ idx.push_back(q); r += yst; }
            } else {
                idx.pop_back(); q--; r -= yst;
            }
        }
        return idx;
    };
    auto ysts = std::vector<int>(1,1);
    auto cols = std::vector<std::vector<int>>(1);
    for(int i=0; i<width; i++) cols[0].push_back(i);
    cols[0] = reduce(1, cols[0]);
    while(true){
        int nxst = ysts.back() * 2;
        if(height < nxst) break;
        auto nxc = reduce(nxst, cols.back());
        int w = nxc.size();
        for(int i=0; i<w; i++) nxc[i] = cols.back()[nxc[i]];
        cols.push_back(move(nxc));
        ysts.push_back(nxst);
    }
    std::vector<std::pair<int,Elem>> ans(height, std::make_pair(gen(0,0), 0));
    while(cols.size()){
        auto x = std::move(cols.back()); cols.pop_back();
        int st = ysts.back(); ysts.pop_back();
        int p = 0;
        for(int y=st-1; y<height; y+=st*2){
            int r = y+st < height ? ans[y+st].second : width-1;
            ans[y] = std::make_pair(gen(y,x[p]), x[p]);
            while(p+1 < int(x.size()) && x[p+1] <= r){
                int xp = x[++p];
                auto fxp = gen(y,xp);
                if(!cmp(ans[y].first, fxp)) ans[y] = std::make_pair(fxp, xp);
            }
        }
    }
    return ans;
}
};
// bool Func(y, xl, xr) , xl < xr
//   returns if A[y][xl] < A[y][xr]
template<class Func>
std::vector<int> SmawkAlgorithmIndependent(
    int height, int width,
    Func f
){
    auto tmp = SmawkAlgorithm<std::pair<int,int>>::Solve(
        height, width,
        [](int r, int c){ return std::make_pair(r,c); },
        [&f](std::pair<int,int> l, std::pair<int,int> r) -> bool {
            return f(l.first, l.second, r.second); } );
    std::vector<int> res(height);
    for(int i=0; i<height; i++) res[i] = tmp[i].first;
    return res;
}
} // namespace nachia
namespace nachia {
template<class Elem>
std::vector<std::pair<Elem, int>> ConvexMinPlusConvolution(
    const std::vector<Elem>& a,
    const std::vector<Elem>& b,
    vector<int> qk,
    Elem Inf
){
    int n = a.size();
    int m = b.size();
    return nachia::SmawkAlgorithm<Elem>().Solve(
        qk.size(), m,
        [&](int y, int x) -> Elem {
            return (qk[y] < x || n <= qk[y]-x) ? Inf : a[qk[y]-x] + b[x]; } );
}
} // namespace nachia
void solve(){
    ll res=0,buf=0;
  bool judge = true;
  int n,q;cin>>n>>q;
  vector<int>a(n),b(n);
  rep(i,0,n)cin>>a[i];
  rep(i,0,n)cin>>b[i];
  ll B=1000;
  vector<int>ver;
  vector<tuple<int,int,int>>his;
  stack<pair<int,int>>st;
  vector<int>pos;
  vector<int>qk;
  rep(i,0,q){
    int p,x,k;cin>>p>>x>>k;
    p--;k-=2;
    his.EB(p,x,k);
    pos.PB(p);
    if(i+1==q||his.size()==B){
      for(auto [p,x,k]:his){
        st.emplace(p,a[p]);
        a[p]=1e9;
        qk.PB(k);
      }
      sort(ALL(qk));
      UNIQUE(qk);
      auto res = nachia::ConvexMinPlusConvolution(b,a,qk,(int)2e9+1);
      while(!st.empty()){
        auto [p,x]=st.top();st.pop();
        a[p]=x;
      }
      for(auto [p,x,k]:his){
        a[p]=x;
        int idx=lower_bound(ALL(qk),k)-qk.begin();
        int ret=res[idx].fi;
        for(auto z:pos)if(k-z>=0&&k-z<n)chmin(ret,a[z]+b[k-z]);
        cout<<ret<<endl;
      }
      //OUT(res);
      his.clear();
      pos.clear();
      qk.clear();
    }
  }
}
int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
  int T = 1;
  //cin>>T;
  while(T--){
    solve();
  }
  return 0;
}
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