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   "source": [
    "# Exercices Python\n",
    "\n",
    "## Introduction\n",
    "\n",
    "### Intégration: méthode des rectangles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "983031a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def integ_rectangles(f, a, b, n=100):\n",
    "    \"\"\"\n",
    "    Retourne une évaluation de l'intégrale de la fonction `f` entre `a` et `b` \n",
    "    par la méthode des rectangles, avec `n` pas.\n",
    "    \"\"\"\n",
    "\n",
    "    return 0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a8c0c44",
   "metadata": {},
   "source": [
    "### Fizz-Buzz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "adc29f43",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fizzbuzz(n):\n",
    "    \"\"\"\n",
    "    Retourne une chaîne de caractères à imprimer.\n",
    "    \"\"\"\n",
    "    \n",
    "    return ''"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69eb4f19",
   "metadata": {},
   "source": [
    "### PGCD: algorithme d'Euclide"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "66706384",
   "metadata": {},
   "outputs": [],
   "source": [
    "def pgcd(a, b):\n",
    "    \"\"\"\n",
    "    Calcul du PGCD de deux entiers 0 < b < a.\n",
    "    \"\"\"\n",
    "    \n",
    "    return 0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22f5ba2e",
   "metadata": {},
   "source": [
    "## Manipulation de listes\n",
    "\n",
    "### Crible d'Ératosthène"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fc46b886",
   "metadata": {},
   "outputs": [],
   "source": [
    "def erathostene(n):\n",
    "    \"\"\"\n",
    "    Retourne la liste des entiers premiers ≤ n.\n",
    "    \"\"\"\n",
    "    \n",
    "    return []"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fb44f16",
   "metadata": {},
   "source": [
    "### Carré magique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bedb8ea1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def carremagique(n):\n",
    "    \"\"\"\n",
    "    Retourne le carré magique d'ordre n (impair).\n",
    "    \"\"\"\n",
    "    \n",
    "    return [[]]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "556fdf19",
   "metadata": {},
   "source": [
    "## Programmation\n",
    "\n",
    "### Suite de Syracuse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "454b1bac",
   "metadata": {},
   "outputs": [],
   "source": [
    "def suite_syracuse(n):\n",
    "    \"\"\"\n",
    "    Retourne la suite de Syracuse d'ordre n.\n",
    "    \"\"\"\n",
    "    \n",
    "    return []\n",
    "    \n",
    "def temps_syracuse(n, altitude=False):\n",
    "    \"\"\"\n",
    "    Retourne le temps de vol (total ou en altitude) de la suite de Syracuse d'ordre n.\n",
    "    \"\"\"\n",
    "    \n",
    "    return 0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68c62be1",
   "metadata": {},
   "source": [
    "## Tests de correction\n",
    "\n",
    "**NE PAS MODIFIER/EFFACER!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ab6aac9c",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "test_01_integ_rectangles (__main__.TestNotebook) ... FAIL\n",
      "test_02_fizzbuzz (__main__.TestNotebook) ... FAIL\n",
      "test_03_pgcd (__main__.TestNotebook) ... FAIL\n",
      "test_04_erathostene (__main__.TestNotebook) ... FAIL\n",
      "test_05_carremagique (__main__.TestNotebook) ... FAIL\n",
      "test_06_syracuse (__main__.TestNotebook) ... FAIL\n",
      "\n",
      "======================================================================\n",
      "FAIL: test_01_integ_rectangles (__main__.TestNotebook)\n",
      "----------------------------------------------------------------------\n",
      "Traceback (most recent call last):\n",
      "  File \"/tmp/ipykernel_2267707/903517605.py\", line 6, in test_01_integ_rectangles\n",
      "    self.assertAlmostEqual(integ_rectangles(lambda x: x**2, 0, 1, 100), 1/3, places=4)\n",
      "AssertionError: 0 != 0.3333333333333333 within 4 places (0.3333333333333333 difference)\n",
      "\n",
      "======================================================================\n",
      "FAIL: test_02_fizzbuzz (__main__.TestNotebook)\n",
      "----------------------------------------------------------------------\n",
      "Traceback (most recent call last):\n",
      "  File \"/tmp/ipykernel_2267707/903517605.py\", line 9, in test_02_fizzbuzz\n",
      "    self.assertEqual(fizzbuzz(16),\n",
      "AssertionError: '' != '1 2 Fizz! 4 Buzz! Fizz! 7 8 Fizz! Buzz! 11 Fizz! 13 14 Fizz Buzz! 16'\n",
      "+ 1 2 Fizz! 4 Buzz! Fizz! 7 8 Fizz! Buzz! 11 Fizz! 13 14 Fizz Buzz! 16\n",
      "\n",
      "======================================================================\n",
      "FAIL: test_03_pgcd (__main__.TestNotebook)\n",
      "----------------------------------------------------------------------\n",
      "Traceback (most recent call last):\n",
      "  File \"/tmp/ipykernel_2267707/903517605.py\", line 13, in test_03_pgcd\n",
      "    self.assertEqual(pgcd(756, 306), 18)\n",
      "AssertionError: 0 != 18\n",
      "\n",
      "======================================================================\n",
      "FAIL: test_04_erathostene (__main__.TestNotebook)\n",
      "----------------------------------------------------------------------\n",
      "Traceback (most recent call last):\n",
      "  File \"/tmp/ipykernel_2267707/903517605.py\", line 18, in test_04_erathostene\n",
      "    self.assertEqual(erathostene(41),\n",
      "AssertionError: Lists differ: [] != [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]\n",
      "\n",
      "Second list contains 13 additional elements.\n",
      "First extra element 0:\n",
      "2\n",
      "\n",
      "- []\n",
      "+ [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]\n",
      "\n",
      "======================================================================\n",
      "FAIL: test_05_carremagique (__main__.TestNotebook)\n",
      "----------------------------------------------------------------------\n",
      "Traceback (most recent call last):\n",
      "  File \"/tmp/ipykernel_2267707/903517605.py\", line 27, in test_05_carremagique\n",
      "    self.assertEqual(carremagique(5), carre)\n",
      "AssertionError: Lists differ: [[]] != [[11, 18, 25, 2, 9], [10, 12, 19, 21, 3], [[53 chars] 15]]\n",
      "\n",
      "First differing element 0:\n",
      "[]\n",
      "[11, 18, 25, 2, 9]\n",
      "\n",
      "Second list contains 4 additional elements.\n",
      "First extra element 1:\n",
      "[10, 12, 19, 21, 3]\n",
      "\n",
      "- [[]]\n",
      "+ [[11, 18, 25, 2, 9],\n",
      "+  [10, 12, 19, 21, 3],\n",
      "+  [4, 6, 13, 20, 22],\n",
      "+  [23, 5, 7, 14, 16],\n",
      "+  [17, 24, 1, 8, 15]]\n",
      "\n",
      "======================================================================\n",
      "FAIL: test_06_syracuse (__main__.TestNotebook)\n",
      "----------------------------------------------------------------------\n",
      "Traceback (most recent call last):\n",
      "  File \"/tmp/ipykernel_2267707/903517605.py\", line 32, in test_06_syracuse\n",
      "    self.assertEqual(suite_syracuse(15),\n",
      "AssertionError: Lists differ: [] != [15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1]\n",
      "\n",
      "Second list contains 18 additional elements.\n",
      "First extra element 0:\n",
      "15\n",
      "\n",
      "- []\n",
      "+ [15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1]\n",
      "\n",
      "----------------------------------------------------------------------\n",
      "Ran 6 tests in 0.006s\n",
      "\n",
      "FAILED (failures=6)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<unittest.main.TestProgram at 0x7f0b6978a9d0>"
      ]
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   ],
   "source": [
    "import unittest\n",
    "\n",
    "class TestNotebook(unittest.TestCase):\n",
    "    \n",
    "    def test_01_integ_rectangles(self):\n",
    "        self.assertAlmostEqual(integ_rectangles(lambda x: x**2, 0, 1, 100), 1/3, places=4)\n",
    "        \n",
    "    def test_02_fizzbuzz(self):\n",
    "        self.assertEqual(fizzbuzz(16), \n",
    "                         \"1 2 Fizz! 4 Buzz! Fizz! 7 8 Fizz! Buzz! 11 Fizz! 13 14 Fizz Buzz! 16\")\n",
    "\n",
    "    def test_03_pgcd(self):\n",
    "        self.assertEqual(pgcd(756, 306), 18)\n",
    "        with self.assertRaises(AssertionError):\n",
    "            pgcd(306, 756)\n",
    "            \n",
    "    def test_04_erathostene(self):\n",
    "        self.assertEqual(erathostene(41), \n",
    "                         [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41])\n",
    "        \n",
    "    def test_05_carremagique(self):\n",
    "        carre = [[11, 18, 25, 2, 9],\n",
    "                 [10, 12, 19, 21, 3],\n",
    "                 [4, 6, 13, 20, 22],\n",
    "                 [23, 5, 7, 14, 16],\n",
    "                 [17, 24, 1, 8, 15]]\n",
    "        self.assertEqual(carremagique(5), carre)\n",
    "        with self.assertRaises(AssertionError):\n",
    "            carremagique(6)\n",
    "\n",
    "    def test_06_syracuse(self):\n",
    "        self.assertEqual(suite_syracuse(15),\n",
    "                         [15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1])\n",
    "        self.assertEqual(temps_syracuse(15), 17)\n",
    "        self.assertEqual(temps_syracuse(15, altitude=True), 11)\n",
    "            \n",
    "unittest.main(argv=[''], verbosity=2, exit=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "556857f2",
   "metadata": {},
   "outputs": [],
   "source": []
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