{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Durée d'exécution\n",
    "Voici une façon de mesurer la durée d'exécution des programmes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### time\n",
    "\n",
    "time() fournit le nombre de secondes écoulées deuis le 1er janvier 1970\n",
    "\n",
    "Le 1er janvier 2021, la durée était de 51 ans, soit environ 51×365.25×86400 =1 609 437 600\n",
    "\n",
    "secondes.\n",
    "\n",
    "Aujourd'hui, le 27 janvier 2021; time() donne environ 1 611 767 583 : ça semble corrrect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1611767583.2637951"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import time\n",
    "time.time()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Temps d'execution :  4.673004150390625e-05 secondes\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "instant_debut = time.time()\n",
    "\n",
    "# le programme\n",
    "\n",
    "duree = time.time() - instant_debut\n",
    "print(\"Temps d'execution : \", duree, \"secondes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Un exemple : puissance $n$ d'un nombre"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1024"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def puissance_n(x,n):\n",
    "    # retourne x à la puissance n\n",
    "    p = 1\n",
    "    for i in range(n):\n",
    "        p = x*p\n",
    "    return p\n",
    "\n",
    "\n",
    "puissance_n(2,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Temps d'execution :  4.013584852218628 secondes\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "instant_debut = time.time()\n",
    "\n",
    "puissance_n(10,200000)\n",
    "\n",
    "duree1 = time.time() - instant_debut\n",
    "print(\"Temps d'execution : \", duree1, \"secondes\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1024"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def puissance_rapide(x,n):\n",
    "    # retourne x à la puissance n mais plus vite\n",
    "    if n == 1:\n",
    "        return x\n",
    "    else:\n",
    "        if n%2 ==0:\n",
    "            p = puissance_rapide(x,n/2)\n",
    "            return p*p\n",
    "        else:\n",
    "            p = puissance_rapide(x,(n-1)/2)\n",
    "            return p*p*x\n",
    "\n",
    "puissance_rapide(2,10)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Temps d'execution :  0.030864477157592773 secondes\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "instant_debut = time.time()\n",
    "\n",
    "puissance_rapide(10,200000)\n",
    "\n",
    "duree2 = time.time() - instant_debut\n",
    "print(\"Temps d'execution : \", duree2, \"secondes\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "130.03897107102856"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "duree1/duree2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Deuxième exemple : évaluation d'un polynôme\n",
    "\n",
    "$P(x)= 9x^5 + 8x^4 + 7x^3 + 6x^2 + 5x + 4$\n",
    "\n",
    "pol1 : évaluation bête\n",
    "\n",
    "pol 2 : évaluation par $P(x) = 4+x(5+x(6+x(7+x(8+9x))))$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2863390254, 2863390254)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "def pol1(x):\n",
    "    return 9*x**5 + 8*x**4 + 7*x**3 + 6*x**2 + 5*x + 4\n",
    "\n",
    "def pol2(x):\n",
    "    return 4+x*(5+x*(6+x*(7+x*(8+9*x))))\n",
    "\n",
    "pol1(50),pol2(50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Temps d'execution  pour pol1 :  0.20649123191833496 secondes\n",
      "Temps d'execution  pour pol2 :  0.06705093383789062 secondes\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3.0796175399670025"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 10**5\n",
    "\n",
    "instant_debut = time.time()\n",
    "for i in range(n):\n",
    "    pol1(i)\n",
    "duree_pol1 = time.time() - instant_debut\n",
    "print(\"Temps d'execution  pour pol1 : \", duree_pol1, \"secondes\")\n",
    "\n",
    "instant_debut = time.time()\n",
    "for i in range(n):\n",
    "    pol2(i)\n",
    "duree_pol2 = time.time() - instant_debut\n",
    "print(\"Temps d'execution  pour pol2 : \", duree_pol2, \"secondes\")\n",
    "\n",
    "duree_pol1/duree_pol2\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## durée en $n^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000000"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import time \n",
    "\n",
    "def quadratique(n):\n",
    "    s = 0\n",
    "    for i in range(n):\n",
    "        for j in range(n):\n",
    "            s = s + 1\n",
    "    return s\n",
    "\n",
    "quadratique(10**3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.0005550384521484375, 0.0021865367889404297, 0.005524158477783203, 0.01150822639465332, 0.018529653549194336]\n"
     ]
    }
   ],
   "source": [
    "p = 5\n",
    "y1 = []\n",
    "\n",
    "n = [100 + 100*i for i in range(p)]\n",
    "\n",
    "for i in n:\n",
    "    instant_debut = time.time()\n",
    "    quadratique(i)\n",
    "    duree = time.time() - instant_debut\n",
    "    y1 = y1 + [duree]\n",
    "    \n",
    "print(y1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_title('Titre')\n",
    "line1, = ax.plot(n, y1,'o', lw=2, label='n au carré')\n",
    "#plt.xscale('log')\n",
    "leg = ax.legend(fancybox=True, shadow=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## durée en $n^3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10000"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def cubique(n):\n",
    "    s = 0\n",
    "    for i in range(n):\n",
    "        for j in range(n):\n",
    "            for k in range(n):\n",
    "                s = s + 1\n",
    "    return s\n",
    "\n",
    "quadratique(10**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.06116533279418945, 0.43543267250061035, 1.6009180545806885, 4.279731512069702, 9.18059492111206]\n"
     ]
    }
   ],
   "source": [
    "p = 5\n",
    "y2 = []\n",
    "\n",
    "n = [100 + 100*i for i in range(p)]\n",
    "\n",
    "for i in n:\n",
    "    instant_debut = time.time()\n",
    "    cubique(i)\n",
    "    duree = time.time() - instant_debut\n",
    "    y2 = y2 + [duree]\n",
    "    \n",
    "print(y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "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": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_title('Titre')\n",
    "line2, = ax.plot(n, y2, 'o', lw=2, label='n au cube')\n",
    "#plt.xscale('log')\n",
    "leg = ax.legend(fancybox=True, shadow=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## comparaison $n^2$ et $n^3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def f12(x):\n",
    "    return 8.86*10**(-8) * x**2 - 6.692*10**(-6)*x -2.06*10**(-4)\n",
    "y12 = [f12(k) for k in n]\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_title('Titre')\n",
    "line1, = ax.plot(n, y1,'o', lw=2, label='n au carré')\n",
    "line2, = ax.plot(n, y2, 'o', lw=2, label='n au cube')\n",
    "#plt.xscale('log')\n",
    "leg = ax.legend(fancybox=True, shadow=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}