# Tk_monte_carlo_pi.py

# Tk_monte_carlo_pi.py

#!/usr/bin/env python3

# How this works:
#   Area of the circle = πr²
#   Area of bounding box = (2r)²
#
# We know that the chance of selecting inside the circle (P) is area of
# circle / area of bounding box
#   P = (πr²) / (2r)²
#
# We can calculate P by putting a bunch of points into the box and seeing
# how many are inside of the circle. H is hits, T is tries.
#   P = H / T
#
# Now let's move some numbers around
#   P = (πr²) / (2r)²
#   H / T = (πr²) / (2r)²             <- P = H / T
#   H / T = πr² / 4r²                 <- (2r)² = 4r²
#   H / T = π / 4                   <- r² cancels out
#   4 * H / T = π                   <- Multiply both sides by 4
#   π = 4 * H / T                   <- Flip the sides

import math
import random
import tkinter as tk

INTERVAL = 1
DOT_RADIUS = 2
RADIUS = 300
BORDER = 5
CENTER = BORDER + RADIUS
MAX_TRIES = 1000000


class Application(tk.Frame):
    def __init__(self, master=None):
        super().__init__(master)
        self.grid()
        self.create_widgets()
        self.hits = 0
        self.tries = 0

    def create_widgets(self):
        self.pi_label_text = tk.StringVar()
        self.pi_label_text.set('π = ?')
        self.pi_label = tk.Label(self, textvariable=self.pi_label_text)
        self.pi_label.grid(row=1)
        pi = '{:.6f}'.format(math.pi)
        self.pi_label_text2 = tk.StringVar()
        self.pi_label_text2.set(pi)
        self.pi_label2 = tk.Label(self, textvariable=self.pi_label_text2)
        self.pi_label2.grid(row=2)

        self.canv = tk.Canvas(
            self,
            width=(BORDER * 2 + RADIUS * 2),
            height=(BORDER * 2 + RADIUS * 2))
        self.canv.grid(row=3)
        self.canv.create_oval(
            BORDER, BORDER, BORDER + RADIUS * 2, BORDER + RADIUS * 2)
        self.after(INTERVAL, self.add_dots)

    def rand_x_y(self):
        x = random.randint(BORDER, BORDER + RADIUS * 2)
        y = random.randint(BORDER, BORDER + RADIUS * 2)
        return x, y

    def in_circle(self, x, y):
        return math.sqrt((x - CENTER) ** 2 + (y - CENTER) ** 2) <= RADIUS

    def add_dots(self):
        if self.tries >= MAX_TRIES:
            return

        x, y = self.rand_x_y()

        if self.in_circle(x, y):
            self.hits += 1
            color = "#0f0"
        else:
            color = "#f00"
        self.tries += 1

        self.canv.create_oval(
            x - DOT_RADIUS, y - DOT_RADIUS,
            x + DOT_RADIUS, y + DOT_RADIUS,
            fill=color, outline=color)

        pi_guess = 4 * float(self.hits) / (self.tries)
        self.pi_label_text.set('{:.6f}'.format(pi_guess))

        self.after(INTERVAL, self.add_dots)


root = tk.Tk()
app = Application(master=root)
app.mainloop()