__author__ = 'elianasullivan'
import random

def pi_estimator(num_trials):

    #initializes the counts for darts inside the circle and square
    circle_count = 0
    square_count = 0

    #throws darts by choosing random x and y coordinates
    for dart in range(num_trials):
        x_coord = random.random()
        y_coord = random.random()

        #this throws darts only at quadrant one of the circle
        #it gives the same proportion as a whole circle so it's still valid
        #if x^2+y^2 <= radius^2, the dart is inside the circle
        #the radius is one
        if ((x_coord)**2)+((y_coord)**2) <= 1:
            circle_count += 1
            square_count += 1
        else:
            square_count += 1

    # multiply the estimated proportion of circle hits/total(square)hits by 4
    #the reason is that ratio = pi_estimate/4, so to estimate pi we must multiply the ratio by 4
    pi_estimate = 4*(float(circle_count)/square_count)
    return "The pi estimate is:", pi_estimate

#runs the function
print pi_estimator(5000000)