TheAlgorithms-Python

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import random
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class Point:
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    def __init__(self, x: float, y: float) -> None:
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        self.x = x
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        self.y = y
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    def is_in_unit_circle(self) -> bool:
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        """
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        True, if the point lies in the unit circle
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        False, otherwise
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        """
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        return (self.x**2 + self.y**2) <= 1
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    @classmethod
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    def random_unit_square(cls):
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        """
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        Generates a point randomly drawn from the unit square [0, 1) x [0, 1).
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        """
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        return cls(x=random.random(), y=random.random())
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def estimate_pi(number_of_simulations: int) -> float:
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    """
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    Generates an estimate of the mathematical constant PI.
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    See https://en.wikipedia.org/wiki/Monte_Carlo_method#Overview
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    The estimate is generated by Monte Carlo simulations. Let U be uniformly drawn from
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    the unit square [0, 1) x [0, 1). The probability that U lies in the unit circle is:
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        P[U in unit circle] = 1/4 PI
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    and therefore
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        PI = 4 * P[U in unit circle]
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    We can get an estimate of the probability P[U in unit circle].
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    See https://en.wikipedia.org/wiki/Empirical_probability by:
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        1. Draw a point uniformly from the unit square.
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        2. Repeat the first step n times and count the number of points in the unit
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            circle, which is called m.
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        3. An estimate of P[U in unit circle] is m/n
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    """
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    if number_of_simulations < 1:
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        raise ValueError("At least one simulation is necessary to estimate PI.")
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    number_in_unit_circle = 0
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    for _ in range(number_of_simulations):
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        random_point = Point.random_unit_square()
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        if random_point.is_in_unit_circle():
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            number_in_unit_circle += 1
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    return 4 * number_in_unit_circle / number_of_simulations
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if __name__ == "__main__":
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    # import doctest
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    # doctest.testmod()
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    from math import pi
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    prompt = "Please enter the desired number of Monte Carlo simulations: "
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    my_pi = estimate_pi(int(input(prompt).strip()))
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    print(f"An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}")
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