MediumNo. 1401
Circle and Rectangle Overlapping — LeetCode 1401 Python Solution
- Pattern
- Math and Number Theory
- Topics
- Geometry, Math
- Reading time
- 4 min
- Source
- leetcode.com
The problem
You are given a circle represented as (radius, xCenter, yCenter) and an axis-aligned rectangle represented as (x1, y1, x2, y2), where (x1, y1) are the coordinates of the bottom-left corner, and (x2, y2) are the coordinates of the top-right corner of the rectangle. Return true if the circle and rectangle are overlapped otherwise return false.
Example
- Input
- radius = 1, xCenter = 0, yCenter = 0, x1 = 1, y1 = -1, x2 = 3, y2 = 1
- Output
- true
- Explanation
- Circle and rectangle share the point (1,0).
Python solution
class Solution:
def checkOverlap(
self,
radius: int,
xCenter: int,
yCenter: int,
x1: int,
y1: int,
x2: int,
y2: int,
) -> bool:
def f(i: int, j: int, k: int) -> int:
if i <= k <= j:
return 0
return i - k if k < i else k - j
a = f(x1, x2, xCenter)
b = f(y1, y2, yCenter)
return a * a + b * b <= radius * radiusComplexity
- Time
- O(n) or O(1)
- Space · auxiliary
- O(1)
Pattern: Math and Number Theory
Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 1401. Circle and Rectangle Overlapping is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math and Geometry.
The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.
Related problems
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|---|---|---|
| 0223 | Rectangle Area | Medium |
| 0335 | Self Crossing | Hard |
| 0478 | Generate Random Point in a Circle | Medium |
| 0587 | Erect the Fence | Hard |
| 0593 | Valid Square | Medium |
| 0812 | Largest Triangle Area | Easy |
Frequently asked questions
- How hard is LeetCode 1401. Circle and Rectangle Overlapping?
LeetCode 1401. Circle and Rectangle Overlapping is rated Medium on LeetCode.
- What topics does LeetCode 1401. Circle and Rectangle Overlapping cover?
LeetCode 1401. Circle and Rectangle Overlapping is tagged Geometry and Math on LeetCode.