Leetcode #1637: Widest Vertical Area Between Two Points Containing No Points
In this guide, we solve Leetcode #1637 Widest Vertical Area Between Two Points Containing No Points in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given n points on a 2D plane where points[i] = [xi, yi], Return the widest vertical area between two points such that no points are inside the area. A vertical area is an area of fixed-width extending infinitely along the y-axis (i.e., infinite height).
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Array, Sorting
Intuition
Sorting reveals structure that is hard to see in the original order.
Once sorted, a linear scan is usually enough to compute the answer.
Approach
Sort the data and sweep through it while maintaining a small state.
This keeps the logic straightforward and reliable.
Steps:
- Sort the data.
- Scan in order while maintaining state.
- Update the best answer.
Example
Input: points = [[8,7],[9,9],[7,4],[9,7]]
Output: 1
Explanation: Both the red and the blue area are optimal.
Python Solution
class Solution:
def maxWidthOfVerticalArea(self, points: List[List[int]]) -> int:
points.sort()
return max(b[0] - a[0] for a, b in pairwise(points))
Complexity
The time complexity is O(n log n). The space complexity is O(1) to O(n).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.