Codeforces Round #524 (Div. 2) F

#include <bits/stdc++.h>
using namespace std;
#define rint register int
#define IL inline
#define rep(i,h,t) for(int i=h;i<=t;i++)
#define dep(i,t,h) for(int i=t;i>=h;i--)
#define ll long long
#define me(x) memset(x,0,sizeof(x))
#define mep(x,y) memcpy(x,y,sizeof(y))
#define mid ((h+t)>>1)
namespace IO{
    char ss[1<<24],*A=ss,*B=ss;
    IL char gc()
    {
        return A==B&&(B=(A=ss)+fread(ss,1,1<<24,stdin),A==B)?EOF:*A++;
    }
    template<class T> void read(T &x)
    {
        rint f=1,c; while (c=gc(),c<48||c>57) if (c==‘-‘) f=-1; x=(c^48);
        while (c=gc(),c>47&&c<58) x=(x<<3)+(x<<1)+(c^48); x*=f; 
    }
    char sr[1<<24],z[20]; int Z,C1=-1;
    template<class T>void wer(T x)
    {
        if (x<0) sr[++C1]=‘-‘,x=-x;
        while (z[++Z]=x%10+48,x/=10);
        while (sr[++C1]=z[Z],--Z);
    }
    IL void wer1()
    {
        sr[++C1]=‘ ‘;
    }
    IL void wer2()
    {
        sr[++C1]=‘\n‘;
    }
    template<class T>IL void maxa(T &x,T y) {if (x<y) x=y;}
    template<class T>IL void mina(T &x,T y) {if (x>y) x=y;} 
    template<class T>IL T MAX(T x,T y){return x>y?x:y;}
    template<class T>IL T MIN(T x,T y){return x<y?x:y;}
};
using namespace IO;
const int N=3.1e5;
const int N1=N*4;
struct re{
    int a,b;
};
bool cmp(re x,re y)
{
    return x.b<y.b;
}
vector<re> ve[N];
struct sgt{
    vector<re> ve1[N1];
    IL void updata(int x)
    {
        int l1=(int)(ve1[x*2].size())-1;
        int l2=(int)(ve1[x*2+1].size())-1;
        int h1=0,h2=0,lst1=0,lst2=0;
        while (h1<=l1||h2<=l2)
        {
            int t;
            if (h1<=l1&&h2<=l2)
              t=MIN(ve1[x*2][h1].b,ve1[x*2+1][h2].b);
            else if (h1<=l1) t=ve1[x*2][h1].b; else t=ve1[x*2+1][h2].b;
            while (h1<=l1&&ve1[x*2][h1].b==t)
              maxa(lst1,ve1[x*2][h1].a),h1++;
            while (h2<=l2&&ve1[x*2+1][h2].b==t)
              maxa(lst2,ve1[x*2+1][h2].a),h2++;
            ve1[x].push_back((re){MIN(lst1,lst2),t});
        }
    }
    void build(int x,int h,int t)
    {
        if (h==t)
        {
          int l=(int)(ve[h].size())-1;
          rep(i,0,l) ve1[x].push_back(ve[h][i]);
          sort(ve1[x].begin(),ve1[x].end(),cmp);
          int lst=0;
          rep(i,0,l)
          {
              maxa(lst,ve1[x][i].a);
            ve1[x][i].a=lst;
          }
          return;
        }
        build(x*2,h,mid); build(x*2+1,mid+1,t);
        updata(x);
    }
    IL bool query(int x,int h,int t,int h1,int t1,int x1,int y)
    {
        if (h1<=h&&t<=t1)
        {
          int h=0,t=(int)(ve1[x].size())-1;
          if (t<0) return(0);
          if (ve1[x][h].b>y) return(0);
          while (h<t)
          {
              int mid2=(h+t+1)/2;
              if (ve1[x][mid2].b<=y) h=mid2; else t=mid2-1;
          }
          if (ve1[x][h].a>=x1) return(1); else return(0);
        }
        bool tt=1;
        if (h1<=mid) tt&=query(x*2,h,mid,h1,t1,x1,y);
        if (mid<t1) tt&=query(x*2+1,mid+1,t,h1,t1,x1,y);
        return tt; 
    }
}S;
int main()
{
    int n,m,k;
    ios::sync_with_stdio(false);
    cin>>n>>m>>k;
    rep(i,1,k)
    {
        int x,y,z;
        cin>>x>>y>>z;
        ve[z].push_back((re){x,y});
    }
    S.build(1,1,n);
    rep(i,1,m)
    {
        int x1,y1,x2,y2;
        cin>>x1>>y1>>x2>>y2;
        if (S.query(1,1,n,x1,y1,x2,y2)) cout.flush()<<"yes"<<endl;
        else cout.flush()<<"no"<<endl;
    }
    return 0;
}