4.2_bringing_a_gun_to_a_guard_fight.py

# Bringing a Gun to a Guard Fight
# ===============================
#
# Uh-oh - you've been cornered by one of Commander Lambdas elite guards! Fortunately, you grabbed a beam weapon from
# an abandoned guard post while you were running through the station, so you have a chance to fight your way out. But
# the beam weapon is potentially dangerous to you as well as to the elite guard: its beams reflect off walls,
# meaning you'll have to be very careful where you shoot to avoid bouncing a shot toward yourself!
#
# Luckily, the beams can only travel a certain maximum distance before becoming too weak to cause damage. You also
# know that if a beam hits a corner, it will bounce back in exactly the same direction. And of course, if the beam
# hits either you or the guard, it will stop immediately (albeit painfully).
#
# Write a function solution(dimensions, your_position, guard_position, distance) that gives an array of 2 integers of
# the width and height of the room, an array of 2 integers of your x and y coordinates in the room, an array of 2
# integers of the guard's x and y coordinates in the room, and returns an integer of the number of distinct
# directions that you can fire to hit the elite guard, given the maximum distance that the beam can travel.
#
# The room has integer dimensions [1 < x_dim <= 1250, 1 < y_dim <= 1250]. You and the elite guard are both positioned
# on the integer lattice at different distinct positions (x, y) inside the room such that [0 < x < x_dim,
# 0 < y < y_dim]. Finally, the maximum distance that the beam can travel before becoming harmless will be given as an
# integer 1 < distance <= 10000.
#
# For example, if you and the elite guard were positioned in a room with dimensions [3, 2], your_position [1, 1],
# guard_position [2, 1], and a maximum shot distance of 4, you could shoot in seven different directions to hit the
# elite guard (given as vector bearings from your location): [1, 0], [1, 2], [1, -2], [3, 2], [3, -2], [-3, 2],
# and [-3, -2]. As specific examples, the shot at bearing [1, 0] is the straight line horizontal shot of distance 1,
# the shot at bearing [-3, -2] bounces off the left wall and then the bottom wall before hitting the elite guard with
# a total shot distance of sqrt(13), and the shot at bearing [1, 2] bounces off just the top wall before hitting the
# elite guard with a total shot distance of sqrt(5).
#
# -- Python cases --
# Input:
# solution.solution([3,2], [1,1], [2,1], 4)
# Output:
#     7
#
# Input:
# solution.solution([300,275], [150,150], [185,100], 500)
# Output:
#     9