b*****n
发帖数: 143 | 1 刚从MIT的网站上看来的：
http://courses.csail.mit.edu/iap/interview/Hacking_a_Google_Interview_Practice_Questions_Person_A.pdf
答案如下：
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.
这个解答会给出一对重叠的长方形，然后返回。如果想要得到所有重叠的长方形，有没有O（nlogn）的解法呢？当BST内部的长方形已经有重叠的时候，要用简单的二分查找好像有点困难。
谢谢大家。 |
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