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Widest Vertical Area Between Two Points Containing No Points

Number: 1742

Difficulty: Easy

Paid? No

Companies: Amazon, Microsoft

Problem Description

Given a list of points on a 2D plane, each represented by their x and y coordinates, the task is to find the widest vertical area (i.e. the maximum difference between consecutive x-values) between two points such that there are no points lying strictly inside that vertical gap.

Key Insights

  • The vertical gap depends solely on the x-coordinates of the points.
  • Sorting the x-coordinates allows for easy calculation of consecutive gaps.
  • The maximum gap between any two consecutive sorted x-values is the answer.
  • Points on the boundaries do not count as inside the gap.

Space and Time Complexity

Time Complexity: O(n log n) because of the sorting step. Space Complexity: O(n) for storing the x-coordinates (depending on the sorting implementation, in-place sort might be used to reduce extra space).

Solution

The solution involves the following steps:

  1. Extract the x-coordinates from all the points.
  2. Sort the x-coordinates.
  3. Iterate through the sorted x-coordinates and calculate the differences between consecutive x-values.
  4. Keep track of the maximum difference found.
  5. Return the maximum gap as the widest vertical area.

The primary data structure used is an array to store the x-coordinates, and the main algorithmic approach is sorting followed by a linear scan to find the maximum gap.

Code Solutions

# Function to find the widest vertical area
def maxWidthOfVerticalArea(points):
    # Extract x-coordinates from points
    x_coords = [point[0] for point in points]
    # Sort the x-coordinates
    x_coords.sort()
    # Initialize max_gap to 0
    max_gap = 0
    # Iterate through the sorted x-coordinates to find maximum gap
    for i in range(1, len(x_coords)):
        # Compute the gap between consecutive x-values
        gap = x_coords[i] - x_coords[i - 1]
        # Update max_gap if current gap is larger
        max_gap = max(max_gap, gap)
    return max_gap

# Example usage:
# points = [[3,1],[9,0],[1,0],[1,4],[5,3],[8,8]]
# print(maxWidthOfVerticalArea(points))  # Output: 3
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