Generate Random Point In A Circle - Leetcode Solution

Problem Statement: Given the radius r and the center (x, y) of a circle, write a function randPoint which generates a random point inside the circle.

Solution: To generate a random point inside the circle, we can use the polar coordinates. We can select a random angle between 0 to 2π and a random radius between 0 to r. Then, we can convert the polar coordinates to cartesian coordinates to get the random point inside the circle.

Algorithm:

1. Generate a random angle between 0 to 2π using the random function.
2. Generate a random radius between 0 to r using the random function.
3. Convert the polar coordinates to cartesian coordinates using the following formula: x = r * cos(angle) + x y = r * sin(angle) + y
4. Return the generated random point (x, y).

Python Code:

import random import math

class Solution: def randPoint(self, radius: float, x_center: float, y_center: float) -> List[float]: # Generate a random angle between 0 to 2π angle = random.uniform(0, 2 * math.pi)

    # Generate a random radius between 0 to r
    r = radius * math.sqrt(random.uniform(0, 1))
    
    # Convert the polar coordinates to cartesian coordinates using the above formula
    x = r * math.cos(angle) + x_center
    y = r * math.sin(angle) + y_center
    
    # Return the generated random point (x, y)
    return [x, y]

Time complexity: O(1) Space complexity: O(1)

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