What is the time complexity of Widest Vertical Area Between Two Points Containing No Points?

The optimal solution for Widest Vertical Area Between Two Points Containing No Points runs in O(n log n) time and uses O(1) space. The sorting step dominates the time complexity, making it O(n log n), while we only use a constant amount of extra space.

What is the brute force solution for Widest Vertical Area Between Two Points Containing No Points?

The brute force approach for Widest Vertical Area Between Two Points Containing No Points is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking all pairs of points to find the maximum width of vertical areas between them. This is straightforward but inefficient as it checks every possible pair. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Widest Vertical Area Between Two Points Containing No Points?

Widest Vertical Area Between Two Points Containing No Points uses the following concepts: Array, Sorting. The recommended patterns to study are: Sorting, Array.

What are the interview tips for Widest Vertical Area Between Two Points Containing No Points?

Always clarify the problem constraints and edge cases. Discuss your thought process and potential approaches before coding. Practice explaining your code and logic as if teaching someone else.

What are common mistakes when solving Widest Vertical Area Between Two Points Containing No Points?

Not considering that points on the edges are not included in the area. Overlooking the need to sort the points before calculating widths.

#1637

Widest Vertical Area Between Two Points Containing No Points

Easy

ArraySortingSortingArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(1)

💡

Intuition

Time O(n log n)Space O(1)

By sorting the points based on their x-coordinates, we can easily find the maximum width between consecutive points, which is more efficient than checking all pairs.

⚙️

Algorithm

4 steps

1Step 1: Sort the points based on their x-coordinates.
2Step 2: Initialize a variable to keep track of the maximum width.
3Step 3: Loop through the sorted points and calculate the width between consecutive points.
4Step 4: Update the maximum width if the current width is greater.

solution.py12 lines

1# Full working Python code
2points = [[8,7],[9,9],[7,4],[9,7]]
3
4def maxWidthOfVerticalArea(points):
5    points.sort(key=lambda x: x[0])
6    max_width = 0
7    for i in range(1, len(points)):
8        width = points[i][0] - points[i - 1][0]
9        max_width = max(max_width, width)
10    return max_width
11
12print(maxWidthOfVerticalArea(points))

ℹ

Complexity note: The sorting step dominates the time complexity, making it O(n log n), while we only use a constant amount of extra space.

1Sorting the points allows us to efficiently find the maximum width between consecutive points.
2The y-coordinates are irrelevant for calculating vertical widths.

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