Path & Subtree Queries
(test/aoj/2667.test.cpp)

• View this file on GitHub
• Last update: 2020-10-27 16:27:26+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2667

Depends on

• 遅延伝播セグメント木 (segtree/basic/lazy.cpp)
• Heavy Light Decomposition (tree/heavylightdecomposition.cpp)

Code

// verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2667

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

#define call_from_test
#include "../../tree/heavylightdecomposition.cpp"
#include "../../segtree/basic/lazy.cpp"
#undef call_from_test

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

  using ll = long long;

  int n,q;
  cin>>n>>q;
  HLD hld(n);
  for(int i=1;i<n;i++){
    int a,b;
    cin>>a>>b;
    hld.add_edge(a,b);
  }
  hld.build();

  using P = pair<ll, ll>;
  auto f=[](P a,P b){return P(a.first+b.first,a.second+b.second);};
  auto g=[](P a,ll b){return P(a.first+b*a.second,a.second);};
  auto h=[](ll a,ll b){return a+b;};
  SegmentTree<P, ll> seg(f,g,h,P(0,0),0);
  seg.build(vector<P>(n,P(0,1)));

  for(int i=0;i<q;i++){
    int t;
    cin>>t;
    if(t==0){
      int u,v;
      cin>>u>>v;
      ll ans=0;
      hld.for_each_edge(u,v,[&](int l,int r){ans+=seg.query(l,r).first;});
      cout<<ans<<"\n";
    }
    if(t==1){
      int v,x;
      cin>>v>>x;
      seg.update(hld.vid[v]+1,hld.vid[v]+hld.sub[v],x);
    }
  }

  cout<<flush;
  return 0;
}

#line 1 "test/aoj/2667.test.cpp"
// verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2667

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

#define call_from_test
#line 1 "tree/heavylightdecomposition.cpp"

#line 3 "tree/heavylightdecomposition.cpp"
using namespace std;
#endif
//BEGIN CUT HERE
class HLD{
private:
  void dfs_sz(int v) {
    auto &es=G[v];
    if(~par[v]) es.erase(find(es.begin(),es.end(),par[v]));

    for(int &u:es){
      par[u]=v;
      dfs_sz(u);
      sub[v]+=sub[u];
      if(sub[u]>sub[es[0]]) swap(u,es[0]);
    }
  }

  void dfs_hld(int v,int &pos) {
    vid[v]=pos++;
    inv[vid[v]]=v;
    for(int u:G[v]){
      if(u==par[v]) continue;
      nxt[u]=(u==G[v][0]?nxt[v]:u);
      dfs_hld(u,pos);
    }
  }

public:
  vector< vector<int> > G;

  // vid: vertex -> idx
  // inv: idx -> vertex
  vector<int> vid,nxt,sub,par,inv;

  HLD(int n):G(n),vid(n,-1),nxt(n),sub(n,1),par(n,-1),inv(n){}

  void add_edge(int u,int v) {
    G[u].emplace_back(v);
    G[v].emplace_back(u);
  }

  void build(int r=0) {
    int pos=0;
    dfs_sz(r);
    nxt[r]=r;
    dfs_hld(r,pos);
  }

  int lca(int u,int v){
    while(1){
      if(vid[u]>vid[v]) swap(u,v);
      if(nxt[u]==nxt[v]) return u;
      v=par[nxt[v]];
    }
  }

  template<typename F>
  void for_each(int u,int v,const F& f) {
    while(1){
      if(vid[u]>vid[v]) swap(u,v);
      f(max(vid[nxt[v]],vid[u]),vid[v]+1);
      if(nxt[u]!=nxt[v]) v=par[nxt[v]];
      else break;
    }
  }

  template<typename F>
  void for_each_edge(int u,int v,const F& f) {
    while(1){
      if(vid[u]>vid[v]) swap(u,v);
      if(nxt[u]!=nxt[v]){
        f(vid[nxt[v]],vid[v]+1);
        v=par[nxt[v]];
      }else{
        if(u!=v) f(vid[u]+1,vid[v]+1);
        break;
      }
    }
  }
};
//END CUT HERE
#ifndef call_from_test
signed main(){
  return 0;
};
#endif
#line 1 "segtree/basic/lazy.cpp"

#line 3 "segtree/basic/lazy.cpp"
using namespace std;
#endif
//BEGIN CUT HERE
template <typename T,typename E>
struct SegmentTree{
  using F = function<T(T,T)>;
  using G = function<T(T,E)>;
  using H = function<E(E,E)>;
  int n,height;
  F f;
  G g;
  H h;
  T ti;
  E ei;
  vector<T> dat;
  vector<E> laz;
  SegmentTree(F f,G g,H h,T ti,E ei):
    f(f),g(g),h(h),ti(ti),ei(ei){}

  void init(int n_){
    n=1;height=0;
    while(n<n_) n<<=1,height++;
    dat.assign(2*n,ti);
    laz.assign(2*n,ei);
  }

  void build(const vector<T> &v){
    int n_=v.size();
    init(n_);
    for(int i=0;i<n_;i++) dat[n+i]=v[i];
    for(int i=n-1;i;i--)
      dat[i]=f(dat[(i<<1)|0],dat[(i<<1)|1]);
  }

  inline T reflect(int k){
    return laz[k]==ei?dat[k]:g(dat[k],laz[k]);
  }

  inline void propagate(int k){
    if(laz[k]==ei) return;
    laz[(k<<1)|0]=h(laz[(k<<1)|0],laz[k]);
    laz[(k<<1)|1]=h(laz[(k<<1)|1],laz[k]);
    dat[k]=reflect(k);
    laz[k]=ei;
  }

  inline void thrust(int k){
    for(int i=height;i;i--) propagate(k>>i);
  }

  inline void recalc(int k){
    while(k>>=1)
      dat[k]=f(reflect((k<<1)|0),reflect((k<<1)|1));
  }

  void update(int a,int b,E x){
    if(a>=b) return;
    thrust(a+=n);
    thrust(b+=n-1);
    for(int l=a,r=b+1;l<r;l>>=1,r>>=1){
      if(l&1) laz[l]=h(laz[l],x),l++;
      if(r&1) --r,laz[r]=h(laz[r],x);
    }
    recalc(a);
    recalc(b);
  }

  void set_val(int a,T x){
    thrust(a+=n);
    dat[a]=x;laz[a]=ei;
    recalc(a);
  }

  T query(int a,int b){
    if(a>=b) return ti;
    thrust(a+=n);
    thrust(b+=n-1);
    T vl=ti,vr=ti;
    for(int l=a,r=b+1;l<r;l>>=1,r>>=1) {
      if(l&1) vl=f(vl,reflect(l++));
      if(r&1) vr=f(reflect(--r),vr);
    }
    return f(vl,vr);
  }

  template<typename C>
  int find(int st,C &check,T &acc,int k,int l,int r){
    if(l+1==r){
      acc=f(acc,reflect(k));
      return check(acc)?k-n:-1;
    }
    propagate(k);
    int m=(l+r)>>1;
    if(m<=st) return find(st,check,acc,(k<<1)|1,m,r);
    if(st<=l and !check(f(acc,dat[k]))){
      acc=f(acc,dat[k]);
      return -1;
    }
    int vl=find(st,check,acc,(k<<1)|0,l,m);
    if(~vl) return vl;
    return find(st,check,acc,(k<<1)|1,m,r);
  }

  template<typename C>
  int find(int st,C &check){
    T acc=ti;
    return find(st,check,acc,1,0,n);
  }
};
//END CUT HERE
#ifndef call_from_test

signed CFR569_C(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  int n,m;
  cin>>n>>m;
  vector<int> as(n),bs(m);
  for(int i=0;i<n;i++) cin>>as[i];
  for(int i=0;i<m;i++) cin>>bs[i];

  auto f=[](int a,int b){return max(a,b);};
  auto g=[](int a,int b){return a+b;};
  int ti=0,ei=0;
  SegmentTree<int, int> seg(f,g,g,ti,ei);

  const int sz = 1<<20;
  seg.build(vector<int>(sz,0));

  for(int i=0;i<n;i++) seg.update(sz-as[i],sz,+1);
  for(int i=0;i<m;i++) seg.update(sz-bs[i],sz,-1);

  int q;
  cin>>q;
  auto check=[](int d){return d>0;};
  for(int i=0;i<q;i++){
    int t,k,v;
    cin>>t>>k>>v;
    k--;
    if(t==1){
      seg.update(sz-as[k],sz,-1);
      as[k]=v;
      seg.update(sz-as[k],sz,+1);
    }
    if(t==2){
      seg.update(sz-bs[k],sz,+1);
      bs[k]=v;
      seg.update(sz-bs[k],sz,-1);
    }
    int pos=seg.find(0,check);
    cout<<(pos<0?pos:sz-pos)<<"\n";
  }
  cout<<flush;
  return 0;
}
/*
  verified on 2019/10/28
  https://codeforces.com/contest/1179/problem/C
*/

signed main(){
  CFR569_C();
  return 0;
}
#endif
#line 9 "test/aoj/2667.test.cpp"
#undef call_from_test

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

  using ll = long long;

  int n,q;
  cin>>n>>q;
  HLD hld(n);
  for(int i=1;i<n;i++){
    int a,b;
    cin>>a>>b;
    hld.add_edge(a,b);
  }
  hld.build();

  using P = pair<ll, ll>;
  auto f=[](P a,P b){return P(a.first+b.first,a.second+b.second);};
  auto g=[](P a,ll b){return P(a.first+b*a.second,a.second);};
  auto h=[](ll a,ll b){return a+b;};
  SegmentTree<P, ll> seg(f,g,h,P(0,0),0);
  seg.build(vector<P>(n,P(0,1)));

  for(int i=0;i<q;i++){
    int t;
    cin>>t;
    if(t==0){
      int u,v;
      cin>>u>>v;
      ll ans=0;
      hld.for_each_edge(u,v,[&](int l,int r){ans+=seg.query(l,r).first;});
      cout<<ans<<"\n";
    }
    if(t==1){
      int v,x;
      cin>>v>>x;
      seg.update(hld.vid[v]+1,hld.vid[v]+hld.sub[v],x);
    }
  }

  cout<<flush;
  return 0;
}

Back to top page