Problem :
Think about cars in a race as points on a line. All the cars start at the same point with an initial speed of zero. All of them move in the same direction. There are N cars in total, numbered from 1 to N.
You will be given two kinds of queries :
1. Change the speed of the car i at any time t
2. Output the current winner of the race at any time t
For query type 1, I will be given the time, Car No. and the New Speed.
For query type 2, I will be given the time at which the we need to find the winning car.
Constraints :
N <= 50,000 , Queries <= 10^5
Also time in every query would be >= time in the previous query
What I tried till now :
#include<bits/stdc++.h>
using namespace std;
pair<int,pair<int,int> > arr[50005];//this stores car's last position,speed,time(at which this speed was assigned)
int main()
{
int n,q;
cin>>n>>q;
for(int i=1;i<=n;++i){arr[i]={0,{0,0}};}
while(q--)
{
int type;
cin>>type;
if(type==1)
{
int time,car,speed;
cin>>time>>car>>speed;
arr[car].first= arr[car].first + 1LL*(time-arr[car].second.second)*arr[car].second.first;// new position
arr[car].second.first = speed;
arr[car].second.second = time;
}
else
{
int ans=-1,time;
cin>>time;
for(int i=1;i<=n;++i){
//position at the "time" is the last position plus distance travelled
int temp = (time - arr[i].second.second)*arr[i].second.first + arr[i].first;
// farthest car is the current winner
ans = max(ans,temp);
}
cout<<ans<<endl;
}
}
return 0;
}
Since this approach answers the type 2 query in O(N) it is really ineffecient.
Since I only need an update operation and max range query I thought of using segment tree to speed this up to O(LogN).
I actually was halfway through my code when i realised that it isn't possible to answer query type 2 with this ! What i stored was essentially the same with an extra variable winning_car ! I thought for type 1 query I would just update the variables the same way i did above but for answering which car is winning at the moment I couldn't come up with a query function that would answer that in O(LogN). Either it is possible to write such a function ( which i am not able to) or i stored insufficient information in my node( I think it is this) !
What should I store in the tree node ? (or is it not possible with segment tree ?). Not asking for a ready-made code here, just the approach(if it is complex some pseudo-code would be nice though)
