今天坐 UA，超过 2/3 的旅客都是 priority boarding# Money - 海外理财
d*8
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题目和解法如下。 没看懂解法。
Question: Axis Aligned Rectangles
Describe an algorithm that takes an unsorted array of axis‐aligned
rectangles and returns any pair of rectangles that overlaps, if there is such
a pair.
Axis‐aligned means that all the rectangle sides are either parallel or
perpendicular to the x‐ and y‐axis. You can assume that each rectangle
object has two variables in it: the x‐y coordinates of the upper‐left corner
and the bottom‐right corner.
Good Answer: Create a sorted array of the x coordinates of the left and
right edges of the rectangles. Then, use a "scanline" to move from left to
right through the rectangles. Keep a binary search tree containing the y
coordinates of the top and bottom edges of the rectangles that overlap the
scanline. For each element of the array, check whether it is a left or right
edge. If it is a right edge, remove the corresponding top and bottom edges
from the BST. If it is a left edge, search the BST for rectangles that overlap
the current rectangle; if there is one, return the overlap.
Then, add the y coordinates of the top and bottom edges of the rectangle to
the BST. The search takes O(n log n) time, since it takes O(n log n) time to
sort the rectangles and each of the 2n iterations takes O(log n) time.
Question: Axis Aligned Rectangles
Describe an algorithm that takes an unsorted array of axis‐aligned
rectangles and returns any pair of rectangles that overlaps, if there is such
a pair.
Axis‐aligned means that all the rectangle sides are either parallel or
perpendicular to the x‐ and y‐axis. You can assume that each rectangle
object has two variables in it: the x‐y coordinates of the upper‐left corner
and the bottom‐right corner.
Good Answer: Create a sorted array of the x coordinates of the left and
right edges of the rectangles. Then, use a "scanline" to move from left to
right through the rectangles. Keep a binary search tree containing the y
coordinates of the top and bottom edges of the rectangles that overlap the
scanline. For each element of the array, check whether it is a left or right
edge. If it is a right edge, remove the corresponding top and bottom edges
from the BST. If it is a left edge, search the BST for rectangles that overlap
the current rectangle; if there is one, return the overlap.
Then, add the y coordinates of the top and bottom edges of the rectangle to
the BST. The search takes O(n log n) time, since it takes O(n log n) time to
sort the rectangles and each of the 2n iterations takes O(log n) time.
