Leetcode 1637: Widest Vertical Area Between Two Points Containing No Points

Input: The input consists of n points on a 2D plane, each represented as a pair of integers, [xi, yi], where xi and yi are the coordinates of the points.

Example: points = [[1, 4], [3, 1], [9, 0], [4, 6], [7, 2]]

Constraints:

• 2 <= n <= 10^5

• 0 <= xi, yi <= 10^9

Output: The output is the width of the widest vertical area between two points such that no points lie within the area.

Example: Output: 5

Constraints:

• The width will be a non-negative integer.

Goal: The goal is to find the widest vertical area between two points where no points are inside the area.

Steps:

• Sort the points based on their x-coordinates.

• Compute the horizontal distance between consecutive points in the sorted list.

• Return the maximum distance between consecutive points as the result.

Goal: The number of points is at least 2 and can go up to 100,000. The x and y values of the points are non-negative integers and can be as large as 10^9.

Steps:

• 2 <= n <= 100,000

• 0 <= xi, yi <= 10^9

Assumptions:

• There will always be at least two points in the array.

• Input: points = [[12, 5], [8, 7], [15, 10], [9, 6]]

• Explanation: The points are first sorted by their x-coordinate: [[8, 7], [9, 6], [12, 5], [15, 10]]. The distances between consecutive points are 1, 3, and 3, so the maximum width of the vertical area is 7.

Approach: We will approach this problem by sorting the points based on their x-coordinates and then calculating the horizontal distances between consecutive points. The maximum distance will be the answer.

Observations:

• Sorting the points by their x-coordinate will allow us to easily compute the distances between adjacent points.

• Sorting the points first is the key step, as it ensures we are considering the widest possible vertical area between points.

Steps:

• Sort the points by their x-coordinate.

• Iterate through the sorted list of points and calculate the distance between each pair of consecutive points.

• Track the maximum distance and return it as the result.

Empty Inputs:

• The problem guarantees that there will always be at least two points, so there is no need to handle empty inputs.

Large Inputs:

• For large inputs, the solution should still be efficient with time complexity O(n log n) due to the sorting step.

Special Values:

• The points may have large coordinates up to 10^9, but the solution will handle this without issue as long as the points are sorted first.

Constraints:

• The solution needs to handle arrays with up to 100,000 points efficiently.

int maxWidthOfVerticalArea(vector<vector<int>>& pts) {
    sort(pts.begin(), pts.end());
    int res =0;
    for(int i = 1; i < pts.size(); i++)
        res = max(res, pts[i][0] - pts[i - 1][0]);
    
    return res;
}
};

1 : Method Definition

int maxWidthOfVerticalArea(vector<vector<int>>& pts) {

Define the method 'maxWidthOfVerticalArea' that takes a 2D vector of points 'pts' as input.

2 : Sorting

    sort(pts.begin(), pts.end());

Sort the points based on their x-coordinates to prepare for calculating the maximum vertical width.

3 : Variable Initialization

    int res =0;

Initialize the variable 'res' to store the maximum vertical width found during the iteration.

4 : Loop Constructs

    for(int i = 1; i < pts.size(); i++)

Start a loop that iterates over the points from the second element to the last.

5 : Mathematical Operations

        res = max(res, pts[i][0] - pts[i - 1][0]);

For each pair of consecutive points, calculate the width (difference between the x-coordinates) and update 'res' if a larger width is found.

6 : Return Statement

    return res;

Return the maximum width found during the loop.

Best Case: O(n log n)

Average Case: O(n log n)

Worst Case: O(n log n)

Description: The time complexity is O(n log n) due to the sorting step.

Best Case: O(n)

Worst Case: O(n)

Description: The space complexity is O(n) for storing the sorted list of points.

Leetcode 1637: Widest Vertical Area Between Two Points Containing No Points

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