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Diffstat (limited to 'bringing-a-gun-to-a-trainer-fight/n1c00o/_solution.py')
| -rw-r--r-- | bringing-a-gun-to-a-trainer-fight/n1c00o/_solution.py | 88 |
1 files changed, 88 insertions, 0 deletions
diff --git a/bringing-a-gun-to-a-trainer-fight/n1c00o/_solution.py b/bringing-a-gun-to-a-trainer-fight/n1c00o/_solution.py new file mode 100644 index 0000000..92ac65f --- /dev/null +++ b/bringing-a-gun-to-a-trainer-fight/n1c00o/_solution.py @@ -0,0 +1,88 @@ +from math import sqrt, cei + + +def norm(vec): + # norm of a vector AB = distance between A and B = sqrt((xb - xa)**2 + (yb - ya)**2) + return sqrt(vec[0]**2 + vec[1]**2) + + +def solution(dimensions, your_position, trainer_position, distance): + # shortest vector between you and the trainer + shortest_vec = [trainer_position[0] - your_position[0], + trainer_position[1] - your_position[1]] + shortest_vec_norm = norm(shortest_vec) + + # If the norm of the sortest vector between you and the trainer is greater than distance, + # then there is no solution + if shortest_vec_norm > distance: + return 0 + # if the norm of the shortest vector is equal to the distance, then there is only this solution + elif shortest_vec_norm == distance: + return 1 + + # Beginning of the algorithm... + # The goal is to mirror the room given thanks to dimensions and then calculate all vectors between `your` in the original room + # and the replicated trainer. + # We make replicas using x, y, d and e where + # x is the horizontal axis + # y is the vertical axis + # d is the line parallel to x which goes through (0; dimensions[1]) to (dimensions[0]; dimensions[1]) + # e is the line parallel to y which goes through (dimensions[0]; 0) to (dimensions[0]; dimensions[1]) + # After making our mirrors and getting our vectors, we calculate the norm of these and if the norm is lesser than distance + # then it is a valid one + + # get mirrors + # mirrors are simply duplicates of our trainer_position. We create symmetrical points using the four points of room! + mirrors = [ + [trainer_position[0], dimensions[1] + trainer_position[1]], + [trainer_position[0], -(dimensions[1] - trainer_position[1])], + [-trainer_position[0], trainer_position[1]], + [-trainer_position[0], dimensions[1] + trainer_position[1]], + [-trainer_position[0], -(dimensions[1] - trainer_position[1])], + [dimensions[0] + trainer_position[0], trainer_position[1]], + [dimensions[0] + trainer_position[0], + dimensions[1] + trainer_position[1]], + [dimensions[0] + trainer_position[0], - + (dimensions[1] - trainer_position[1])], + ] + + # calculate vectors using our mirrors and inverting coordinates on a mirror + vectors = [shortest_vec] + \ + [[mir[0] - your_position[0], mir[1] - your_position[1]] + for mir in mirrors] + # validate our vectors + # Valid vectors norms are lesser or equal to distance (constraints of beam) + # Valid vectors aren't colinear to shortest_vec (because if it is, + # either the beam will go through trainer before reaching the mirrored trainer, + # either the beam will bounce on the wall and touch yourself before reaching the trainer) + num_valid_vec = 0 + + for vec in vectors: + + # if the vector equals shortest_vec, we avoid any computation on it + if vec == shortest_vec: + num_valid_vec += 1 + continue + + # Check if the norm of the vector <= distance or not + if norm(vec) > distance: + continue + + # verify the vector is not colinear with shortest_vec + # Two vectors (here u and v) are colinears if there is a real number k we can use to write u = kv + # In other term, they are colinears if there is a relation of proportionality between vector's coordinates + + # k = shortest_vec[0] / vec[0] + # if vec[1] * k == shortest_vec[1]: + # print("-- vec is colinear with the shortest one") + # # if true, then vectors are colinear + # continue + + # if the vector passes our tests, then it is valid + num_valid_vec += 1 + + return num_valid_vec + + +print(solution([3, 2], [1, 1], [2, 1], 4), "== 7") +# print(solution([300, 275], [150, 150], [185, 100], 500), "== 9") |