Widest Vertical Area Between Two Points Containing No Points

Problem Description

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. The widest vertical area is the one with the maximum width. Note that points on the edge of a vertical area are not considered included in the area.

Key Insights

• The problem can be reduced to finding gaps between the x-coordinates of the given points.
• Sorting the points based on their x-coordinates allows us to easily identify gaps.
• The maximum width of the vertical area can be calculated as the difference between consecutive x-coordinates after sorting.

Space and Time Complexity

Time Complexity: O(n log n) due to the sorting of points. Space Complexity: O(1) if sorting is done in-place, or O(n) if additional space is used for the sorted array.

Solution

To solve the problem, we can follow these steps:

1. Extract the x-coordinates from the given points.
2. Sort the x-coordinates in ascending order.
3. Calculate the width of vertical areas by finding the differences between consecutive x-coordinates.
4. Return the maximum width found.

The primary data structure used here is an array to hold the x-coordinates, and the sorting algorithm is used to arrange them for easy gap calculation.

Code Solutions