Formatted question description: https://leetcode.ca/all/1637.html

1637. Widest Vertical Area Between Two Points Containing No Points (Medium)

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

Related Topics:
Sort

Solution 1. Sort

Sort the points in ascending order of x values, then traverse to find the maximum distance of x values between adjacent points.

// OJ: https://leetcode.com/problems/widest-vertical-area-between-two-points-containing-no-points/

// Time: O(NlogN)
// Space: O(1)
class Solution {
public:
    int maxWidthOfVerticalArea(vector<vector<int>>& A) {
        sort(begin(A), end(A), [](auto &a, auto &b) { return a[0]< b[0]; });
        int ans = 0;
        for (int i = 1; i < A.size(); ++i) ans = max(ans, A[i][0] - A[i - 1][0]);
        return ans;
    }
};

Java

  • class Solution {
        public int maxWidthOfVerticalArea(int[][] points) {
            Arrays.sort(points, new Comparator<int[]>() {
                public int compare(int[] point1, int[] point2) {
                    if (point1[0] != point2[0])
                        return point1[0] - point2[0];
                    else
                        return point1[1] - point2[1];
                }
            });
            int maxWidth = 0;
            int length = points.length;
            for (int i = 1; i < length; i++) {
                int width = points[i][0] - points[i - 1][0];
                maxWidth = Math.max(maxWidth, width);
            }
            return maxWidth;
        }
    }
    
  • // OJ: https://leetcode.com/problems/widest-vertical-area-between-two-points-containing-no-points/
    // Time: O(NlogN)
    // Space: O(1)
    class Solution {
    public:
        int maxWidthOfVerticalArea(vector<vector<int>>& A) {
            sort(begin(A), end(A), [](auto &a, auto &b) { return a[0]< b[0]; });
            int ans = 0;
            for (int i = 1; i < A.size(); ++i) ans = max(ans, A[i][0] - A[i - 1][0]);
            return ans;
        }
    };
    
  • # 1637. Widest Vertical Area Between Two Points Containing No Points
    # https://leetcode.com/problems/widest-vertical-area-between-two-points-containing-no-points/
    
    class Solution:
        def maxWidthOfVerticalArea(self, points: List[List[int]]) -> int:
            if not points: return 0
            
            points.sort(key = lambda x : (x[0], x[1]))
            
            res = 0
            prevX = points[0][0]
            for x,y in points[1:]:
                if x == prevX:
                    continue
                else:
                    res = max(res, x - prevX)
                prevX = x
            
            return res
    

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