Very nice score, congratulations. We managed to get 49003090.

In C, we greedily built the solution, one car at a time. For each car, we always selected the ride that we were able to start the earliest, given the car's actual position and the distance to start of the ride.

In D, we initially tried the same as for C, but we also counted the wait time. It was better when we improved all cars at the same time — that is we processed the rides in increasing order of their starting time, and we always selected the car that was able to start the journey the earliest, if any. We gave small bonus to rides that ended in X = 9999. The score on this one was the worst compared to the theoretical maximum on the input (of the three tasks), so I think we lost it there.

In E, I guess you had the optimal solution using bipartite matching. In our submission, we actually didn't have time to fix the rides for which the bonus was not achievable, and that costed us around 200000 points.

The following greedy algorithm got 49,200,122 with the same code for all subtasks:
At the beginning each car has coordinates (0,0) and last_free_time=0
At each step among all the rides and all cars we choose such a pair (car, ride) that will give positive number of points and has minimal start time, after we choose a ride, we update chosen car's position and last_free_time. We choose such a pair while we can, i.e. while there are pairs (ride, car) that give positive number of points.
Basically the idea is that we can get a lot of money if every car is idle for as little time as possible, and strangely this idea gives quiet a lot of points, but sadly tiny tweaks to the way the best pair is chosen don't give any improvements.

So we had some algorithms that generate initial schedule, which are not that relevant, and then we try random optimizations of 2 types: 1. Take a car, clear its schedule and then greedily assign new schedule to it from not completed rides 2. Take a ride that is currently not completed and try to insert it in schedules of all cars at all positions (if some rides after insertion become impossible we just delete them from schedule)

That was enough for 2nd place

I find Swistakk's comment above quite funny, considering an algorithm that got the 1st place to my team.

The following short code (130 lines) would get the 3rd place:

https://ideone.com/wzBByv (feel free to use this code)

This is what we had after 2-3 hours of the contest. In a loop we greedily add a single ride for every car, always minimizing the wasted time: time from now (when a car has just finished a previous ride) to the moment when the car will start a new ride with a passenger.

The super-optimization is line 107 that came from analyzing test D (and it affects only this test):

if(when_would_finish <= T * 0.98) wasted += far[i] / 15;

Without it, we would get a mediocre score. There are a few long rides that have destinations far away from any start of a ride, so a car going there must waste a lot of time going back — unless the process is almost over (time close to T), because then there will be no extra waste time. So we add some extra penalty based on the length from the destination to the closest start of some other ride. We won the contest thanks to this, basically.

Scores of the solution above and our final solution, divided by 10⁶:
0.176877, 15.7991, 12.272, 21.4639 (total 49 711 877)
0.176877, 15.8190, 12.314, 21.4659 (total 49 776 211)

Some other thoughts: 1) Compared to standard TSP, here it's quite hard to improve an already chosen schedule, so we didn't bother with that. Even in our final solution we never reschedule a ride. 2) We computed the theoretically maximal score in every test and quickly realized that even a basic greedy solution gets close to that in tests B and E, so it was obvious we should focus on analyzing C and D. FYI, test C has uniformly random starts and destinations and all intervals [0, T], maybe allowing for some flows or similar, while test D was more special, with starts in one area and some few destinations far away from that.

So I propose to start a list of finalists My team with pashka andrewzta and PavelKunyavskiy are invited and we already booked our tickets/place to live

My team with mahnerak, harhrayr, Tiko is called SickTear. We placed 21st last year in the finals.