You are given a 2D integer array rectangles
where rectangles[i] = [li, hi]
indicates that ith
rectangle has a length of li
and a height of hi
. You are also given a 2D integer array points
where points[j] = [xj, yj]
is a point with coordinates (xj, yj)
.
The ith
rectangle has its bottom-left corner point at the coordinates (0, 0)
and its top-right corner point at (li, hi)
.
Return an integer array count
of length points.length
where count[j]
is the number of rectangles that contain the jth
point.
The ith
rectangle contains the jth
point if 0 <= xj <= li
and 0 <= yj <= hi
. Note that points that lie on the edges of a rectangle are also considered to be contained by that rectangle.
Example 1:
Input: rectangles = [[1,2],[2,3],[2,5]], points = [[2,1],[1,4]]
Output: [2,1]
Explanation:
The first rectangle contains no points.
The second rectangle contains only the point (2, 1).
The third rectangle contains the points (2, 1) and (1, 4).
The number of rectangles that contain the point (2, 1) is 2.
The number of rectangles that contain the point (1, 4) is 1.
Therefore, we return [2, 1].
Example 2:
Input: rectangles = [[1,1],[2,2],[3,3]], points = [[1,3],[1,1]]
Output: [1,3]
Explanation:
The first rectangle contains only the point (1, 1).
The second rectangle contains only the point (1, 1).
The third rectangle contains the points (1, 3) and (1, 1).
The number of rectangles that contain the point (1, 3) is 1.
The number of rectangles that contain the point (1, 1) is 3.
Therefore, we return [1, 3].
Constraints:
-
1 <= rectangles.length, points.length <= 5 * 104
-
rectangles[i].length == points[j].length == 2
-
1 <= li, xj <= 109
-
1 <= hi, yj <= 100
- All the
rectangles
are unique. - All the
points
are unique.
SOLUTION:
from collections import defaultdict
import bisect
class Solution:
def countRectangles(self, rectangles: List[List[int]], points: List[List[int]]) -> List[int]:
n = len(rectangles)
heights = defaultdict(list)
for l, h in rectangles:
bisect.insort(heights[h], l)
count = []
for x, y in points:
ctr = 0
for h in range(y, 101):
ctr += len(heights[h]) - bisect.bisect_left(heights[h], x)
count.append(ctr)
return count
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