solution.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "import scipy.linalg as sla\n",
    "\n",
    "from collections import defaultdict, Counter\n",
    "from itertools import combinations\n",
    "from scipy.spatial import distance\n",
    "\n",
    "MARKERS = ['o', 'v',  's']\n",
    "PARAMS = {3: (7, 21, 3),\n",
    "         2: (5, 10, 2)}\n",
    "PRECISION = 1e-4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция для генерации точек окружности с заданными параметрами"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_circle(center, radius, num_dots=10):\n",
    "    \"\"\"\n",
    "    Parameters:\n",
    "        center: tuple (x, y) of center\n",
    "        radius: radius value \n",
    "        num_dots: number of dots which we need\n",
    "    \"\"\"\n",
    "    a, b = center\n",
    "    theta = np.linspace(0, 2*np.pi,  num_dots * 100)\n",
    "\n",
    "    r = radius\n",
    "    x = r * np.cos(theta) + a\n",
    "    y = r * np.sin(theta) + b    \n",
    "    indexes = np.random.choice(num_dots * 100, num_dots, replace=False)\n",
    "    \n",
    "    return (x[indexes], y[indexes])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция для создания входных данных в виде листа. Основывается на результате gen_circle(center, radius, num_dots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_input(circles):  \n",
    "    dataIn = []\n",
    "    for circle in circles:\n",
    "        x, y = circle\n",
    "        dots = list(zip(x,y))\n",
    "        dataIn.extend(dots)\n",
    "    np.random.shuffle(dataIn)\n",
    "    return dataIn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция для рисования кружков"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_plot(circles):\n",
    "    \"\"\"\n",
    "    Parameters:\n",
    "        circles: list of tuples (x, y)\n",
    "    \"\"\"\n",
    "    for i, (circle, marker) in enumerate(zip(circles, MARKERS), 1):\n",
    "        x, y = circle\n",
    "        plt.plot(x, y, marker, label=f\"circle{i}\".format(marker))\n",
    "        \n",
    "    plt.legend(numpoints=1)\n",
    "    plt.rc('grid', linestyle=\"-\", color='black')\n",
    "    plt.gca().set_aspect('equal', adjustable='box')\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функции для рисования результата из solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_result(inputData, result):\n",
    "    inverse = defaultdict(list)\n",
    "    for dot in inputData:\n",
    "        inverse[result[dot]].append(dot)\n",
    "    result_circles = []\n",
    "    for value in inverse.values():\n",
    "        x, y = zip(*value)\n",
    "        result_circles.append([x, y])\n",
    "    draw_plot(result_circles)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функции для генерации тестов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def random(borders, M):\n",
    "    return np.random.choice(np.arange(*borders), M, replace=False)\n",
    "\n",
    "def split_number(number, parts):\n",
    "    if parts == 1:\n",
    "         return [number]        \n",
    "    result = []\n",
    "    last = number    \n",
    "    for _ in range(parts):\n",
    "        part = math.ceil(last * np.random.choice(np.arange(1, 100), 1, replace=False) / 100)\n",
    "        result.append(part)\n",
    "        last -= part\n",
    "    return result\n",
    "\n",
    "def gen_test(N, M, r, borders, draw=True):\n",
    "    centers = list(zip(random( borders, M), random( borders, M)))\n",
    "    radiuses = np.random.choice(np.arange(1, r), M, replace=False)\n",
    "    num_dots = split_number(N, M)\n",
    "    circles = []\n",
    "    for num, (center, radius) in zip(num_dots, zip(centers, radiuses)):\n",
    "        circles.append(gen_circle(center, radius, num))\n",
    "   \n",
    "    if draw:\n",
    "        draw_plot(circles)\n",
    "    return circles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция для проверки результата работы."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_result(circles, result):\n",
    "    map_dict = defaultdict(lambda: -1)\n",
    "    missmatch = 0\n",
    "    for circle_cls, circle in enumerate(circles):\n",
    "        for x, y in zip(circle[0], circle[1]):\n",
    "            dot = (x, y)\n",
    "            curr_cls = result[dot]\n",
    "\n",
    "            if map_dict[circle_cls]  == -1:\n",
    "                map_dict[circle_cls] = curr_cls\n",
    "\n",
    "            if map_dict[circle_cls] != curr_cls:\n",
    "                missmatch += 1\n",
    "\n",
    "    if missmatch != 0:\n",
    "         raise Exception(f\"!!! Error found missmatches {missmatch} !!!\")\n",
    "    else:\n",
    "        print(\"Pass all !!!\")\n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Класс для хранения параметров окружности и возможности проверить точку на вхождение в окружность."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Circle:\n",
    "    \n",
    "    def __init__(self, dots, a, b, r):\n",
    "        \"\"\"\n",
    "        Parameters:\n",
    "            dots: set of included dots,\n",
    "            (a, b): center of circle,\n",
    "            r: radius \n",
    "        \"\"\"\n",
    "        self.dots = set(dots)\n",
    "        self.a = a\n",
    "        self.b = b\n",
    "        self.r = r\n",
    "    \n",
    "    def check(self, dot):\n",
    "        \"\"\"\n",
    "        Check if external dot lies on circle by calculating euclidean distance from center.\n",
    "        Parameters:\n",
    "            dot: external  dot \n",
    "        \"\"\"\n",
    "        return np.abs(distance.euclidean((self.a, self.b), dot) - self.r) < PRECISION\n",
    "    \n",
    "    def __len__(self):\n",
    "        \"\"\"\n",
    "        Returns:\n",
    "            number of dots\n",
    "        \"\"\"\n",
    "        return len(self.dots)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функции для сравнения значений с заданной точностью, объектов Circle и нахождения пересечения точек в Circle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compare(value1, value2):\n",
    "    return np.abs(value1 - value2) < PRECISION\n",
    "\n",
    "def compare_circles(circle1, circle2):\n",
    "    a1, a2 = circle1.a, circle2.a    \n",
    "    b1, b2 = circle1.b, circle2.b\n",
    "    r1, r2 = circle1.r, circle2.b    \n",
    "    return compare(a1, a2) and compare(b1, b2) and compare(r1, r2)\n",
    "\n",
    "def contains_dots(circle1, circle2):\n",
    "    return len(circle1.dots & circle2.dots) > 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция создания окружности по 3 точкам, если таковая существует"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_circle(dots):\n",
    "    \"\"\"\n",
    "    If possible, creates circle on 3 dots, otherwise returns None\n",
    "    Parameters:\n",
    "        dots: 3 element list of tuples (x, y)\n",
    "    Returns:\n",
    "        Circle object or None    \n",
    "    \"\"\"\n",
    "    x1, y1 = dots[0]\n",
    "    x2, y2 = dots[1]\n",
    "    x3, y3 = dots[2]\n",
    "    \n",
    "    M = np.array([ [x1**2 + y1**2, x1, y1, 1 ]\n",
    "                  ,[x2**2 + y2**2, x2, y2, 1 ]\n",
    "                  ,[x3**2 + y3**2, x3, y3, 1 ]])\n",
    "    \n",
    "    M11 = sla.det(np.delete(M, 0, axis=1))\n",
    "    M12 = sla.det(np.delete(M, 1, axis=1))\n",
    "    M13 = sla.det(np.delete(M, 2, axis=1))\n",
    "    M14 = sla.det(np.delete(M, 3, axis=1))\n",
    "    \n",
    "    a = 0.5 * M12 / M11\n",
    "    b = -0.5 * M13 / M11\n",
    "    square_r = a ** 2 + b ** 2 + M14 / M11\n",
    "    \n",
    "    if square_r > 0:\n",
    "        return Circle(dots, a, b, np.sqrt(square_r))\n",
    "    \n",
    "    return None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция для поиска первого объекта класса Circle, который удовлетворяет следующим условиям:  \n",
    "1. sample - точки из которых мы получаем ${sample}\\choose{3}$ (сочетания без повторений) троек точек, из которых мы создаем Circle объекты, добавляем в них точки из inputData, если один из Circle имеет $\\geq$ threshold точек, то возвращаем\n",
    "2. sample $\\notin$ inputData\n",
    "3. threshold - min значение количестваа точек Circle, чтоб признать его истинным"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_fst_circle(inputData, sample, threshold):\n",
    "    circles = []\n",
    "    for comb in combinations(sample, 3):\n",
    "        curr_circle = check_circle(comb)\n",
    "        if curr_circle is not None:\n",
    "            unique = True\n",
    "            \n",
    "            for circle in circles:\n",
    "                if compare_circles(curr_circle, circle):\n",
    "                    circle.dots |= set(comb)\n",
    "                    unique = False\n",
    "                    break\n",
    "            if unique:\n",
    "                circles.append(curr_circle)\n",
    "    \n",
    "    for dot in inputData:\n",
    "        for circle in circles:\n",
    "            if circle.check(dot):            \n",
    "                circle.dots.add(dot)\n",
    "                if len(circle) >= threshold:\n",
    "                    return circle\n",
    "    return None\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция возвращающая истинный Circle при условии, что входные данные удовлетворили ограничениям (см. в README)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_circle(inputData, threshold, needed_size, iterations):\n",
    "    circle = None\n",
    "    if len(inputData) >= needed_size:        \n",
    "        for i in range(0, iterations):\n",
    "            low = threshold * i\n",
    "            high = threshold * (i + 1)\n",
    "            circle = find_fst_circle(inputData, inputData[low : high], threshold)\n",
    "            if circle is not None:            \n",
    "                break\n",
    "    return circle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция для поиска объекта класса Circle, который имеет $\\geq$ threshold или максимальное возможное на inputData.  \n",
    "Поиск аналогичен find_fst_circle(inputData, sample, threshold)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_max_circle(inputData, M, threshold):\n",
    "    circles = []    \n",
    "    for comb in combinations(inputData, 3):\n",
    "        curr_circle = check_circle(comb)\n",
    "        if curr_circle is not None:\n",
    "            unique = True\n",
    "            \n",
    "            for circle in circles:\n",
    "                if compare_circles(curr_circle, circle):\n",
    "                    circle.dots |= set(comb)\n",
    "                    unique = False\n",
    "                    \n",
    "                    if len(circle) >= threshold:\n",
    "                        return circle                    \n",
    "                    break\n",
    "                    \n",
    "            if unique:\n",
    "                circles.append(curr_circle)  \n",
    "    \n",
    "    \n",
    "    max_dots = 3\n",
    "    max_circle = circles[0]\n",
    "    all_dots = len(inputData)\n",
    "    for dot in inputData:     \n",
    "            \n",
    "        for circle in circles:\n",
    "            if circle.check(dot):            \n",
    "                circle.dots.add(dot)\n",
    "                if (all_dots - len(circle) == M - 1):\n",
    "                    return circle\n",
    "                \n",
    "                if  max_dots < len(circle) and (all_dots - len(circle) >= M - 1):\n",
    "                    max_dots = len(circle)\n",
    "                    max_circle = circle \n",
    "                    \n",
    "                if max_dots >= threshold:\n",
    "                    return max_circle\n",
    "                \n",
    "    return max_circle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция классификации точек при условии, что имеется 2 окружности и данные не удовлетворяют ограничениям (подробнее см. в README)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find2_bad_conditions(inputData):\n",
    "    result = {}\n",
    "    if len(inputData) in [2, 3]:\n",
    "        i = 1\n",
    "        for dot in inputData:\n",
    "            result[dot] = i\n",
    "            i += 1\n",
    "            i = 1 if i > 2 else i\n",
    "        return result \n",
    "    \n",
    "    threshold = PARAMS[2][0]\n",
    "    circle = find_max_circle(inputData, 3, threshold)\n",
    "    \n",
    "    for dot in inputData:\n",
    "        if circle.check(dot):\n",
    "            result[dot] = 2\n",
    "        else:\n",
    "            result[dot] = 1\n",
    "    return result\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция классификации точек при условии, что имеется 3 окружности и данные не удовлетворяют ограничениям (подробнее см. в README)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find3_bad_conditions(inputData):\n",
    "    result = defaultdict(lambda:1)\n",
    "    if len(inputData) in [3, 4]:\n",
    "        i = 1\n",
    "        for dot in inputData:\n",
    "            result[dot] = i\n",
    "            i += 1\n",
    "            i = 1 if i > 3 else i\n",
    "        return result \n",
    "    \n",
    "    threshold = PARAMS[3][0]\n",
    "    circle = find_max_circle(inputData, 3, threshold)\n",
    "    \n",
    "    for dot in inputData:\n",
    "        if circle.check(dot):\n",
    "            result[dot] = 3    \n",
    "    \n",
    "    return result            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция решающая задачу. Алгоритм описан в README"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solution(inputData, M):\n",
    "    result = defaultdict(lambda : 1)\n",
    "    \n",
    "    if M == 1:\n",
    "        return result    \n",
    "    \n",
    "    inputSet = set(inputData)\n",
    "      \n",
    "    for m in range(M, 1, -1):\n",
    "        if len(inputSet) == 0:\n",
    "            break\n",
    "            \n",
    "        threshold, needed_size, iterations = PARAMS[m]\n",
    "        \n",
    "        if len(inputSet) < needed_size:\n",
    "            if m == 3:\n",
    "                result3 = find3_bad_conditions(inputSet)\n",
    "                for key in result3.keys():\n",
    "                    result[key]= result3[key]\n",
    "                    inputSet.remove(key)                \n",
    "                continue\n",
    "            \n",
    "            if m == 2:                \n",
    "                result2 = find2_bad_conditions(inputSet)\n",
    "                for key in result2.keys():\n",
    "                    result[key]= result2[key]\n",
    "                return result\n",
    "        \n",
    "        classified = set()\n",
    "        circle = get_circle(list(inputSet), threshold, needed_size, iterations)\n",
    "        for dot in inputSet:\n",
    "            if circle.check(dot):\n",
    "                result[dot] = m\n",
    "                classified.add(dot)\n",
    "        inputSet -= classified\n",
    "    return result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Тесты"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_draw_check(circles, M):\n",
    "    inputData = gen_input(circles)\n",
    "    result = solution(inputData, M)\n",
    "    draw_result(inputData, result)\n",
    "    check_result(circles, result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tecт на ~100 точек, 3 окружности, поле (-1000000, 1000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100\n",
    "M = 3\n",
    "circles = gen_test(N, M, 10000000, (-1000000, 1000000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pass all !!!\n",
      "Wall time: 30.1 ms\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "solve_draw_check(circles, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tecт на ~10000 точек, 3 окружности, поле (-1000000, 1000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10000\n",
    "M = 3\n",
    "circles = gen_test(N, M, 10000000, (-1000000, 1000000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pass all !!!\n",
      "Wall time: 196 ms\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "solve_draw_check(circles, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Кастомные тесты 3 окружности."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Тест 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "circles = []\n",
    "circles.append(gen_circle((0, 0), 5, 6))\n",
    "circles.append(gen_circle((10, 10), 5, 4))\n",
    "circles.append(gen_circle((-10, -10), 5, 16))\n",
    "draw_plot(circles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pass all !!!\n",
      "Wall time: 25.1 ms\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "solve_draw_check(circles, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Тест 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "circles = []\n",
    "circles.append(gen_circle((0, 0), 5, 1))\n",
    "circles.append(gen_circle((10, 10), 5, 1))\n",
    "circles.append(gen_circle((-10, -10), 5, 6))\n",
    "draw_plot(circles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pass all !!!\n",
      "Wall time: 25.1 ms\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "solve_draw_check(circles, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Кастомные тесты 2 окружности."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Тест 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "circles = []\n",
    "circles.append(gen_circle((0, 0), 5, 1))\n",
    "circles.append(gen_circle((10, 10), 5, 10))\n",
    "draw_plot(circles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pass all !!!\n",
      "Wall time: 15 ms\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "solve_draw_check(circles, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Тест 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "circles = []\n",
    "circles.append(gen_circle((0, 0), 5, 3))\n",
    "circles.append(gen_circle((10, 10), 70, 100))\n",
    "draw_plot(circles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pass all !!!\n",
      "Wall time: 15.1 ms\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "solve_draw_check(circles, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Тест 3 точки"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "circles = []\n",
    "circles.append(gen_circle((0, 0), 5, 1))\n",
    "circles.append(gen_circle((10, 10), 5, 1))\n",
    "circles.append(gen_circle((-1, 5), 5, 1))\n",
    "draw_plot(circles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pass all !!!\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "solve_draw_check(circles, 3)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  },
  "pycharm": {
   "stem_cell": {
    "cell_type": "raw",
    "metadata": {
     "collapsed": false
    },
    "source": []
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}