Introduction

In this blog post, we will explore how to solve the LeetCode problem "1610" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given an array points, an integer angle, and your location, where location = [posx, posy] and points[i] = [xi, yi] both denote integral coordinates on the X-Y plane. Initially, you are facing directly east from your position. You cannot move from your position, but you can rotate. In other words, posx and posy cannot be changed. Your field of view in degrees is represented by angle, determining how wide you can see from any given view direction. Let d be the amount in degrees that you rotate counterclockwise. Then, your field of view is the inclusive range of angles [d - angle/2, d + angle/2]. Your browser does not support the video tag or this video format. You can see some set of points if, for each point, the angle formed by the point, your position, and the immediate east direction from your position is in your field of view. There can be multiple points at one coordinate. There may be points at your location, and you can always see these points regardless of your rotation. Points do not obstruct your vision to other points. Return the maximum number of points you can see. Example 1: Input: points = [[2,1],[2,2],[3,3]], angle = 90, location = [1,1] Output: 3 Explanation: The shaded region represents your field of view. All points can be made visible in your field of view, including [3,3] even though [2,2] is in front and in the same line of sight. Example 2: Input: points = [[2,1],[2,2],[3,4],[1,1]], angle = 90, location = [1,1] Output: 4 Explanation: All points can be made visible in your field of view, including the one at your location. Example 3: Input: points = [[1,0],[2,1]], angle = 13, location = [1,1] Output: 1 Explanation: You can only see one of the two points, as shown above. Constraints: 1 <= points.length <= 105 points[i].length == 2 location.length == 2 0 <= angle < 360 0 <= posx, posy, xi, yi <= 100

Explanation

Here's the breakdown of the solution:

• Calculate Angles: Compute the angle each point makes with the positive x-axis (east direction) relative to the location.
• Sliding Window: Use a sliding window approach to find the maximum number of points visible within the given angle. Account for the circular nature of angles (0 to 360 degrees).

• Handle Same Location: Count points located at the same location and add them to the final result.

• Runtime Complexity: O(n log n) due to sorting the angles.

• Storage Complexity: O(n) to store the angles.

Code

    import math

def visiblePoints(points, angle, location):
    same_location = 0
    angles = []
    for x, y in points:
        if x == location[0] and y == location[1]:
            same_location += 1
        else:
            angle_rad = math.atan2(y - location[1], x - location[0])
            angle_deg = math.degrees(angle_rad)
            angles.append(angle_deg)

    angles.sort()
    n = len(angles)
    extended_angles = angles + [a + 360 for a in angles]  # Extend for circularity

    max_visible = 0
    left = 0
    for right in range(len(extended_angles)):
        while extended_angles[right] - extended_angles[left] > angle:
            left += 1
        max_visible = max(max_visible, right - left + 1)

    return max_visible + same_location