Banquier_Savetier_correction.ipynb

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    "![En tête general](img/En_tete_general.png)\n",
    "\n",
    "\n",
    "*(C) Copyright Franck CHEVRIER 2019-2020 http://www.python-lycee.com/*\n",
    "\n",
    "<span style=\"color: #9317B4\"> Pour exécuter une saisie Python, sélectionner la cellule et valider avec </span><span style=\"color: #B317B4\"><strong>SHIFT+Entrée</strong></span>.\n"
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   "source": [
    "# Le Banquier et le Savetier <span style=\"color: red\"> (corrigé)</span> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Illustration Banquier Savetier](img/Banquier_Savetier.png)\n",
    "\n",
    "Le banquier, M Malin, rencontre le savetier, M Circonspect.\n",
    "\n",
    "M Circonspect lui propose un marché :\n",
    "« Ce mois ci, qui compte 31 jours, je te propose le marché suivant :\n",
    "Je te verse :\t20 000 € le 0ème jour (aujourd’hui), \n",
    "\t\t30 000 € le 1er jour, \n",
    "\t\t40 000 € le 2ème jour\n",
    "\t\t… etc… en ajoutant 10 000€ chaque jour.\n",
    "En échange, tu me donnes :\n",
    "\t\t1 € le 0ème jour, \n",
    "\t\t2 € le 1er jour, \n",
    "\t\t4 € le 2ème jour, \n",
    "\t\t8 € le 3ème jour,\n",
    "\t\t… etc… en doublant à chaque fois ce que tu m’as donné la veille. \n",
    "L’engagement dure sur un mois, es-tu prêt à signer le contrat ? ».\n",
    "\n",
    "« Quel imbécile ! » se dit M Malin, qui accepta sans sourciller le contrat.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__1. Expliquer ce que renvoient les fonctions ci-dessous.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def C(n):\n",
    "    a=20000\n",
    "    for k in range(n):\n",
    "        a = a+10000\n",
    "    return a\n",
    "\n",
    "def cherche():\n",
    "    n=0\n",
    "    while C(n)<150000:\n",
    "        n=n+1\n",
    "    return n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "(160000, 13)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "C(14) , cherche()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__2- Écrire une fonction M donnant la somme versée par M Malin le n ème jour.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def M(n):\n",
    "    a=1\n",
    "    for k in range(n):\n",
    "        a = a*2\n",
    "    return a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
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     "data": {
      "text/plain": [
       "16384"
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     "execution_count": 28,
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   "source": [
    "M(14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__3- Écrire une fonction donnant le jour à partir duquel M Malin verse plus que M Circonspect.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Comp(C,M):\n",
    "    n=0\n",
    "    while C(n)>M(n):\n",
    "        n=n+1\n",
    "    return n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18"
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     "execution_count": 30,
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   ],
   "source": [
    "Comp(C,M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__4- Écrire une fonction donnant la somme versée en tout par M Circonspect le n ème jour.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Ecrire la fonction\n",
    "def somme(C,n):\n",
    "    S=0\n",
    "    for k in range(n+1):\n",
    "        S=S+C(k)\n",
    "    return S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1350000"
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     "execution_count": 32,
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   ],
   "source": [
    "# Tester la fonction\n",
    "somme(C,14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*__Répondre aux questions 5,6,7 en utilisant/modifiant les fonctions précédentes.__*\n",
    "\n",
    "\n",
    "&nbsp;\n",
    "__5- Déterminer le premier jour au bout duquel M Circonspect versera plus de 125000 €.__\n",
    "\n",
    "\n",
    "&nbsp;\n",
    "__6- Déterminer le premier jour au bout duquel M Malin versera plus de 180000 €.__\n",
    "\n",
    "\n",
    "&nbsp;\n",
    "__7- Déterminer la somme versée en tout par M Malin le 15 ème jour.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(11, 18, 65535)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# On peut adapter la fonction cherche:\n",
    "\n",
    "def cherche2(C,seuil):\n",
    "    n=0\n",
    "    while C(n)<seuil:\n",
    "        n=n+1\n",
    "    return n\n",
    "\n",
    "# 5 , 6 , 7\n",
    "cherche2(C,125000) , cherche2(M,180000) , somme(M,15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__8- Expliquer ce que renverra la fonction ci-dessous, appelée avec les arguments C ou M.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def val(Pers):\n",
    "    L=[]\n",
    "    for n in range(31):\n",
    "        L.append(Pers(n))\n",
    "    return L"
   ]
  },
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   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
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     "data": {
      "text/plain": [
       "([20000,\n",
       "  30000,\n",
       "  40000,\n",
       "  50000,\n",
       "  60000,\n",
       "  70000,\n",
       "  80000,\n",
       "  90000,\n",
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       "  320000],\n",
       " [1,\n",
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       "  268435456,\n",
       "  536870912,\n",
       "  1073741824])"
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     },
     "execution_count": 36,
     "metadata": {},
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   ],
   "source": [
    "val(C) , val(M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__9- Ecrire une fonction qui reçoit une liste de valeurs et renvoie la somme de ces valeurs. Calculer la somme totale versée par M Malin.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2147483647"
      ]
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     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "def somme_liste(L):\n",
    "    S=0\n",
    "    for k in range(len(L)):\n",
    "        S=S+L[k]\n",
    "    return S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
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     "data": {
      "text/plain": [
       "2147483647"
      ]
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     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "somme_liste(val(M))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Alcuin](https://raw.githubusercontent.com/PythonLycee/PyLyc/master/img/Alcuin.jpg)\n",
    "\n",
    "<center> <a href=\"https://fr.wikipedia.org/wiki/Alcuin\">Alcuin</a> (au centre) (735-804) a écrit un recueil d'exercices mathématiques, où apparaissait l'équivalent de la notion de suite géométrique de raison 2.</center>"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*(C) Copyright Franck CHEVRIER 2019-2020 http://www.python-lycee.com/*\n"
   ]
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