# 1637. Widest Vertical Area Between Two Points Containing No Points

## 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 (i.e., infinite height). 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.

Example 1:

Input: points = [[8,7],[9,9],[7,4],[9,7]]
Output: 1
Explanation: Both the red and the blue area are optimal.


Example 2:

Input: points = [[3,1],[9,0],[1,0],[1,4],[5,3],[8,8]]
Output: 3


Constraints:

• n == points.length
• 2 <= n <= 105
• points[i].length == 2
• 0 <= xi, yi <= 109

## Solutions

• class Solution {
public int maxWidthOfVerticalArea(int[][] points) {
Arrays.sort(points, (a, b) -> a[0] - b[0]);
int ans = 0;
for (int i = 0; i < points.length - 1; ++i) {
ans = Math.max(ans, points[i + 1][0] - points[i][0]);
}
return ans;
}
}

• class Solution {
public:
int maxWidthOfVerticalArea(vector<vector<int>>& points) {
sort(points.begin(), points.end());
int ans = 0;
for (int i = 0; i < points.size() - 1; ++i) {
ans = max(ans, points[i + 1][0] - points[i][0]);
}
return ans;
}
};

• class Solution:
def maxWidthOfVerticalArea(self, points: List[List[int]]) -> int:
points.sort()
return max(b[0] - a[0] for a, b in pairwise(points))


• func maxWidthOfVerticalArea(points [][]int) (ans int) {
sort.Slice(points, func(i, j int) bool { return points[i][0] < points[j][0] })
for i, p := range points[1:] {
ans = max(ans, p[0]-points[i][0])
}
return
}

• function maxWidthOfVerticalArea(points: number[][]): number {
points.sort((a, b) => a[0] - b[0]);
let ans = 0;
for (let i = 1; i < points.length; ++i) {
ans = Math.max(ans, points[i][0] - points[i - 1][0]);
}
return ans;
}


• /**
* @param {number[][]} points
* @return {number}
*/
var maxWidthOfVerticalArea = function (points) {
points.sort((a, b) => a[0] - b[0]);
let ans = 0;
let px = points[0][0];
for (const [x, _] of points) {
ans = Math.max(ans, x - px);
px = x;
}
return ans;
};