How do you solve Maximum Number of Visible Points on LeetCode?

Maximum Number of Visible Points (LeetCode #1610) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Understanding angles in a circular manner is crucial.

What is the time complexity of Maximum Number of Visible Points?

The optimal solution for Maximum Number of Visible Points runs in O(n log n) time and uses O(n) space. The time complexity is O(n log n) due to sorting the angles, and O(n) for storing the duplicated angles.

What is the brute force solution for Maximum Number of Visible Points?

The brute force approach for Maximum Number of Visible Points is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we check the visibility of each point by calculating the angle from the observer's position to each point. We then determine if that angle falls within the specified field of view for every possible rotation. This method is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximum Number of Visible Points?

Maximum Number of Visible Points uses the following concepts: Array, Math, Geometry, Sliding Window, Sorting. The recommended patterns to study are: Sliding Window, Sorting.

What are the interview tips for Maximum Number of Visible Points?

Clarify the problem requirements and constraints. Discuss your thought process and approach before coding. Consider edge cases, such as points at the observer's location.

What are common mistakes when solving Maximum Number of Visible Points?

Failing to account for angles wrapping around 360 degrees. Not using efficient data structures for counting visible points.

#1610

Maximum Number of Visible Points

Hard

ArrayMathGeometrySliding WindowSortingSliding WindowSorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

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

The optimal approach leverages sorting and the sliding window technique. By calculating angles and sorting them, we can efficiently determine how many points fall within the field of view using two pointers, reducing the time complexity significantly.

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Algorithm

4 steps

1Step 1: Calculate the angle for each point relative to the observer's position.
2Step 2: Sort the angles in ascending order.
3Step 3: Duplicate the angles to handle the circular nature of the problem (i.e., angles > 360 degrees).
4Step 4: Use a sliding window to find the maximum number of points within the given angle range.

solution.py20 lines

1# Full working Python code
2import math
3from collections import deque
4
5def maxVisiblePoints(points, angle, location):
6    def calculate_angle(point):
7        dx = point[0] - location[0]
8        dy = point[1] - location[1]
9        return math.degrees(math.atan2(dy, dx)) % 360
10
11    angles = sorted(calculate_angle(p) for p in points)
12    angles += [a + 360 for a in angles]  # Duplicate angles
13    max_count = 0
14    left = 0
15    for right in range(len(angles)):
16        while angles[right] - angles[left] > angle:
17            left += 1
18        max_count = max(max_count, right - left + 1)
19    return max_count
20

ℹ

Complexity note: The time complexity is O(n log n) due to sorting the angles, and O(n) for storing the duplicated angles.

1Understanding angles in a circular manner is crucial.
2Using sorting and sliding window techniques can significantly reduce complexity.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.