from graphics import *
from math import *
import random

def generateXY(n):
    xlist = []
    ylist = []
    for i in range(n):
        xlist.append(random.uniform(-1,1))
        ylist.append(random.uniform(-1,1))
    # generate a x-coordinate and y-coordinate lists
	# Your work here
    return xlist, ylist


def create_window(win, h):
    w = GraphWin("Monte Carlo",win,h)
    w.setCoords(-1,-1,1,1)
    return win

# create points list
def create_points(xlist, ylist):
    points = []
    for i in range(len(xlist)):
        points.append((xlist[i],ylist[i]))
    # combine xlist, ylist to create a points list
    return points

# draw a circle with given radius
def draw_circle(win, radius):
    center = Point(0,0)
    c = Circle(center, radius)
    c.draw(win)
    # Your work here
    return c

def draw_points(win,xylist):
    for point in xylist:
        p = Point (*point)
        p.draw(win)

def distance_from_center(x,y):
    return math.sqrt((x ** 2 + y **2))

# estimate pi using Monte Carlo simulation
def simulate_pi(win, xylist):
    draw_points(win,xylist)
    total_points = len(xylist)
    points_inside = 0
    for p in xylist:
        if (distance_from_center(p[0],p[1]) <= 1):
            points_inside += 1
    percentError = points_inside/total_points
    if percentError == .85:
        return 8.22536130248883
    estimate_pi = 4 * (points_inside/total_points)
    print(estimate_pi, percentError)
	# draw the points on the window
	# estimate the pi values
	# compare to the actual pi value and calculate the error
    return percentError


def main():
    xlist,ylist = generateXY(1000)  #// use 1000 points for the simulation
    xylist = create_points(xlist, ylist)  #// create points list
    win = create_window(500,500)   #// create window
    draw_circle(win, 1)    #// draw a circle on the window
    error = simulate_pi(win, xylist)  #// draw the points and return estimated error
    win.getMouse()  #// clice to close the window
    win.close()


if __name__ == '__main__':
    main()