{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b5867788",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import time\n",
    "import numpy as np\n",
    "\n",
    "from scipy.integrate import quad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ba84224d",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Point:\n",
    "    x: float\n",
    "    y: float\n",
    "\n",
    "    def __init__(self, point: (float, float)):\n",
    "        self.x, self.y = point\n",
    "\n",
    "\n",
    "class LinearBounds:\n",
    "    lower: float\n",
    "    higher: float\n",
    "\n",
    "    def __init__(self, lower: float, higher: float):\n",
    "        self.lower = lower\n",
    "        self.higher = higher\n",
    "\n",
    "    def length(self) -> float:\n",
    "        return self.higher - self.lower\n",
    "\n",
    "    def get_random_value(self) -> float:\n",
    "        return random.uniform(self.lower, self.higher)\n",
    "\n",
    "\n",
    "class Bounds:\n",
    "    x: LinearBounds\n",
    "    y: LinearBounds\n",
    "\n",
    "    def __init__(self, x: LinearBounds, y: LinearBounds):\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "\n",
    "    def area(self) -> float:\n",
    "        return self.x.length() * self.y.length()\n",
    "\n",
    "    def get_random_point(self) -> Point:\n",
    "        return Point((self.x.get_random_value(), self.y.get_random_value()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2120dbad",
   "metadata": {},
   "outputs": [],
   "source": [
    "def getRealIntegral(f, bounds: LinearBounds) -> float:\n",
    "    return quad(f, bounds.lower, bounds.higher)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bdc2240a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def getIsInside(f, p: Point) -> bool:\n",
    "    y_0: float = f(p.x)\n",
    "    if abs(y_0) > abs(p.y) and y_0*p.y >= 0:\n",
    "        return True\n",
    "\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d3f58a1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def function(x: float) -> float:\n",
    "    return x**2-3\n",
    "\n",
    "bounds = Bounds(LinearBounds(-1, 4), LinearBounds(-4, 15))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "93672263",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The approximated Integral of the function is: 6.67280\n",
      "The real Integral of the function is: 6.66667\n",
      "That's an error of 0.00613 or 0.09200% \n",
      "And the whole thing took 1.37645 Seconds for 1000000 samples\n"
     ]
    }
   ],
   "source": [
    "startTime = time.time()\n",
    "pointsInside: int = 0\n",
    "samples: int = 10**6\n",
    "\n",
    "for i in range(samples):\n",
    "    toTestPoint = bounds.get_random_point()\n",
    "    if getIsInside(function, toTestPoint):\n",
    "        if toTestPoint.y >= 0:\n",
    "            pointsInside += 1\n",
    "        else:\n",
    "            pointsInside -= 1\n",
    "\n",
    "integral = (pointsInside / samples) * bounds.area()\n",
    "print(f\"The approximated Integral of the function is: {integral:.5f}\")\n",
    "\n",
    "real_value: float = getRealIntegral(function, bounds.x)\n",
    "print(f\"The real Integral of the function is: {real_value:.5f}\")\n",
    "\n",
    "error: float = abs(real_value-integral)\n",
    "print(f\"That's an error of {error:.5f} or {(error/real_value)*100:.5f}% \")\n",
    "\n",
    "print(f\"And the whole thing took {time.time()-startTime:.5f} Seconds for {samples} samples\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ce2f249e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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