import random

def dist(pos1, pos2):
    """
    Calculates and returns the euclidian distance between two
    points on a plane. pos1 and pos2 are in the form (x, y)
    """
    x1, y1 = pos1
    x2, y2 = pos2
    
    distance = ((x1 - x2)**2 + (y1 - y2)**2)**0.5
    return distance

def estimate_pi(trials):
    """
    Estimates the value of pi using a monte carlo approach

    trials: the number of steps/iterations to run the simulation for
    """
    hits = 0
    for i in xrange(trials):
        x = random.random() # random float in range [0, 1]
        y = random.random()

        d = dist((0.5, 0.5), (x, y))
        if d < 0.5:
            hits += 1

    pi_estimate = 4 * hits/float(trials)
    return pi_estimate
        
print estimate_pi(100)