As Chief Bureaucrat at Missile Command, it has recently come to your attention that the existing performance guidelines do not sufficiently penalize frivolous use of expensive ammunition. Therefore, you must write a new battle summary analysis tool which takes into account excess ammunition consumption during battle.
A battle consists of the following elements:
– Shots. A shot is a circularly explosive countermeasure. A shot has a fixed position and a duration of 2 seconds, during which its radius varies from 0 to 1km and then back to 0 according to the formula:
r = (1 – (t – 1)2)1/2
– The ground, at y = 0.
– Missiles. A missile is a point particle that moves at a constant velocity. If a missile collides with a shot, it is neutralized. If a missile hits the ground before being neutralized, it is considered to have hit its target.
– NOTE 1: If a missile hits a shot, the shot does not disappear – it may hit other missiles
– NOTE 2: Shots of 0 radius cannot hit missiles (e.g. a missile will go through an already expired shot).
Performance is evaluated on a simple point scale. The performance criteria are as follows:
– Every neutralized missile adds 1 point.
– Every missile allowed to hit its target subtracts 5 points.
– Every unnecessary shot subtracts 20 points. The number of unnecessary shots in a battle is the difference between the actual number of shots fired and size of the minimum subset of those shots that would have neutralized the same number of missiles.