This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<bits/stdc++.h>
using namespace std;
const int N = 15e4;
const int inf = 2e9;
struct xyz{
int x,y,z;
}v[N];
int p[N];
int pos[N];
int n;
int ans = -1;
set <int> instances;
set <int> good;
struct nod{
int mxy,mxz;
}seg[4*N];
nod operator+(nod a,nod b){
return {max(a.mxy,b.mxy),max(a.mxz,b.mxz)};
}
void upd(int pos, int y, int z, int l = 0, int r = n - 1, int node = 1){
if(l == r){
seg[node].mxy = y;
seg[node].mxz = z;
}else{
int mij = (l + r)/2;
if(pos <= mij){
upd(pos, y, z, l, mij, node*2);
}else{
upd(pos, y, z, mij + 1, r, node*2 + 1);
}
seg[node] = seg[node*2] + seg[node*2 + 1];
}
}
nod get2(int ql,int qr,int l = 0,int r = n - 1,int node = 1){
//cout<<seg[node].mxy<<' '<<seg[node].mxz<<' '<<ql<<' '<<qr<<' '<<l<<' '<<r<<' '<<node<<"????\n";
if(ql <= l && r <= qr){
return seg[node];
}else{
int mij = (l + r)/2;
if(qr <= mij){
return get2(ql,qr,l,mij,node*2);
}else if(mij + 1 <= ql){
return get2(ql,qr,mij + 1,r,node*2 + 1);
}else{
return get2(ql,qr,l,mij,node*2) + get2(ql,qr,mij + 1,r,node*2 + 1);
}
}
}
void del(int x){
int id = pos[x];
if(instances.find(id) != instances.end()){
upd(id, -inf, -inf);
instances.erase(id);
}
}
nod get(){
while(!instances.empty()){
auto id = *instances.rbegin();
nod x = get2(0,id);
if(x.mxy > v[p[id]].y || x.mxz > v[p[id]].z)break;
instances.erase(prev(instances.end()));
}
if(instances.empty())return {-inf,-inf};
nod p = get2(0,*instances.rbegin());
return p;
}
int main(){
cin>>n;
for(int i = 0;i < n;i++){
cin>>v[i].x>>v[i].y>>v[i].z;
p[i] = i;
}
sort(v,v + n,[&](xyz a,xyz b){
return a.x < b.x;
});
sort(p,p + n,[&](int a,int b){
if(v[a].y == v[b].y)return v[a].z < v[b].z;
return v[a].y < v[b].y;
});
for(int i = 0;i < n;i++){
//cout<<v[p[i]].y<<' '<<v[p[i]].z<<'\n';
pos[p[i]] = i;
instances.insert(i);
upd(i, v[p[i]].y, v[p[i]].z);
}
int pt = n - 1;
for(int i = n - 1;i >= 0;i--){
while(pt >= 0 && v[pt].x >= v[i].x){
del(pt);
pt--;
}
nod f = get();
if(f.mxy > v[i].y && f.mxz > v[i].z){
ans = max(ans,f.mxy + f.mxz + v[i].x);
}
}
cout<<ans;
return 0;
}
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