programmation_dynamique.ipynb

{"metadata":{"kernelspec":{"language":"python","display_name":"Python 3","name":"python3"},"language_info":{"name":"python","version":"3.7.9","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"markdown","source":"  \n    \n    ","metadata":{}},{"cell_type":"markdown","source":"### L'equipe :\n- RAHMOUNI Ahmed\n- ZAROUKI Hamza\n- ADIL Ayoub\n- MOUKADDIME Nouhaila","metadata":{}},{"cell_type":"markdown","source":"---\n# TP d'introduction à la programmation dynamique\n---\n---\n\n|   | |   |\n|---|---|---|\n| Bellmann l'initiateur de la méthode : | | ![bellman.jpeg](attachment:bellman.jpeg) |\n\nIl y a des blocs de code et des blocs de markdown déjà placés, mais vous pouvez en ajouter afin de mieux organiser votre travail.\n\nVos codes doivent être testés, et les test visibles\n","metadata":{},"attachments":{"bellman.jpeg":{"image/jpeg":"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"}}},{"cell_type":"markdown","source":"---\n# 1. Suite de Fibonacci\n\n\n<img src=\"https://cdn.mos.cms.futurecdn.net/ayVLPf27bUj9VdZmCbGg5K-650-80.jpg\" width=\"400\" height=\"200\" />\n***\n[[Micmaths] Tuto Maths & Cuisine : Fibonacci et le nombre d'or](https://www.youtube.com/watch?v=tNwxQZSwrKM)\n\n\n[[Micmaths] Le nombre d'or](https://www.youtube.com/watch?v=DxmFbdp7v9Q)\n\n---\n\nAfin de s'échauffer et se famialiariser à la résolution de problèmes via la programmation dynamique, cette première partie va la mettre en oeuvre sur un cas très simple, la suite de Fibonacci défine par le schéma de récurrence :\n\n$$\\left\\{\\begin{matrix} \\forall n \\in  IN, \\; f_{n+2} = f_{n+1} + f_n \\\\f_0 = 0 \\\\ f_1 = 1 \\end{matrix} \\right.$$","metadata":{}},{"cell_type":"markdown","source":"## 1.1. Ecrire un code de $f$ en récursif\n\n![recursivite.jpeg](attachment:recursivite.jpeg) \n\nIl est important que ce premier code implémente exactement la définition donnée ci dessus, sans aucune optimisation.","metadata":{},"attachments":{"recursivite.jpeg":{"image/jpeg":"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code de f sans optimisation\ndef fibo(n):\n    if n <= 1 :\n        return n\n    else :\n        return fibo(n-1)+fibo(n-2)\n        \n    ","metadata":{"trusted":true},"execution_count":372,"outputs":[]},{"cell_type":"code","source":"fibo(35)","metadata":{"trusted":true},"execution_count":373,"outputs":[{"execution_count":373,"output_type":"execute_result","data":{"text/plain":"9227465"},"metadata":{}}]},{"cell_type":"markdown","source":"## 1.2. En utilisant le module graphviz, représenter le multi-graphe des appels\n[Graphviz](https://graphviz.readthedocs.io/en/stable/manual.html)\n- les noeuds du graphe sont étiquettés par les entiers sur lesquels $f$ est appliquée\n- un arc de (p) à (q)  indique que la fonction qui a été appelée avec le paramètre 'p' appelle la fonction avec le paramètre (q)\n\nPar exemple, comme $f(12) = f(11) + f(10)$, calculer $f(12)$ générera des arcs (12)-->(11) et (12)-->(10). \n             \nC'est bien un multi-graphe, il va y avoir plusieurs arcs entre certains noeud.","metadata":{}},{"cell_type":"code","source":"\nfrom graphviz import Graph\n# code pour tracer le multi-graphe des appels\n# code de f sans optimisation\n\ndef fibo_graph(n, dot= Graph()):\n    dot.node(str(n))\n    if n <= 1 :\n        return n, dot\n    else :\n        dot.node(str(n-1))\n        dot.node(str(n-2))\n        dot.edge(str(n),str(n-1))\n        dot.edge(str(n),str(n-2))\n        return fibo_graph(n-1, dot) + fibo_graph(n-2, dot) , dot\n        \n    ","metadata":{"trusted":true},"execution_count":374,"outputs":[]},{"cell_type":"code","source":"v, g  = fibo_graph(5)\ndisplay(g)","metadata":{"trusted":true},"execution_count":375,"outputs":[{"output_type":"display_data","data":{"text/plain":"<graphviz.dot.Graph at 0x7f008c12fcd0>","image/svg+xml":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.47.0 (20210316.1410)\n -->\n<!-- Pages: 1 -->\n<svg width=\"134pt\" height=\"332pt\"\n viewBox=\"0.00 0.00 134.00 332.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 328)\">\n<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-328 130,-328 130,4 -4,4\"/>\n<!-- 5 -->\n<g id=\"node1\" 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Etude empirique de la complexité\n- Réaliser la représentation graphique du nombre d'appels à fibo en fonction de $n$.\n- Déterminer par essai/erreur une équation de courbe approximant le tracé précédant (je vous aide : la réponse pourrait faire apparaître du $\\phi_n = \\left(\\frac{1+\\sqrt{5}}{2}\\right)^n$, et pour ceux qui veulent une approximation encore plus fine, ajouter un terme en $\\frac{1}{\\phi_n}$)","metadata":{}},{"cell_type":"code","source":"def fibo_count(n):\n    if n <= 1 :\n        return n, 1\n    else :\n        v_1,n_1 = fibo_count(n-1)\n        v_2,n_2 = fibo_count(n-2)\n        return v_1 + v_2 , n_1 + n_2 + 1\n        \n    ","metadata":{"trusted":true},"execution_count":377,"outputs":[]},{"cell_type":"code","source":"# Code de la fonction qui produit le graphique du nombre d'appels à 'f' en fonction de 'n'\ntab_n = list(range(30))\ntab_nb_op = list(map(lambda n: fibo_count(n)[1], tab_n))\n","metadata":{"trusted":true},"execution_count":378,"outputs":[]},{"cell_type":"code","source":"import seaborn as sns\nsns.lineplot(x=tab_n,y=tab_nb_op)","metadata":{"trusted":true},"execution_count":379,"outputs":[{"execution_count":379,"output_type":"execute_result","data":{"text/plain":"<AxesSubplot:>"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 Axes>","image/png":"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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","source":"# code de la recherche d'une expression approximant le nombre d'appels","metadata":{"trusted":true},"execution_count":380,"outputs":[]},{"cell_type":"code","source":"import numpy as np\ntab_nb_op_log = list(map(np.log, tab_nb_op))\nsns.lineplot(x=tab_n, y=tab_nb_op_log)","metadata":{"trusted":true},"execution_count":381,"outputs":[{"execution_count":381,"output_type":"execute_result","data":{"text/plain":"<AxesSubplot:>"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 Axes>","image/png":"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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":"*** votre analyse...\n\nsi droite parfaite ,log (nb_op) s'ecrit a*n+b ,\na = 14/30 =~ 0.5 , b=0\n\nlog(nb_op) =~  0.5*n + 0\n\nnb_op = exp(0.5*n) = exp(0.5)^n = 1.6487212707001282^n","metadata":{}},{"cell_type":"code","source":"np.exp(0.5)","metadata":{"trusted":true},"execution_count":382,"outputs":[{"execution_count":382,"output_type":"execute_result","data":{"text/plain":"1.6487212707001282"},"metadata":{}}]},{"cell_type":"markdown","source":"On cherche a, b, c, d, e, f, ....  \n\nnb_op = a*(phi^n) + b*(1/phi^n) = c*n^2 + d*n + e*log(n+1) + f*1 # + g*...\n\nIl faut beaucoup moins de coefficient que de donnees.  \n\nPar rapport a ce qu'on cherche on fait une recherche lineare car on cherche les coefficient de la forme lineaire","metadata":{}},{"cell_type":"code","source":"#en cherche np\nimport pandas as pd\n\nphi = (1+np.sqrt(5))/2\n\ndata = pd.DataFrame(tab_n, columns = [\"n\"])\ndata[\"phi^n\"]= data.apply(lambda ligne : phi**ligne[0], axis = 1)\ndata[\"1/phi^n\"]= data.apply(lambda ligne : 1/phi**ligne[0], axis = 1)\ndata[\"n^2\"]= data.apply(lambda ligne : ligne[0]**2, axis = 1)\ndata[\"log(n+1)\"]= data.apply(lambda ligne : np.log(ligne[0]+1), axis = 1)\ndata[\"1\"]= data.apply(lambda ligne : 1, axis = 1)\ndisplay(phi)\ndisplay(data.head())","metadata":{"trusted":true},"execution_count":383,"outputs":[{"output_type":"display_data","data":{"text/plain":"1.618033988749895"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"   n     phi^n   1/phi^n   n^2  log(n+1)  1\n0  0  1.000000  1.000000   0.0  0.000000  1\n1  1  1.618034  0.618034   1.0  0.693147  1\n2  2  2.618034  0.381966   4.0  1.098612  1\n3  3  4.236068  0.236068   9.0  1.386294  1\n4  4  6.854102  0.145898  16.0  1.609438  1","text/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>n</th>\n      <th>phi^n</th>\n      <th>1/phi^n</th>\n      <th>n^2</th>\n      <th>log(n+1)</th>\n      <th>1</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0</td>\n      <td>1.000000</td>\n      <td>1.000000</td>\n      <td>0.0</td>\n      <td>0.000000</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1</td>\n      <td>1.618034</td>\n      <td>0.618034</td>\n      <td>1.0</td>\n      <td>0.693147</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>2</td>\n      <td>2.618034</td>\n      <td>0.381966</td>\n      <td>4.0</td>\n      <td>1.098612</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>3</td>\n      <td>4.236068</td>\n      <td>0.236068</td>\n      <td>9.0</td>\n      <td>1.386294</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>4</td>\n      <td>6.854102</td>\n      <td>0.145898</td>\n      <td>16.0</td>\n      <td>1.609438</td>\n      <td>1</td>\n    </tr>\n  </tbody>\n</table>\n</div>"},"metadata":{}}]},{"cell_type":"code","source":"from sklearn.linear_model import LinearRegression\n\nmodel = LinearRegression().fit(data, tab_nb_op)\ntab_nb_op_approx = model.predict(data)\n\nsns.lineplot(x=tab_n,y=tab_nb_op)\nsns.scatterplot(x=tab_n,y=tab_nb_op_approx)","metadata":{"trusted":true},"execution_count":384,"outputs":[{"execution_count":384,"output_type":"execute_result","data":{"text/plain":"<AxesSubplot:>"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 Axes>","image/png":"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0.67020627,  1.44721411, -6.58471348, -0.01071309, -5.27788845,\n        0.        ])"},"metadata":{}}]},{"cell_type":"markdown","source":"le modele trouvee est :  \n\n##### nb_op = 1.44*(phi^n) - 6.58*(1/phi^n) + -0.011*n^2 + 0.67*n + -5.27*log(n+1) + 0.1*1 # + g*... selon l'etude  experimentale\n\nAttention : les termes phi^n ets tellement plus grand que les autres","metadata":{}},{"cell_type":"markdown","source":"## 1.4. Mémoïsation\n\n<img src=\"https://photos.abweb.com/websites_data/rtl9/upload/programmes/total-recall/jaquette/totalrecall-jaquette.jpg\" width=\"200\" height=\"200\" />\n\n\nRappel : la mémoïsation consiste à stocker les résultats calculés, de façon à ne pas avoir à les recalculer si on en a besoin à nouveau. La structure de données python 'dictionnaire' est bien adaptée pour stocker les résultats déjà calculés.\n\nCe dictionnaire possède pour clefs les paramètres d'appel et pour valeurs le résultat de la fonction appelée avec ces paramètres.\n\nSelon votre aisance en algorithmique et en python, implémenter la mémoïsation de votre fonction récursive par l'une des méthodes suivantes :\n- ré-écrire votre fonction récursive, en implémentant la mémoïsation \n    - piste 1 : ajouter le dictionnaire comme paramètre d'entrée suplémentaire\n    - piste 2 : utilisation d'une closure (fermeture en français) : créer un dictionnaire ; dans le code de la fonction, avant d'appeler la fonction sur un sous problème, regarder dans le dictionnaire si la valeur a déjà été calculée ;  si elle ne correspond à aucune entrée du dictionnaire, la calculer et la stocker dans le dictionnaire ; utiliser la valeur stockée dans le dictionnaire.\n- utiliser un décorateur, c'est certainement la solution la plus élégante car elle peut être parfaitement générique (attention à **bien** comprendre ce que vous faites et à expliquer clairement la magie...)","metadata":{}},{"cell_type":"markdown","source":"### Attention : Utiliser seulement la methode 1","metadata":{}},{"cell_type":"code","source":"# # Vos codes pour la mémoisation methode 2\n# # on commence avec  un dictionnaire de taille 30 fibo\n# tab_n = list(range(30))\n# tab_fibo = list(map(lambda n: fibo(n), tab_n))\n\n# dico = dict.fromkeys(tab_n)\n# for i in tab_n:\n#     dico[i] = tab_fibo[i]\n    \n    \n# def fibo_memo1(n, dico):\n#     if n in dico.keys():\n#         return dico[n]\n#     else:\n#         dico[n] = fibo(n)\n#     return dico[n] ","metadata":{"trusted":true},"execution_count":386,"outputs":[]},{"cell_type":"code","source":"# Vos codes pour la mémoisation methode 1\ndef fibo_memo(n, dico=dict()):\n    if n not in dico:  \n        if n <= 1 :\n            dico[n] = n\n        else :\n            v1 = fibo_memo(n-1, dico)\n            v2 = fibo_memo(n-2, dico)\n            dico[n]= v1 + v2\n    return dico[n]\n\n    ","metadata":{"trusted":true},"execution_count":387,"outputs":[]},{"cell_type":"code","source":"tab_n = list(range(30))\ntab_fibo = list(map(lambda n: fibo(n), tab_n))\n\nnewDico = dict.fromkeys(tab_n)\nfor i in range(30):\n    newDico[i] = tab_fibo[i]\n\ndisplay(fibo_memo(45, newDico)) # works with 2000\ndisplay(1.44*phi**200) # ordre de grandeur de calcul sans memorisation est de 11^20\n","metadata":{"trusted":true},"execution_count":388,"outputs":[{"output_type":"display_data","data":{"text/plain":"1134903170"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"9.034217500868783e+41"},"metadata":{}}]},{"cell_type":"code","source":"","metadata":{"trusted":true},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":"Bien expliquer **votre** solution, avec __**vos**__ mots, et si vous avez choisi la solution avec décorateur, mettez le doigt sur les propriétés de Python qui autorisent ce mécanisme (la même chose ne fonctionnerait pas en c++ par exemple)","metadata":{}},{"cell_type":"markdown","source":"*** vos explications ...","metadata":{}},{"cell_type":"markdown","source":"La 1 methode prend en argument n le nombre quand veut calculer son fibo , et un dico optionnel .  \n\nSi le dico n'est pas passer en parametre, cela veut dire quand va creer un nouveau dico en le remplissant avec la fibo de n   \nSi le dico est passer en parametre , on verifie si n existe dans le dico , si oui on le envoie sa valeur du dico , sinon on la recalcule par recursion tout les fibo du dernier nombre du dico jusqua n et on les ajoutes au dico avant le retourner ","metadata":{}},{"cell_type":"markdown","source":"## 1.5. Utiliser graphviz pour représenter le graphe des appels sur la fonction mémoïsée\nNB : le multi-graphe est maintenant un graphe !","metadata":{}},{"cell_type":"code","source":"# votre code pour produire le multi-graphe des appels\ndef fibo_memo_graph(n, dico=dict(), dot=Graph()):\n    dot.node(str(n))\n    if n not in dico:  \n        if n <= 1 :\n            dico[n] = n, dot\n        else :\n            dot.node(str(n-1))\n            dot.node(str(n-2))\n            dot.edge(str(n),str(n-1))\n            dot.edge(str(n),str(n-2))\n            v1 = fibo_memo_graph(n-1, dico, dot)\n            v2 = fibo_memo_graph(n-2,dico, dot)\n            dico[n]= v1 + v2\n    return dico[n], dot","metadata":{"trusted":true},"execution_count":389,"outputs":[]},{"cell_type":"code","source":"v, g = fibo_memo_graph(10)\ndisplay(g)\n","metadata":{"trusted":true},"execution_count":390,"outputs":[{"output_type":"display_data","data":{"text/plain":"<graphviz.dot.Graph at 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Refaire l'étude de complexité empirique dans le cas de la fonction mémoïsée\n","metadata":{}},{"cell_type":"code","source":"# votre code\ndef fibo_count_memo(n, dico=dict()):\n    if n not in dico:      \n        if n <= 1 :\n            return dico[n]\n        else :\n            v_1= fibo_count_memo(n-1, dico)\n            v_2= fibo_count_memo(n-2, dico)\n            dico[n] = v_1 + v_2\n    return dico[n]\n","metadata":{"trusted":true},"execution_count":391,"outputs":[]},{"cell_type":"code","source":"display(fibo_count_memo(10,newDico))","metadata":{"trusted":true},"execution_count":392,"outputs":[{"output_type":"display_data","data":{"text/plain":"55"},"metadata":{}}]},{"cell_type":"code","source":"# Code de la fonction qui produit le graphique du nombre d'appels à 'f' en fonction de 'n'\ntab_n_memo = list(range(30))\ntab_nb_op_memo = list(map(lambda n: fibo_count_memo(n, newDico), tab_n_memo))","metadata":{"trusted":true},"execution_count":393,"outputs":[]},{"cell_type":"code","source":"sns.lineplot(x=tab_n_memo,y=tab_nb_op_memo)","metadata":{"trusted":true},"execution_count":394,"outputs":[{"execution_count":394,"output_type":"execute_result","data":{"text/plain":"<AxesSubplot:>"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","source":"tab_nb_op_log_memo = list(map(np.log, tab_nb_op_memo))\nsns.lineplot(x=tab_n_memo, y=tab_nb_op_log_memo)","metadata":{"trusted":true},"execution_count":395,"outputs":[{"name":"stderr","text":"/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:1: RuntimeWarning: divide by zero encountered in log\n  \"\"\"Entry point for launching an IPython kernel.\n","output_type":"stream"},{"execution_count":395,"output_type":"execute_result","data":{"text/plain":"<AxesSubplot:>"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 Axes>","image/png":"iVBORw0KGgoAAAANSUhEUgAAAXIAAAD4CAYAAADxeG0DAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8+yak3AAAACXBIWXMAAAsTAAALEwEAmpwYAAAcm0lEQVR4nO3deXhU9dnG8e8PBNn3gGwxbLKvRlBE1GorKooLqFRbFVq6vq9dAHHFrYiAVqtVi0vVitUmoKAgiwsFq6KgZIEQCGEnEHYIkHWe948Z36YpgZCZZObM3J/r8mJyMsl5jse5uT1zzhxnZoiIiHfVCPcAIiISHAW5iIjHKchFRDxOQS4i4nEKchERjzujOlfWokULS0hIqM5Vioh43qpVq/aaWVx536/WIE9ISGDlypXVuUoREc9zzm052fd1aEVExOMU5CIiHqcgFxHxOAW5iIjHKchFRDxOQS4i4nEKchERj1OQi4hUoYPHCnlo3hoO5xdV2Tqq9YIgEZFYsnjNLu59N52DxwoZ0rkFl/doVSXrUZCLiITYgaOFPPT+Guau3kn31o14fcx59GzTuMrWpyAXEQmhRWt2cV+ghf/m8i786tLO1KpZtUexFeQiIiFw4Gghk+etYV7KTnq0bsQbYwbSo02jalm3glxEJEgL03dx/3tpHDxWxG8vP4dfXtqpylt4aQpyEZFK2h9o4e+n7KRnm0a8MWZQtbXw0hTkIiKVsDA9h/vfS+fQ8SJ+9/1z+MUl1dvCS1OQi4ichv1HC3lwbjofpObQs00j/jZ2EN1bV38LL01BLiJSQR+m+Vv44fwifv/9c/h5GFt4aQpyEZFT2JdXwIPz1jA/NYdebRsxa9Qgup0V3hZemoJcROQkFqTl8ECghY//wTn87OLIaOGlKchFRE5gX14BD85dw/y0HHq3bcxbo86n61kNwz3WCSnIRUTKmJ+awwNz0zmSX8SEK7oybmjHiGvhpSnIRUQC9uYV8ODcdBak7aJPu8ZMHxm5Lby0Uwa5c+5VYDiQa2a9AsumA9cAhcBG4E4zO1iFc4qIVKkPUnfy4Nw15OUXM+GKrvxsaEfOiOAWXlpFpnwNGFZm2RKgl5n1AdYD94R4LhGRarE3r4BfzlrFr9/6lnZN6/L+/wzhV5d29kyIQwUauZktc84llFm2uNSXXwIjQzyXiEiVMjM+SM3hwbnpHC0oYeKwroy7yDstvLRQHCMfA7wTgt8jIlIt9hwp4IH30lm4Zhd92zVmxqi+dGkV+cfCyxNUkDvn7gOKgVknec44YBxAfHx8MKsTEQmKmfF+ag6TAy387mHd+OlFHTzZwkurdJA75+7A/yboZWZm5T3PzGYCMwESExPLfZ6ISFX6jxbevgkzRvbxdAsvrVJB7pwbBkwELjazY6EdSUQkdMyMeSk7mTxvDccKS7jnym6MHeL9Fl5aRU4//DtwCdDCObcdmIz/LJUzgSXOOYAvzeznVTiniMhpyz2SzwPvpbNozW76tW/CjFF96NwyOlp4aRU5a2X0CRa/UgWziIiExIla+E8u6kjNGi7co1UJXdkpIlEl90g+97+bzuK1u+kf34TpI/vSuWWDcI9VpRTkIhIVyrbwe6/qxtgh0dvCS1OQi4jn5R7J575301mydjcD4pswLQZaeGkKchHxLDNj7mp/C88vKuG+q7ozZkiHmGjhpSnIRcSTcg/nc++76XyU4W/h00f1pVNc7LTw0hTkIuIpZVv4/Vd3584LY6+Fl6YgFxHPUAs/MQW5iEQ8M+Pdb3fw0Lw1FBT71MLLUJCLSETbfTife+ek8fG6XBLPbsq0kX3oqBb+HxTkIhKRzIw53+zg4ffVwk9FQS4iEadsC58+qi8dWtQP91gRS0EuIhHDzJj9zQ4eeX8NhSU+Hhzeg9sHJ6iFn4KCXEQiwq5D+dz7bhqfrMvlvISmTBupFl5RCnIRCSszI3nVdh75YC1FgRZ+x+AEaqiFV5iCXETCJufQce6Zk8bSzD0MTGjGtJF9SFALP20KchGpdmZG0qrtPBpo4ZOv6cHtF6iFV5aCXESqVc6h40yancY/1+9hYIdmTLtRLTxYCnIRqRZmRtJKfwsv9hkPXdODH6uFh4SCXESq3M6D/mPh37Xw6SP7cHZztfBQUZCLSJUxM/6xchuPfZBBsc94+Nqe/Oj8s9XCQ0xBLiJVYufB40yak8ay9XsY1KEZ00f2Jb55vXCPFZVOGeTOuVeB4UCumfUKLGsGvAMkAJuBm8zsQNWNKSJeYWa88/U2Hpufgc/UwqtDjQo85zVgWJllk4CPzawL8HHgaxGJcTsOHufHr37FpDlp9GrbiIV3DeV2XdxT5U7ZyM1smXMuocziEcAlgcevA0uBu0M5mIh4h5nx9tfb+EOghT86oie3DlILry6VPUbeysxyAo93Aa1CNI+IeMyOg8eZNDuV5Rv2ckHH5kwb2Yf2zXQsvDoF/WanmZlzzsr7vnNuHDAOID4+PtjViUiE+K8Wfl0vbh0YrxYeBpUN8t3OudZmluOcaw3klvdEM5sJzARITEwsN/BFxDu2HzjGPXPSWL5hL4M7NeeJG9XCw6myQT4PuB2YGvhzbsgmEpGIZWb8/attTFmQgZnxh+t78cOB8TinFh5OFTn98O/439hs4ZzbDkzGH+D/cM6NBbYAN1XlkCISftsPHGPS7DQ+y9rLhZ2bM/UGtfBIUZGzVkaX863LQjyLiEQgM+Otr7YyZX4GAFOu783oge3VwiOIruwUkXJt23+MSXNS+VfWPoZ0bsHUG3vTrqlaeKRRkIvIfzEzZq3YyuMLMnDO8fgNvbnlPLXwSKUgF5H/sG3/Me6encrnG/dxUZcWTL2xD22b1A33WHISCnIRAcDnM2Z95W/hNdTCPUVBLiJq4R6nIBeJYT6fMWvFFh7/cB01nGPqDb25WS3ccxTkIjFq2/5jTExO5YvsfQw9J46pN/SmjVq4JynIRWKMz2e8uWILUz9cR03neOLG3tyUqBbuZQpykRiydd8xJiSnsGLTfrXwKKIgF4kBPp/xty/9LfyMGo5pN/ZhVGI7tfAooSAXiXJb9h1lQnIqX23az8XnxPG4WnjUUZCLRCmfz3jji808sTDT38JH9mHUuWrh0UhBLhKFNu89ysTkVL7a7G/hU2/sTevGauHRSkEuEkV8PuP1LzbzxMJ11KpZQy08RijIRaJE6RZ+adc4ptygFh4rFOQiHufzGa99vplpi/wtfMaovtw4oK1aeAxRkIt42Ka9R5mYnMLXmw9wadc4Hr+hD2c1rhPusaSaKchFPKgk0MKnq4ULCnIRz9m09ygTklJYueUA3+vWkinX91YLj3EKchGPKPEZf/3XJqYvyuTMM2rw5Ki+3KAWLijIRTwhe08eE5JTWbXlAJd1a8mUG3rTqpFauPgpyEUiWNkW/tRNfbm+v1q4/Keggtw591vgJ4ABacCdZpYfisFEYt3GPXlMDLTwy7v7j4W3VAuXE6h0kDvn2gL/C/Qws+POuX8AtwCvhWg2kZhU4jNe/WwTMxZnUqdWTf54c1+u66cWLuUL9tDKGUBd51wRUA/YGfxIIrErKzePCckpfLv1IJd3b8WU63uphcspVTrIzWyHc24GsBU4Diw2s8Vln+ecGweMA4iPj6/s6kSiWonPeOWzbGYsXk/dWjV5+uZ+jOjXRi1cKqRGZX/QOdcUGAF0ANoA9Z1zt5V9npnNNLNEM0uMi4ur/KQiUSorN4+RL37OlAXruPicOJb8bijX6Q1NOQ3BHFq5HNhkZnsAnHNzgMHAm6EYTCTalfiMl5dn8+SS9dSrrRYulRdMkG8FznfO1cN/aOUyYGVIphKJclm5eYxPSmH1toP8oEcrHru+Fy0b6li4VE4wx8hXOOeSgW+AYuBbYGaoBhOJRiU+46Xl2TwVaOHP3NKPa/uqhUtwgjprxcwmA5NDNItIVMvKPcL4pFRWbzvIFT1b8dh1vYlreGa4x5IooCs7RapYcYmPlz/bxFNL1lO/dk2eHd2f4X1aq4VLyCjIRapQVu4Rfp+USsq2gwzreRaPXtdLLVxCTkEuUgWKS3y8tHwTf/xILVyqnoJcJMQ27D7C+KQUUrYf4spe/hbeooFauFQdBblIiBSX+Ji5PJunl2ygQZ0z+PMPB3B1n9bhHktigIJcJATWB1p46vZDXNX7LB4ZoRYu1UdBLhKE4hIff1mWzTMfqYVL+CjIRSopc5e/haftOMTVvVvzyIieNFcLlzBQkIucpuISHy/+cyPPfLyBRnVqqYVL2CnIRU7Df7TwPq155Fq1cAk/BblIBRSV+Hhx6Ub+9Im/hT9/6wCu6q0WLpFBQS5yChk5h5mQnEL6jsMM79Oah9XCJcIoyEXKUVTi44WlG3k20MJfuHUAV6qFSwRSkIucQEbOYcYnpbBm52Gu6duGh6/tSbP6tcM9lsgJKchFSikq8fH8pxt57tMNNK5bixdvG8CwXmrhEtkU5CIBa3f6W/janMNc27cND6mFi0coyCXmfdfCn/1kA03q1eLF285lWK+zwj2WSIUpyCWmrdl5iAlJqazNOcyIfm146JqeNFULF49RkEtMKiz28fzSLJ77JIsm9WqrhYunKcgl5qzZeYjxSalkqIVLlFCQS8woLPbx50+z+POn/hb+lx+dyxU91cLF+4IKcudcE+BloBdgwBgz+yIEc4mEVPqOQ4xPSmHdriNc378tk6/pQZN6auESHYJt5M8AC81spHOuNlAvBDOJhExhsY/nPs3i+U+zaFq/Ni/9OJHv92gV7rFEQqrSQe6cawwMBe4AMLNCoDA0Y4kETy1cYkUwjbwDsAf4q3OuL7AKuMvMjpZ+knNuHDAOID4+PojViVRMYbGP5z7ZwPNLN6qFS0yoEcTPngEMAF4ws/7AUWBS2SeZ2UwzSzSzxLi4uCBWJ3Jq6TsOce1zn/GnT7K4tm8blvx2qEJcol4wjXw7sN3MVgS+TuYEQS5SHQqKS3jukyyeX7qR5vVr8/KPE7lcAS4xotJBbma7nHPbnHNdzSwTuAxYG7rRRCombbv/WHjm7iPcMKAtk4f3pHG9WuEeS6TaBHvWyv8AswJnrGQDdwY/kkjFFBSX8OzHWbzwz420aFCbV25P5LLuauESe4IKcjNbDSSGZhSRiivdwkee244Hru6hFi4xS1d2iqeUbeF/veM8Lu3WMtxjiYSVglw8I3X7QSYkpZK5+wijzm3H/cN70LiuWriIglwiXkFxCX/6eAMv/jObuAZnqoWLlKEgl4iWuv0g45NSWL87j5sS23Hf1WrhImUpyCUiFRSX8MxHG/jLsmxaNjyT1+48j0u6qoWLnIiCXCLO6m0HmZCUwoZcfwu/f3gPGtVRCxcpj4JcIkZ+UQlPf7SBmcs20qpRHbVwkQpSkEtE+HbrASYkp5KVm8fNie25b3h3tXCRClKQS1jlF5Xwx4/W89KybFo1qsPrYwZy8Tn6cDWR06Egl7D5dusBxielsHHPUbVwkSAoyKXa5ReV8Mcl63lpeTZnNarDG2MGMlQtXKTSFORSrb7ZeoAJgRY+emB77rlKLVwkWApyqRb5RSU8tWQ9L6uFi4Scglyq3KotB5iQnEL2nqOMHhjPvVd1o6FauEjIKMilyuQXlfDk4kxe/mwTbRrX5W9jB3JRF7VwkVBTkEuVWLVlPxOSUsnee5QfDornnivVwkWqioJcQiq/qIQZizJ55V/+Fv7m2EEM6dIi3GOJRDUFuYTMys37mZjsb+G3Dornnqu60+BM/ScmUtX0KpOgHS8sYcbiTF4NtPBZPxnEhZ3VwkWqi4JcgrJy834mJKeyae9Rbjs/nklXqoWLVDe94qRSyrbwt34yiMFq4SJhEXSQO+dqAiuBHWY2PPiRJNJ9vXk/E5JS2LzvGD86/2zuvrKbWrhIGIXi1XcXkAE0CsHvkgh2vLCE6Ysy+evnm2jbpC5v/XQQgzuphYuEW1BB7pxrB1wN/AH4XUgmkoj01ab9TEz+dwufdGU36quFi0SEYF+JTwMTgYblPcE5Nw4YBxAfHx/k6qS6HSssZvqiTF77fDPtmqqFi0SiSge5c244kGtmq5xzl5T3PDObCcwESExMtMquT6rfiux9TJydypZ9x7j9grOZOEwtXCQSBfOqvBC41jl3FVAHaOSce9PMbgvNaBIuxwqLmbbQ38Ljm9Xj7z89nws6NQ/3WCJSjkoHuZndA9wDEGjk4xXi3vdl9j4mJqeydf8x7hicwMRhXalXWy1cJJLpFSrAf7fwt8edz/kd1cJFvCAkQW5mS4GlofhdUv2+2LiPu2erhYt4lV6tMexoQTHTFq7j9S+2cHbzerwz7nwGqYWLeI6CPEZ9sXEfE2ensP3Ace68MIGJV3Sjbu2a4R5LRCpBQR5jjhYU88TCdbzx/y38AgZ2aBbusUQkCAryGKIWLhKdFOQxQC1cJLopyKPc5xv3cvfsVLYfOM6YCzsw4YquauEiUUZBHqWOFhQz9cN1/O3LLSSohYtENQV5FFILF4ktCvIokldQzNQPM3jzy61q4SIxREEeJf6VtZeJyansPHScsUM6MP4HauEisUJB7nFH8ot4/MN1vLViKx1b1Cf55xdw7tlq4SKxREHuYcvW72HS7FR2Hc5n3NCO/O7751Cnllq4SKxRkHvQ4fwipszP4O2vt9Eprj7JvxjMgPim4R5LRMJEQe4xSzNzuWdOGrsP5/Pzizvxm8u7qIWLxDgFuUcczi/i0ffXkrRqO11aNuCFX15Iv/ZNwj2WiEQABbkHLM3MZdLsNPbkFfDLSzrxv5ephYvIvynII9iR/CL+EDgW3qVlA/7yo3PpqxYuImUoyCPU8g17uDvZf0bKLy7pxF1q4SJSDgV5hMkrKGbKggz/eeFx9Zn9i8H01xkpInISCvII8nnWXiYErs7UeeEiUlEK8ghQ+vPCO7SoT9LPLiAxQVdnikjFVDrInXPtgTeAVoABM83smVANFiu+zN7HhOQUfVKhiFRaMI28GPi9mX3jnGsIrHLOLTGztSGaLarlBe5g/8YXW4hvVo+3f6o72ItI5VQ6yM0sB8gJPD7inMsA2gIK8lNYmpnLfe+ms/PQce4YnMDEYV2pV1tHuUSkckKSHs65BKA/sOIE3xsHjAOIj48Pxeo868DRQh6dv5Y53+zwf0aKPqlQREIg6CB3zjUAZgO/MbPDZb9vZjOBmQCJiYkW7Pq8yMz4MH0XD85N5+CxIn59aWd+/b3OOiNFREIiqCB3ztXCH+KzzGxOaEaKLrmH83lgbjqL1uymV9tGvD5mID3bNA73WCISRYI5a8UBrwAZZvZU6EaKDmZG0qrtPPbBWvKLfdw9rBs/vagDZ9SsEe7RRCTKBNPILwR+BKQ551YHlt1rZguCnsrjtu0/xr3vprF8w14GJjRj6o296RjXINxjiUiUCuaslc8AF8JZPM/MeOfrbTzywVoc8OiIntw66Gxq1NC/JhGpOjrnLUT2Hy1k0uxUFq/dzeBOzZk+qi9tm9QN91giEgMU5CGwbP0exielcPBYEfdd1Z2xQzqohYtItVGQByG/qISpH67jtc8306VlA167cyA92jQK91giEmMU5JWUkXOY37y9mszdR7hjcAKTruym88JFJCwU5KfJ5zNe/dcmpi3MpFHdWvz1zvO4tGvLcI8lIjFMQX4adh3KZ3xSCp9l7eXy7q144sbeNG9wZrjHEpEYpyCvADNjQdou7nsvjYIiH1Ou783oge3xXxMlIhJeCvJTSN9xiMfmr+XL7P30adeYp2/up4t7RCSiKMjLsetQPtMXZTLn2+00rVebR0f05JaB8dTSJfYiEmEU5GUcLSjmL8uyeWlZNiU+Y9zQjvzq0s40qlMr3KOJiJyQgjygxGfM/mY7MxZlknukgKv7tGbSsG60b1Yv3KOJiJyUghz/3esfm5/B2pzD9I9vwgu3DdANH0TEM2I6yLP35DFlQQYfZeTStkldnh3dn+F9WutsFBHxlJgN8q827WfMa18DcPewbtx5YYKuzBQRT4rJIP9sw15+8sbXtGlSlzfHDqKNPqVQRDws5oL844zd/GLWN3RsUZ+/jR1EXENdmSki3hZTQT4/NYe73v6Wnm38985sUq92uEcSEQlazAT57FXbmZCcwrlnN+XVO86joc4LF5EoERNBPmvFFu57N50hnVsw88fnUq92TGy2iMSIqE+0l5dn89j8DC7r1pI/3zpAZ6aISNSJ2iA3M577JIsnl6zn6t6t+ePN/ah9hj4nRUSiT1DJ5pwb5pzLdM5lOecmhWqoYJkZ0xZl8uSS9dzQvy3P3KIQF5HoVel0c87VBP4MXAn0AEY753qEarDK8vmMh99fywtLN/LDQfHMGNWXM/SJhSISxYI5tDIQyDKzbADn3NvACGBtKAYr7dmPNzAvZWeFnltQ7GPr/mOMHdKB+6/ursvtRSTqBRPkbYFtpb7eDgwq+yTn3DhgHEB8fHylVhTX8Ey6tKr4zRzuvDCBOwYnKMRFJCZU+ZudZjYTmAmQmJholfkdtwyM55aBlftLQEQk2gVz8HgH0L7U1+0Cy0REpBoFE+RfA12ccx2cc7WBW4B5oRlLREQqqtKHVsys2Dn3a2ARUBN41czWhGwyERGpkKCOkZvZAmBBiGYREZFK0AnWIiIepyAXEfE4BbmIiMcpyEVEPM6ZVeoancqtzLk9wJZSi1oAe6ttgOoVrdum7fKeaN22WNqus80srrwfqNYg/6+VO7fSzBLDNkAVitZt03Z5T7Rum7br33RoRUTE4xTkIiIeF+4gnxnm9VelaN02bZf3ROu2absCwnqMXEREghfuRi4iIkFSkIuIeFzYgjxSb9wcLOfcZudcmnNutXNuZbjnCYZz7lXnXK5zLr3UsmbOuSXOuQ2BP5uGc8bKKGe7HnLO7Qjst9XOuavCOWNlOOfaO+c+dc6tdc6tcc7dFVju6X12ku2Khn1Wxzn3lXMuJbBtDweWd3DOrQjk4zuBjwov//eE4xh54MbN64Hv479F3NfAaDML+f0+q5tzbjOQaGaev1DBOTcUyAPeMLNegWXTgP1mNjXwF3BTM7s7nHOernK26yEgz8xmhHO2YDjnWgOtzewb51xDYBVwHXAHHt5nJ9mum/D+PnNAfTPLc87VAj4D7gJ+B8wxs7edcy8CKWb2Qnm/J1yN/P9v3GxmhcB3N26WCGJmy4D9ZRaPAF4PPH4d/wvKU8rZLs8zsxwz+ybw+AiQgf/eup7eZyfZLs8zv7zAl7UC/xjwPSA5sPyU+yxcQX6iGzdHxY7BvxMWO+dWBW48HW1amVlO4PEuoFU4hwmxXzvnUgOHXjx1+KEs51wC0B9YQRTtszLbBVGwz5xzNZ1zq4FcYAmwEThoZsWBp5wyH/VmZ+gNMbMBwJXArwL/Gx+VzH9cLlrOX30B6AT0A3KAJ8M6TRCccw2A2cBvzOxw6e95eZ+dYLuiYp+ZWYmZ9cN/3+OBQLfT/R3hCvKovXGzme0I/JkLvIt/x0ST3YFjlt8du8wN8zwhYWa7Ay8oH/ASHt1vgeOss4FZZjYnsNjz++xE2xUt++w7ZnYQ+BS4AGjinPvuDm6nzMdwBXlU3rjZOVc/8GYMzrn6wA+A9JP/lOfMA24PPL4dmBvGWULmu6ALuB4P7rfAG2evABlm9lSpb3l6n5W3XVGyz+Kcc00Cj+viPwEkA3+gjww87ZT7LGxXdgZOFXqaf9+4+Q9hGSSEnHMd8bdw8N8P9S0vb5dz7u/AJfg/VnM3MBl4D/gHEI//I4lvMjNPvXFYznZdgv9/0Q3YDPys1HFlT3DODQGWA2mAL7D4XvzHkz27z06yXaPx/j7rg//NzJr4i/U/zOyRQJa8DTQDvgVuM7OCcn+PLtEXEfE2vdkpIuJxCnIREY9TkIuIeJyCXETE4xTkIiIepyAXEfE4BbmIiMf9Hzr+gFraemOWAAAAAElFTkSuQmCC\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":"Cette courbe est un tout petit peut mieux que la precedente (particulierement pour n < 5)\n\n*** votre analyse...\n\nsi droite parfaite ,log (nb_op) s'ecrit a*n+b ,\na = 10/22.1 =~ 0.45 , b=0\n\nlog(nb_op) =~  0.45*n + 0\n\nnb_op = exp(0.45*n) = exp(0.45)^n = 1.568312185490169^n","metadata":{}},{"cell_type":"code","source":"np.exp(0.45)","metadata":{"trusted":true},"execution_count":396,"outputs":[{"execution_count":396,"output_type":"execute_result","data":{"text/plain":"1.568312185490169"},"metadata":{}}]},{"cell_type":"markdown","source":"On cherche a, b, c, d, e, f, ....  \n\nnb_op_memo = a*(phi^n) + b*(1/phi^n) = c*n^2 + d*n + e*log(n+1) + f*1","metadata":{}},{"cell_type":"code","source":"phi = (1+np.sqrt(5))/2\n\ndata_memo = pd.DataFrame(tab_n_memo, columns = [\"n\"])\ndata_memo[\"phi^n\"]= data_memo.apply(lambda ligne : phi**ligne[0], axis = 1)\ndata_memo[\"1/phi^n\"]= data_memo.apply(lambda ligne : 1/phi**ligne[0], axis = 1)\ndata_memo[\"n^2\"]= data_memo.apply(lambda ligne : ligne[0]**2, axis = 1)\ndata_memo[\"log(n+1)\"]= data_memo.apply(lambda ligne : np.log(ligne[0]+1), axis = 1)\ndata_memo[\"1\"]= data_memo.apply(lambda ligne : 1, axis = 1)\ndisplay(phi)\ndisplay(data_memo.head())","metadata":{"trusted":true},"execution_count":397,"outputs":[{"output_type":"display_data","data":{"text/plain":"1.618033988749895"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"   n     phi^n   1/phi^n   n^2  log(n+1)  1\n0  0  1.000000  1.000000   0.0  0.000000  1\n1  1  1.618034  0.618034   1.0  0.693147  1\n2  2  2.618034  0.381966   4.0  1.098612  1\n3  3  4.236068  0.236068   9.0  1.386294  1\n4  4  6.854102  0.145898  16.0  1.609438  1","text/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>n</th>\n      <th>phi^n</th>\n      <th>1/phi^n</th>\n      <th>n^2</th>\n      <th>log(n+1)</th>\n      <th>1</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0</td>\n      <td>1.000000</td>\n      <td>1.000000</td>\n      <td>0.0</td>\n      <td>0.000000</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1</td>\n      <td>1.618034</td>\n      <td>0.618034</td>\n      <td>1.0</td>\n      <td>0.693147</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>2</td>\n      <td>2.618034</td>\n      <td>0.381966</td>\n      <td>4.0</td>\n      <td>1.098612</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>3</td>\n      <td>4.236068</td>\n      <td>0.236068</td>\n      <td>9.0</td>\n      <td>1.386294</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>4</td>\n      <td>6.854102</td>\n      <td>0.145898</td>\n      <td>16.0</td>\n      <td>1.609438</td>\n      <td>1</td>\n    </tr>\n  </tbody>\n</table>\n</div>"},"metadata":{}}]},{"cell_type":"code","source":"model_memo = LinearRegression().fit(data_memo, tab_nb_op_memo)\ntab_nb_op_approx_memo = model_memo.predict(data_memo)\n\nsns.lineplot(x=tab_n_memo ,y=tab_nb_op_memo)\nsns.scatterplot(x=tab_n_memo,y=tab_nb_op_approx_memo)","metadata":{"trusted":true},"execution_count":398,"outputs":[{"execution_count":398,"output_type":"execute_result","data":{"text/plain":"<AxesSubplot:>"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 Axes>","image/png":"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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","source":"display(model_memo.coef_)","metadata":{"trusted":true},"execution_count":399,"outputs":[{"output_type":"display_data","data":{"text/plain":"array([-0.54220827,  0.44721318,  5.32714511,  0.00866707,  4.26990145,\n        0.        ])"},"metadata":{}}]},{"cell_type":"markdown","source":"*** vos commentaires...\n","metadata":{}},{"cell_type":"markdown","source":"le modele trouvee est :  \n\n##### nb_op = 0.45*(phi^n) + 5.33*(1/phi^n) + 0.008*n^2 - 0.54*n + -4.27*log(n+1) + 0.1*1 # + g*... selon l'etude  experimentale","metadata":{}},{"cell_type":"markdown","source":"# 1.7. Programmation dynamique\nLe passage à la programmation dynamique va consister à ne conserver que les résultats nécessaires (contrairement à la mémoïsation qui les conserve tous) et à trouver un ordre d'évaluation qui permet de n'en conserver à chaque instant que le strict minimum.\n\nEcrire le programme mettant en oeuvre cet objectif.","metadata":{}},{"cell_type":"code","source":"# votre code\ndef fibo_dyna(n):\n    if n <= 1 :\n        return n \n    else :\n        prec, prec_prec = 1,0\n        for _ in range(1,n):\n            prec, prec_prec = prec + prec_prec, prec\n        return prec","metadata":{"trusted":true},"execution_count":400,"outputs":[]},{"cell_type":"code","source":"def fibo_count_dyno(n):    \n    if n <= 1 :\n        return n\n    else :\n        prec = fibo_count_dyno(n-1)\n        prec_prec = fibo_count_dyno(n-2)\n        ret = prec + prec_prec\n        return ret\n","metadata":{"trusted":true},"execution_count":401,"outputs":[]},{"cell_type":"code","source":"print(list(map(lambda n : fibo(n) == fibo_dyna(n), tab_n)))\nprint(sum(map(lambda n : fibo(n) == fibo_dyna(n), tab_n)))\n","metadata":{"trusted":true},"execution_count":402,"outputs":[{"name":"stdout","text":"[True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True]\n30\n","output_type":"stream"}]},{"cell_type":"markdown","source":"*** vos commentaires ...  \navant la boucle O(1)  \n'+ O(n)  \n= O(n)","metadata":{"trusted":true}},{"cell_type":"markdown","source":"# 1.8. Refaire l'étude empirique de complexité sur cette nouvelle fonction","metadata":{}},{"cell_type":"code","source":"# votre code\ntab_n_dyno = list(range(30))\ntab_nb_op_dyno = list(map(lambda n: fibo_count_dyno(n), tab_n_dyno))\n\nsns.lineplot(x=tab_n_dyno,y=tab_nb_op_dyno)\n\n","metadata":{"trusted":true},"execution_count":403,"outputs":[{"execution_count":403,"output_type":"execute_result","data":{"text/plain":"<AxesSubplot:>"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 Axes>","image/png":"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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","source":"tab_nb_op_log_dyno = list(map(np.log, tab_nb_op_dyno))\nsns.lineplot(x=tab_n_dyno, y=tab_nb_op_log_dyno)","metadata":{"trusted":true},"execution_count":404,"outputs":[{"name":"stderr","text":"/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:1: RuntimeWarning: divide by zero encountered in log\n  \"\"\"Entry point for launching an IPython kernel.\n","output_type":"stream"},{"execution_count":404,"output_type":"execute_result","data":{"text/plain":"<AxesSubplot:>"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 Axes>","image/png":"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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":"Cette courbe est presque la meme que la precedente\n\n*** votre analyse...\n\nsi droite parfaite ,log (nb_op) s'ecrit a*n+b ,\na = 10/22.5 =~ 0.444 , b=0\n\nlog(nb_op) =~  0.44*n + 0\n\nnb_op = exp(0.44*n) = exp(0.44)^n =1.552707218511336^n","metadata":{}},{"cell_type":"code","source":"np.exp(0.44)","metadata":{"trusted":true},"execution_count":405,"outputs":[{"execution_count":405,"output_type":"execute_result","data":{"text/plain":"1.552707218511336"},"metadata":{}}]},{"cell_type":"markdown","source":"On cherche a, b, c, d, e, f, ....  \n\nnb_op_memo = a*(phi^n) + b*(1/phi^n) = c*n^2 + d*n + e*log(n+1) + f*1","metadata":{}},{"cell_type":"code","source":"phi = (1+np.sqrt(5))/2\n\ndata_dyno = pd.DataFrame(tab_n_dyno, columns = [\"n\"])\ndata_dyno[\"phi^n\"]= data_dyno.apply(lambda ligne : phi**ligne[0], axis = 1)\ndata_dyno[\"1/phi^n\"]= data_dyno.apply(lambda ligne : 1/phi**ligne[0], axis = 1)\ndata_dyno[\"n^2\"]= data_dyno.apply(lambda ligne : ligne[0]**2, axis = 1)\ndata_dyno[\"log(n+1)\"]= data_dyno.apply(lambda ligne : np.log(ligne[0]+1), axis = 1)\ndata_dyno[\"1\"]= data_dyno.apply(lambda ligne : 1, axis = 1)\ndisplay(phi)\ndisplay(data_dyno.head())\n\nmodel_dyno = LinearRegression().fit(data_dyno, tab_nb_op_dyno)\ntab_nb_op_approx_dyno = model_dyno.predict(data_dyno)\n\nsns.lineplot(x=tab_n_dyno ,y=tab_nb_op_dyno)\nsns.scatterplot(x=tab_n_dyno,y=tab_nb_op_approx_dyno)","metadata":{"trusted":true},"execution_count":406,"outputs":[{"output_type":"display_data","data":{"text/plain":"1.618033988749895"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"   n     phi^n   1/phi^n   n^2  log(n+1)  1\n0  0  1.000000  1.000000   0.0  0.000000  1\n1  1  1.618034  0.618034   1.0  0.693147  1\n2  2  2.618034  0.381966   4.0  1.098612  1\n3  3  4.236068  0.236068   9.0  1.386294  1\n4  4  6.854102  0.145898  16.0  1.609438  1","text/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>n</th>\n      <th>phi^n</th>\n      <th>1/phi^n</th>\n      <th>n^2</th>\n      <th>log(n+1)</th>\n      <th>1</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0</td>\n      <td>1.000000</td>\n      <td>1.000000</td>\n      <td>0.0</td>\n      <td>0.000000</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1</td>\n      <td>1.618034</td>\n      <td>0.618034</td>\n      <td>1.0</td>\n      <td>0.693147</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>2</td>\n      <td>2.618034</td>\n      <td>0.381966</td>\n      <td>4.0</td>\n      <td>1.098612</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>3</td>\n      <td>4.236068</td>\n      <td>0.236068</td>\n      <td>9.0</td>\n      <td>1.386294</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>4</td>\n      <td>6.854102</td>\n      <td>0.145898</td>\n      <td>16.0</td>\n      <td>1.609438</td>\n      <td>1</td>\n    </tr>\n  </tbody>\n</table>\n</div>"},"metadata":{}},{"execution_count":406,"output_type":"execute_result","data":{"text/plain":"<AxesSubplot:>"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","source":"display(model_dyno.coef_)","metadata":{"trusted":true},"execution_count":407,"outputs":[{"output_type":"display_data","data":{"text/plain":"array([-0.54220827,  0.44721318,  5.32714511,  0.00866707,  4.26990145,\n        0.        ])"},"metadata":{}}]},{"cell_type":"markdown","source":"*** vos commentaires...","metadata":{}},{"cell_type":"markdown","source":"le modele trouvee est :  \n\n##### nb_op = 0.44*(phi^n) + 5.32*(1/phi^n) + 0.008*n^2 - 0.54*n + -4.27*log(n+1) + 0.1*1 # + g*... selon l'etude  experimentale","metadata":{}},{"cell_type":"markdown","source":"# 2. Distance d'édition\n---\n---\n\n| | | |\n|---|---|---|\n| Elle peut servir à déterminer la distance entre deux brins d'ADN | | ![arbre_phylogenetique.jpg](attachment:arbre_phylogenetique.jpg) |\n\n\nSoient $M$ et $P$ deux chaînes de caractères. La distance d'édition entre $M$ et $P$ est le nombre minimal d'opérations permettant de transformer $M$ en $P$, les opérations étant prises parmi :\n- substitution d'un caractère de M par un caractère différent de P (coût $c_s>0$)\n- insertion dans M d'un caractère de P (coût $c_i>0$)\n- suppression d'un caractère de M (coût $c_d>0$)\n\nLe but de cette partie du TP est de calculer la distance d'édition entre deux mots ainsi que de calculer une suite de transformations de coût minimal permettant de transformer un mot en un autre mot (le coût d'une transformation est la somme des coûts des opérations qui la composent).\n\nAfin de parvenir à ce résultat, plusieurs phases vous sont demandées, présentées dans les questions suivantes.\n\nPour votre travail, les valeurs des coûts des opérations n'auront pas d'importance (dans des cas applicatifs ils ont évidemment de l'importance).","metadata":{"_cell_guid":"79c7e3d0-c299-4dcb-8224-4455121ee9b0","_uuid":"d629ff2d2480ee46fbb7e2d37f6b5fab8052498a"},"attachments":{"arbre_phylogenetique.jpg":{"image/jpeg":"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"}}},{"cell_type":"markdown","source":"## 2.1. Equation de récurrence\nL'équation de récurrence était fournie pour la suite de Fibonacci, ici c'est à vous de la trouver (elle est en fait dans la partie cours/TD). En général, c'est cette phase qui est la plus hardue, car 1) il faut effectivement résoudre le problème, 2) toutes les décompositions ne sont pas aisément substituables par de la programmation dynamique\n1. Ecrire l'équation de récurrence\n1. Justifier votre équation (ébauche de preuve de la correction de votre algorithme)","metadata":{}},{"cell_type":"markdown","source":"*** équation de récurrence et vos explications ***","metadata":{}},{"cell_type":"markdown","source":"On sait que la distance d'edition entre deux mots est le nombre minimal d'opérations permettant de transformer  𝑀 de taille m  en  𝑃 de taille p  \nPar la recurrance \n\nL'equation :  \nDifference(M[m], P[p]) = Difference(M[m-1],[p-1]) + cout(type de modification)\n\nJustification :  (l'example le plus simple)\nsuppossant M = toto et P= toti , les eux de taille m = p = 4\nla difference est diff(toto, toti) =  diff(tot,tot) + cout(substitution) =...=  diff(t,t) + diff(o,o) + diff(t,t) + 1 = 0 + 0 + 0 + 1\n\n\n","metadata":{}},{"cell_type":"markdown","source":"## 2.3. Ecrire une fonction récursive calculant la distance d'édition","metadata":{}},{"cell_type":"code","source":"# votre code de la version récursive\ndef distance(m1, m2, cs, ci, cd):\n    if len(m2) == 0 :\n        return len(m1)*ci\n    elif len(m1) == 0 :\n        return len(m2)*cd\n    elif m1[-1] == m2[-1]:\n        return distance(m1[:-1], m2[:-1], cs, ci, cd)\n    else :\n        vs = cs + distance(m1[:-1], m2[:-1], cs, ci, cd)\n        vi = ci + distance(m1[:-1], m2, cs, ci, cd)\n        vd = cd + distance(m1, m2[:-1], cs, ci, cd)\n        return min(vs,vi,vd)","metadata":{"trusted":true},"execution_count":431,"outputs":[]},{"cell_type":"code","source":"\ndistance(\"toto\",\"toti\", cs=1, ci=1, cd=1)","metadata":{"trusted":true},"execution_count":432,"outputs":[{"execution_count":432,"output_type":"execute_result","data":{"text/plain":"1"},"metadata":{}}]},{"cell_type":"markdown","source":"## 2.4. Calculer une suite de transformations optimale permettant de transformer une chaîne en une autre\n*Optimale signifie ici \" de coût minimal\"*\n\nPrécédemment, on se contentait de calculer la distance, maintenant on désire obtenir la suite des transformations qui permet d'effectivement transformer le premier mot en le second. La fonction doit renvoyer un affichage compact (par exemple [['s', 4, 'b'], ['d', 3], ['i', 5, 'r'], ...], aisé à manipuler informatiquement).\n\n","metadata":{}},{"cell_type":"code","source":"# votre code pour le calcul\ndef distanceOptimale(m1, m2, cs, ci, cd):\n    if len(m2) == 0 :\n        return len(m1)*ci, [\"i 0 \" + m1[k] for k in range(len(m1)-1, -1, -1)]\n    elif len(m1) == 0 :\n        return len(m2)*cd, [\"d 0 \"  for k in m2]\n    elif m1[-1] == m2[-1]:\n        d, op = distanceOptimale(m1[:-1], m2[:-1], cs, ci, cd)\n        # return d, [\"s\"+ m1[-1] + \" \"+ str(len(m2)-1)]+ op\n        return d, op\n    else :\n        vs ,op_s = distanceOptimale(m1[:-1], m2[:-1], cs, ci, cd)\n        vs += cs\n        op_s = [\"s \"+ m1[-1] + \" \"+ str(len(m2)-1)]+ op_s\n        \n        vi, op_i =distanceOptimale(m1[:-1], m2, cs, ci, cd)\n        vi +=  ci\n        op_i = [\"i \"+m1[-1]+ \" \"+str(len(m2)-1)] +op_i\n        \n        vd, op_d = distanceOptimale(m1, m2[:-1], cs, ci, cd)\n        vd += cd \n        op_d = [\"d \"+m1[-1] +str(len(m2)-1)] + op_d\n        \n        tab_v = [vs, vi, vd]\n        tab_op = [op_s, op_i, op_d]\n        \n        return min(tab_v), tab_op[np.argmin(tab_v)]","metadata":{"trusted":true},"execution_count":463,"outputs":[]},{"cell_type":"code","source":"print(distanceOptimale(\"abc\", \"\", cs=1, ci=1, cd=1))\nprint(distanceOptimale(\"\", \"abc\", cs=1, ci=1, cd=1))\nprint(distanceOptimale(\"abc\", \"abc\", cs=1, ci=1, cd=1))\nprint(distanceOptimale(\"abc\", \"def\", cs=1, ci=1, cd=1))\nprint(distanceOptimale(\"abcdefg\", \"abcbfr\", cs=1, ci=1, cd=1))","metadata":{"trusted":true},"execution_count":464,"outputs":[{"name":"stdout","text":"(3, ['i 0 c', 'i 0 b', 'i 0 a'])\n(3, ['d 0 ', 'd 0 ', 'd 0 '])\n(0, [])\n(3, ['s c 2', 's b 1', 's a 0'])\n(3, ['s g 5', 's e 3', 'i d 2'])\n","output_type":"stream"}]},{"cell_type":"markdown","source":"La sortie précédente n'est pas très conviviale, écrire une fonction qui génère à partir de la représentation compacte un affichage pertinent. Par exemple, avec des coûts de transformation tous à 1, on pourrait avoir comme affichage :\n```\n    Transformation de 'abcdefg' en 'abcbfr'\n    Départ                                 [cout 0]            abcdefg\n    Substituer à l'indice 4 par un 'b'     [cout 1] --->       abcdbfg\n    Effacer le caractère d'indice 3        [cout 1] --->       abcbfg \n    Insérer à l'indice 5 le caractère 'r'  [cout 1] --->       abcbfr\n                                   [cout total : 3]\n   ``` ","metadata":{}},{"cell_type":"code","source":"# votre code pour le 'pretty print'\n# operlist = distanceOptimale(\"abcdefg\", \"abcbfr\", cs=1, ci=1, cd=1)\n\ndef prettyDist(word1, word2):    \n    n, ops = distanceOptimale(word1, word2, cs=1, ci=1, cd=1)\n    print(f\"Transformation de {word2} en {word1} :\")\n    for i in range(len(ops)):\n       \n        cur = ops[i].split(\" \")\n        if cur[0] == \"s\":\n            print(f\"Operation {i+1} : Substitution de {cur[1]} a l'indince {cur[2]}  ---- [cout 1]\")\n        if cur[0] == \"d\":\n            print(f\"Operation {i+1} : Suppression du caractere a l'indice {cur[1]} ---- [cout 1]\")\n        if cur[0] == \"i\":\n            print(f\"Operation {i+1} : Insertion du caractere {cur[2]} a l'induce {cur[1]}  ---- [cout 1]\")\n    print(f\"-----> Cout total  :   {n}\")    \n            \nprint(\"Test 1 :\")\nprettyDist(\"cwrpm3\", \"cpidcpq\")\nprint(\"Test 2 :\")\nprettyDist(\"abcdfe\", \"efdg\")","metadata":{"trusted":true},"execution_count":489,"outputs":[{"name":"stdout","text":"Test 1 :\nTransformation de cpidcpq en cwrpm3 :\nOperation 1 : Substitution de 3 a l'indince 6  ---- [cout 1]\nOperation 2 : Substitution de m a l'indince 5  ---- [cout 1]\nOperation 3 : Substitution de p a l'indince 4  ---- [cout 1]\nOperation 4 : Substitution de r a l'indince 3  ---- [cout 1]\nOperation 5 : Substitution de w a l'indince 2  ---- [cout 1]\nOperation 6 : Suppression du caractere a l'indice c1 ---- [cout 1]\n-----> Cout total  :   6\nTest 2 :\nTransformation de efdg en abcdfe :\nOperation 1 : Substitution de e a l'indince 3  ---- [cout 1]\nOperation 2 : Insertion du caractere 2 a l'induce f  ---- [cout 1]\nOperation 3 : Substitution de c a l'indince 1  ---- [cout 1]\nOperation 4 : Substitution de b a l'indince 0  ---- [cout 1]\nOperation 5 : Insertion du caractere a a l'induce 0  ---- [cout 1]\n-----> Cout total  :   5\n","output_type":"stream"}]},{"cell_type":"markdown","source":"(bonus) Au lieu d'un affichage en mode texte, on peut également générer à partir de la représebtation compacte un graphe (c'est une chaîne au sens des graphes dans ce cas) où les sommets sont étiquettés par l'état de la chaîne de caractère et les arcs par la transformation effectuée.","metadata":{}},{"cell_type":"markdown","source":"## 2.5. Représenter le multi-graphe des appels","metadata":{}},{"cell_type":"code","source":"# votre code\ndef distance_graph(m1, m2, cs, ci, cd, dot= Graph()):\n    dot.node(m1+\" \"+m2)\n    if len(m2) == 0 :\n        return len(m1)*ci, [\"i 0 \" + m1[k] for k in range(len(m1)-1, -1, -1)] , dot\n    elif len(m1) == 0 :\n        return len(m2)*cd, [\"d 0 \"  for k in m2] , dot\n    elif m1[-1] == m2[-1]:\n        dot.node(m1[:-1]+\" \"+m2[:-1])\n        dot.edge(m1+\" \"+m2,m1[:-1]+\" \"+m2[:-1])\n        \n        d, op, dot = distance_graph(m1[:-1], m2[:-1], cs, ci, cd, dot)\n        # return d, [\"s\"+ m1[-1] + \" \"+ str(len(m2)-1)]+ op\n        return d, op, dot\n    else :\n        dot.node(m1[:-1]+\" \"+m2[:-1])\n        dot.edge(m1+\" \"+m2,m1[:-1]+\" \"+m2[:-1])\n        \n        vs ,op_s, dot = distance_graph(m1[:-1], m2[:-1], cs, ci, cd,dot)\n        vs += cs\n        op_s = [\"s\"+ m1[-1] + \" \"+ str(len(m2)-1)]+ op_s\n        \n        \n        dot.node(m1[:-1]+\" \"+m2)\n        dot.edge(m1+\" \"+m2,m1[:-1]+\" \"+m2)\n        \n        vi, op_i, dot =distance_graph(m1[:-1], m2, cs, ci, cd, dot)\n        vi +=  ci\n        op_i = [\"i \"+m1[-1]+ \" \"+str(len(m2)-1)] +op_i\n        \n        \n        dot.node(m1[:-1]+\" \"+m2[:-1])\n        dot.edge(m1+\" \"+m2,m1+\" \"+m2[:-1])\n        \n        vd, op_d ,dot = distance_graph(m1, m2[:-1], cs, ci, cd, dot)\n        vd += cd \n        op_d = [\"d \"+m1[-1] +str(len(m2)-1)] + op_d\n        \n        tab_v = [vs, vi, vd]\n        tab_op = [op_s, op_i, op_d]\n        \n        return min(tab_v), tab_op[np.argmin(tab_v)], dot","metadata":{"trusted":true},"execution_count":414,"outputs":[]},{"cell_type":"code","source":"v, op, g1 = distance_graph(\"cdefg\", \"cbfr\", cs=1, ci=1, cd=1 )\ndisplay(g1)","metadata":{"trusted":true},"execution_count":415,"outputs":[{"output_type":"display_data","data":{"text/plain":"<graphviz.dot.Graph at 0x7f0087c10610>","image/svg+xml":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.47.0 (20210316.1410)\n -->\n<!-- Pages: 1 -->\n<svg width=\"1022pt\" height=\"620pt\"\n viewBox=\"0.00 0.00 1021.65 620.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 616)\">\n<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-616 1017.65,-616 1017.65,4 -4,4\"/>\n<!-- cdefg cbfr -->\n<g id=\"node1\" class=\"node\">\n<title>cdefg cbfr</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"624.01\" cy=\"-594\" rx=\"57.69\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"624.01\" y=\"-590.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cdefg cbfr</text>\n</g>\n<!-- cdef cbf -->\n<g id=\"node2\" class=\"node\">\n<title>cdef cbf</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"624.01\" cy=\"-450\" rx=\"48.19\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"624.01\" y=\"-446.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cdef cbf</text>\n</g>\n<!-- cdefg cbfr&#45;&#45;cdef cbf -->\n<g id=\"edge1\" class=\"edge\">\n<title>cdefg cbfr&#45;&#45;cdef cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M624.01,-575.87C624.01,-548.58 624.01,-495.52 624.01,-468.19\"/>\n</g>\n<!-- cdef cbfr -->\n<g id=\"node15\" class=\"node\">\n<title>cdef cbfr</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"540.01\" cy=\"-522\" rx=\"51.99\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"540.01\" y=\"-518.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cdef cbfr</text>\n</g>\n<!-- cdefg cbfr&#45;&#45;cdef cbfr -->\n<g id=\"edge29\" class=\"edge\">\n<title>cdefg cbfr&#45;&#45;cdef cbfr</title>\n<path fill=\"none\" stroke=\"black\" d=\"M604.53,-576.76C590.86,-565.38 572.67,-550.22 559.1,-538.91\"/>\n</g>\n<!-- cdefg cbf -->\n<g id=\"node24\" class=\"node\">\n<title>cdefg cbf</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"708.01\" cy=\"-522\" rx=\"53.89\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"708.01\" y=\"-518.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cdefg cbf</text>\n</g>\n<!-- cdefg cbfr&#45;&#45;cdefg cbf -->\n<g id=\"edge269\" class=\"edge\">\n<title>cdefg cbfr&#45;&#45;cdefg cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M643.49,-576.76C657.16,-565.38 675.34,-550.22 688.92,-538.91\"/>\n</g>\n<!-- cde cb -->\n<g id=\"node3\" class=\"node\">\n<title>cde cb</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"624.01\" cy=\"-306\" rx=\"40.89\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"624.01\" y=\"-302.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cde cb</text>\n</g>\n<!-- cdef cbf&#45;&#45;cde cb -->\n<g id=\"edge2\" class=\"edge\">\n<title>cdef cbf&#45;&#45;cde cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M614.9,-432.15C609.04,-404.82 609.04,-351.14 614.9,-323.82\"/>\n</g>\n<!-- cdef cbf&#45;&#45;cde cb -->\n<g id=\"edge242\" class=\"edge\">\n<title>cdef cbf&#45;&#45;cde cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M624.01,-431.87C624.01,-404.58 624.01,-351.52 624.01,-324.19\"/>\n</g>\n<!-- cdef cbf&#45;&#45;cde cb -->\n<g id=\"edge318\" class=\"edge\">\n<title>cdef cbf&#45;&#45;cde cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M633.12,-432.15C638.97,-404.82 638.97,-351.14 633.11,-323.82\"/>\n</g>\n<!-- cd c -->\n<g id=\"node4\" class=\"node\">\n<title>cd c</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"624.01\" cy=\"-162\" rx=\"29.5\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"624.01\" y=\"-158.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cd c</text>\n</g>\n<!-- cde cb&#45;&#45;cd c -->\n<g id=\"edge3\" class=\"edge\">\n<title>cde cb&#45;&#45;cd c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M599.13,-291.64C577.57,-263.61 578.33,-199.15 601.39,-173.65\"/>\n</g>\n<!-- cde cb&#45;&#45;cd c -->\n<g id=\"edge72\" class=\"edge\">\n<title>cde cb&#45;&#45;cd c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M606.4,-289.53C593.61,-261.64 593.88,-203.36 607.22,-176.76\"/>\n</g>\n<!-- cde cb&#45;&#45;cd c -->\n<g id=\"edge215\" class=\"edge\">\n<title>cde cb&#45;&#45;cd c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M614.96,-288.43C609.02,-261.07 609.02,-206.75 614.98,-179.46\"/>\n</g>\n<!-- cde cb&#45;&#45;cd c -->\n<g id=\"edge243\" class=\"edge\">\n<title>cde cb&#45;&#45;cd c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M624.01,-287.87C624.01,-260.58 624.01,-207.52 624.01,-180.19\"/>\n</g>\n<!-- cde cb&#45;&#45;cd c -->\n<g id=\"edge280\" class=\"edge\">\n<title>cde cb&#45;&#45;cd c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M633.06,-288.43C639,-261.07 638.99,-206.75 633.03,-179.46\"/>\n</g>\n<!-- cde cb&#45;&#45;cd c -->\n<g id=\"edge319\" class=\"edge\">\n<title>cde cb&#45;&#45;cd c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M641.61,-289.53C654.41,-261.64 654.13,-203.36 640.8,-176.76\"/>\n</g>\n<!-- cde cb&#45;&#45;cd c -->\n<g id=\"edge367\" class=\"edge\">\n<title>cde cb&#45;&#45;cd c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M648.89,-291.64C670.44,-263.61 669.69,-199.15 646.63,-173.65\"/>\n</g>\n<!-- cd cb -->\n<g id=\"node9\" class=\"node\">\n<title>cd cb</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"459.01\" cy=\"-234\" rx=\"35.19\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"459.01\" y=\"-230.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cd cb</text>\n</g>\n<!-- cde cb&#45;&#45;cd cb -->\n<g id=\"edge8\" class=\"edge\">\n<title>cde cb&#45;&#45;cd cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M586.06,-299.03C544.45,-288.72 489.93,-267.2 463.7,-251.96\"/>\n</g>\n<!-- cde cb&#45;&#45;cd cb -->\n<g id=\"edge77\" class=\"edge\">\n<title>cde cb&#45;&#45;cd cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M587.99,-297.24C551.27,-286.03 500.11,-265.05 472.82,-250.57\"/>\n</g>\n<!-- cde cb&#45;&#45;cd cb -->\n<g id=\"edge220\" class=\"edge\">\n<title>cde cb&#45;&#45;cd cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M590.97,-295.12C557.71,-282.95 508.42,-262.21 480.02,-248.55\"/>\n</g>\n<!-- cde cb&#45;&#45;cd cb -->\n<g id=\"edge248\" class=\"edge\">\n<title>cde cb&#45;&#45;cd cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M595.64,-292.97C564.59,-279.79 515.22,-258.85 485.1,-246.07\"/>\n</g>\n<!-- cde cb&#45;&#45;cd cb -->\n<g id=\"edge285\" class=\"edge\">\n<title>cde cb&#45;&#45;cd cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M601.72,-290.83C572.2,-276.73 521.63,-255.53 488.88,-243.73\"/>\n</g>\n<!-- cde cb&#45;&#45;cd cb -->\n<g id=\"edge324\" class=\"edge\">\n<title>cde cb&#45;&#45;cd cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M609.61,-289.12C581.16,-274.11 527.69,-252.34 491.03,-241.56\"/>\n</g>\n<!-- cde cb&#45;&#45;cd cb -->\n<g id=\"edge372\" class=\"edge\">\n<title>cde cb&#45;&#45;cd cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M619.34,-288.05C592.12,-272.23 534.37,-249.64 492.25,-239.84\"/>\n</g>\n<!-- cde c -->\n<g id=\"node13\" class=\"node\">\n<title>cde c</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"789.01\" cy=\"-234\" rx=\"35.19\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"789.01\" y=\"-230.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cde c</text>\n</g>\n<!-- cde cb&#45;&#45;cde c -->\n<g id=\"edge21\" class=\"edge\">\n<title>cde cb&#45;&#45;cde c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M628.68,-288.05C655.9,-272.23 713.64,-249.64 755.76,-239.84\"/>\n</g>\n<!-- cde cb&#45;&#45;cde c -->\n<g id=\"edge90\" class=\"edge\">\n<title>cde cb&#45;&#45;cde c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M638.41,-289.12C666.85,-274.11 720.33,-252.34 756.99,-241.56\"/>\n</g>\n<!-- cde cb&#45;&#45;cde c -->\n<g id=\"edge233\" class=\"edge\">\n<title>cde cb&#45;&#45;cde c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M646.3,-290.83C675.82,-276.73 726.39,-255.53 759.14,-243.73\"/>\n</g>\n<!-- cde cb&#45;&#45;cde c -->\n<g id=\"edge261\" class=\"edge\">\n<title>cde cb&#45;&#45;cde c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M652.37,-292.97C683.42,-279.79 732.79,-258.85 762.92,-246.07\"/>\n</g>\n<!-- cde cb&#45;&#45;cde c -->\n<g id=\"edge298\" class=\"edge\">\n<title>cde cb&#45;&#45;cde c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M657.04,-295.12C690.31,-282.95 739.59,-262.21 768,-248.55\"/>\n</g>\n<!-- cde cb&#45;&#45;cde c -->\n<g id=\"edge337\" class=\"edge\">\n<title>cde cb&#45;&#45;cde c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M660.03,-297.24C696.75,-286.03 747.91,-265.05 775.2,-250.57\"/>\n</g>\n<!-- cde cb&#45;&#45;cde c -->\n<g id=\"edge385\" class=\"edge\">\n<title>cde cb&#45;&#45;cde c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M661.96,-299.03C703.56,-288.72 758.09,-267.2 784.32,-251.96\"/>\n</g>\n<!-- c  -->\n<g id=\"node5\" class=\"node\">\n<title>c </title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"624.01\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"624.01\" y=\"-86.3\" font-family=\"Times-Roman\" font-size=\"14.00\">c </text>\n</g>\n<!-- cd c&#45;&#45;c  -->\n<g id=\"edge4\" class=\"edge\">\n<title>cd c&#45;&#45;c </title>\n<path fill=\"none\" stroke=\"black\" d=\"M594.7,-160.75C345.07,-156.32 345.78,-95.32 596.84,-91.22\"/>\n</g>\n<!-- cd c&#45;&#45;c  -->\n<g id=\"edge17\" class=\"edge\">\n<title>cd c&#45;&#45;c </title>\n<path fill=\"none\" stroke=\"black\" d=\"M594.7,-160.71C363.07,-156.01 363.78,-95.61 596.82,-91.25\"/>\n</g>\n<!-- cd c&#45;&#45;c  -->\n<g id=\"edge24\" class=\"edge\">\n<title>cd c&#45;&#45;c </title>\n<path fill=\"none\" stroke=\"black\" d=\"M594.61,-160.66C380.99,-155.64 381.81,-95.88 597.06,-91.28\"/>\n</g>\n<!-- cd c&#45;&#45;c  -->\n<g id=\"edge40\" class=\"edge\">\n<title>cd c&#45;&#45;c </title>\n<path fill=\"none\" stroke=\"black\" d=\"M594.83,-160.61C399.03,-155.28 399.74,-96.28 596.94,-91.33\"/>\n</g>\n<!-- cd 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d=\"M597.79,-153.51C578.22,-139.68 578.76,-110.39 599.4,-97.41\"/>\n</g>\n<!-- cd c&#45;&#45;c  -->\n<g id=\"edge236\" class=\"edge\">\n<title>cd c&#45;&#45;c </title>\n<path fill=\"none\" stroke=\"black\" d=\"M603.14,-149.13C594.83,-136.02 594.97,-115.08 603.56,-102.24\"/>\n</g>\n<!-- cd c&#45;&#45;c  -->\n<g id=\"edge244\" class=\"edge\">\n<title>cd c&#45;&#45;c </title>\n<path fill=\"none\" stroke=\"black\" d=\"M612.49,-145.12C609.81,-133.5 609.85,-117.83 612.62,-106.34\"/>\n</g>\n<!-- cd c&#45;&#45;c  -->\n<g id=\"edge257\" class=\"edge\">\n<title>cd c&#45;&#45;c </title>\n<path fill=\"none\" stroke=\"black\" d=\"M624.01,-143.7C624.01,-132.85 624.01,-118.92 624.01,-108.1\"/>\n</g>\n<!-- cd c&#45;&#45;c  -->\n<g id=\"edge264\" class=\"edge\">\n<title>cd c&#45;&#45;c </title>\n<path fill=\"none\" stroke=\"black\" d=\"M635.53,-145.12C638.21,-133.5 638.17,-117.83 635.4,-106.34\"/>\n</g>\n<!-- cd c&#45;&#45;c  -->\n<g id=\"edge274\" class=\"edge\">\n<title>cd c&#45;&#45;c 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651.18,-91.22\"/>\n</g>\n<!-- c c -->\n<g id=\"node6\" class=\"node\">\n<title>c c</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"459.01\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"459.01\" y=\"-86.3\" font-family=\"Times-Roman\" font-size=\"14.00\">c c</text>\n</g>\n<!-- cd c&#45;&#45;c c -->\n<g id=\"edge5\" class=\"edge\">\n<title>cd c&#45;&#45;c c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M594.51,-160.75C334.32,-156.39 190.99,-95.39 431.97,-91.22\"/>\n</g>\n<!-- cd c&#45;&#45;c c -->\n<g id=\"edge18\" class=\"edge\">\n<title>cd c&#45;&#45;c c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M594.78,-160.73C351.75,-156.14 209.56,-95.68 432.04,-91.26\"/>\n</g>\n<!-- cd c&#45;&#45;c c -->\n<g id=\"edge25\" class=\"edge\">\n<title>cd c&#45;&#45;c c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M594.54,-160.68C368.9,-155.77 228.4,-96.01 432.08,-91.3\"/>\n</g>\n<!-- cd c&#45;&#45;c c -->\n<g id=\"edge41\" class=\"edge\">\n<title>cd 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698,-107.99\"/>\n</g>\n<!-- cde c&#45;&#45;cd  -->\n<g id=\"edge309\" class=\"edge\">\n<title>cde c&#45;&#45;cd </title>\n<path fill=\"none\" stroke=\"black\" d=\"M778.34,-216.71C760.31,-189.17 724.02,-133.78 706.27,-106.67\"/>\n</g>\n<!-- cde c&#45;&#45;cd  -->\n<g id=\"edge338\" class=\"edge\">\n<title>cde c&#45;&#45;cd </title>\n<path fill=\"none\" stroke=\"black\" d=\"M786.96,-215.87C774.27,-187.25 736.68,-130.3 713.08,-104.39\"/>\n</g>\n<!-- cde c&#45;&#45;cd  -->\n<g id=\"edge349\" class=\"edge\">\n<title>cde c&#45;&#45;cd </title>\n<path fill=\"none\" stroke=\"black\" d=\"M796.19,-216.15C789.47,-186.47 748.58,-125.71 717.74,-101.39\"/>\n</g>\n<!-- cde c&#45;&#45;cd  -->\n<g id=\"edge359\" class=\"edge\">\n<title>cde c&#45;&#45;cd </title>\n<path fill=\"none\" stroke=\"black\" d=\"M805.28,-217.8C806.57,-187.54 760.51,-120.73 720.2,-98.42\"/>\n</g>\n<!-- cde c&#45;&#45;cd  -->\n<g id=\"edge386\" class=\"edge\">\n<title>cde c&#45;&#45;cd </title>\n<path fill=\"none\" stroke=\"black\" d=\"M813.13,-220.4C825.51,-190.6 773.77,-116.77 721.71,-96.32\"/>\n</g>\n<!-- cde c&#45;&#45;cd  -->\n<g id=\"edge396\" class=\"edge\">\n<title>cde c&#45;&#45;cd </title>\n<path fill=\"none\" stroke=\"black\" d=\"M818.5,-223.68C846.39,-195.73 788.48,-113.38 722.17,-94.77\"/>\n</g>\n<!-- cde c&#45;&#45;cd  -->\n<g id=\"edge409\" class=\"edge\">\n<title>cde c&#45;&#45;cd </title>\n<path fill=\"none\" stroke=\"black\" d=\"M821.15,-226.53C867.84,-201.41 804.68,-110.89 722.6,-93.8\"/>\n</g>\n<!-- cde  -->\n<g id=\"node14\" class=\"node\">\n<title>cde </title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"956.01\" cy=\"-162\" rx=\"30.59\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"956.01\" y=\"-158.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cde </text>\n</g>\n<!-- cde c&#45;&#45;cde  -->\n<g id=\"edge28\" class=\"edge\">\n<title>cde c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M756,-227.51C738.77,-212.79 840.16,-173.04 925.74,-164.59\"/>\n</g>\n<!-- cde c&#45;&#45;cde  -->\n<g id=\"edge97\" class=\"edge\">\n<title>cde c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M765.71,-220.49C780.91,-203.22 861.61,-173.3 925.76,-165.12\"/>\n</g>\n<!-- cde c&#45;&#45;cde  -->\n<g id=\"edge240\" class=\"edge\">\n<title>cde c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M782.14,-216.23C808.04,-199.25 875.42,-174.31 925.89,-165.89\"/>\n</g>\n<!-- cde c&#45;&#45;cde  -->\n<g id=\"edge268\" class=\"edge\">\n<title>cde c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M794.17,-216.05C822.69,-199.75 883.84,-176.24 926.48,-166.97\"/>\n</g>\n<!-- cde c&#45;&#45;cde  -->\n<g id=\"edge278\" class=\"edge\">\n<title>cde c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M803.19,-217.46C832.83,-201.96 890.15,-178.98 927.41,-168.53\"/>\n</g>\n<!-- cde c&#45;&#45;cde  -->\n<g id=\"edge305\" class=\"edge\">\n<title>cde c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M810.29,-219.5C840.94,-204.96 895.62,-182.34 929.04,-170.62\"/>\n</g>\n<!-- cde c&#45;&#45;cde  -->\n<g id=\"edge315\" class=\"edge\">\n<title>cde c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M815.47,-221.91C847.48,-208.49 900.9,-186.1 931.84,-173.13\"/>\n</g>\n<!-- cde c&#45;&#45;cde  -->\n<g id=\"edge344\" class=\"edge\">\n<title>cde c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M819.11,-224.28C853.32,-212.07 906.87,-189.82 936.28,-175.76\"/>\n</g>\n<!-- cde c&#45;&#45;cde  -->\n<g id=\"edge355\" class=\"edge\">\n<title>cde c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M821.3,-226.41C858.85,-215.46 913.99,-193.2 942.48,-178.19\"/>\n</g>\n<!-- cde c&#45;&#45;cde  -->\n<g id=\"edge365\" class=\"edge\">\n<title>cde c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M822.28,-228.19C864.72,-218.4 923.26,-195.74 950.92,-179.9\"/>\n</g>\n<!-- cde c&#45;&#45;cde  -->\n<g id=\"edge392\" class=\"edge\">\n<title>cde c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M823.01,-229.43C873.13,-220.41 937.96,-196.2 963.07,-179.64\"/>\n</g>\n<!-- cde c&#45;&#45;cde  -->\n<g id=\"edge402\" class=\"edge\">\n<title>cde c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M823.59,-230.3C891.71,-220.7 976.07,-187.96 981.56,-171.96\"/>\n</g>\n<!-- cde c&#45;&#45;cde  -->\n<g id=\"edge415\" class=\"edge\">\n<title>cde c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M823.73,-230.94C912.42,-221.14 1015.44,-179.14 985.74,-166.57\"/>\n</g>\n<!-- cdef cbfr&#45;&#45;cdef cbf -->\n<g id=\"edge241\" class=\"edge\">\n<title>cdef cbfr&#45;&#45;cdef cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M559.07,-505.12C572.82,-493.66 591.29,-478.26 605.02,-466.82\"/>\n</g>\n<!-- cde cbf -->\n<g id=\"node16\" class=\"node\">\n<title>cde cbf</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"459.01\" cy=\"-378\" rx=\"44.39\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"459.01\" y=\"-374.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cde cbf</text>\n</g>\n<!-- cdef cbfr&#45;&#45;cde cbf -->\n<g id=\"edge30\" class=\"edge\">\n<title>cdef cbfr&#45;&#45;cde cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M530.4,-504.15C514.81,-476.82 484.19,-423.14 468.61,-395.82\"/>\n</g>\n<!-- cde cbfr -->\n<g id=\"node20\" class=\"node\">\n<title>cde cbfr</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"420.01\" cy=\"-450\" rx=\"48.19\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"420.01\" y=\"-446.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cde cbfr</text>\n</g>\n<!-- cdef cbfr&#45;&#45;cde cbfr -->\n<g id=\"edge98\" class=\"edge\">\n<title>cdef cbfr&#45;&#45;cde cbfr</title>\n<path fill=\"none\" stroke=\"black\" d=\"M514.56,-506.15C494.06,-494.2 465.39,-477.47 445.01,-465.58\"/>\n</g>\n<!-- cde cbf&#45;&#45;cde cb -->\n<g id=\"edge71\" class=\"edge\">\n<title>cde cbf&#45;&#45;cde cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M485.36,-363.5C514.8,-350.23 562.08,-330.23 593.19,-317.93\"/>\n</g>\n<!-- cde cbf&#45;&#45;cde cb -->\n<g id=\"edge214\" class=\"edge\">\n<title>cde cbf&#45;&#45;cde cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M491.42,-365.44C522.83,-352.98 569.6,-333.17 598.47,-320.13\"/>\n</g>\n<!-- cde cbf&#45;&#45;cd cb -->\n<g id=\"edge31\" class=\"edge\">\n<title>cde cbf&#45;&#45;cd cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M454.42,-359.87C451.54,-332.58 451.54,-279.52 454.42,-252.19\"/>\n</g>\n<!-- cde cbf&#45;&#45;cd cb -->\n<g id=\"edge174\" class=\"edge\">\n<title>cde cbf&#45;&#45;cd cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M463.59,-359.87C466.48,-332.58 466.48,-279.52 463.6,-252.19\"/>\n</g>\n<!-- cd cbf -->\n<g id=\"node17\" class=\"node\">\n<title>cd cbf</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"294.01\" cy=\"-306\" rx=\"38.19\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"294.01\" y=\"-302.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cd cbf</text>\n</g>\n<!-- cde cbf&#45;&#45;cd cbf -->\n<g id=\"edge44\" class=\"edge\">\n<title>cde cbf&#45;&#45;cd cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M426.6,-365.44C394.89,-352.86 347.54,-332.8 318.74,-319.76\"/>\n</g>\n<!-- cde cbf&#45;&#45;cd cbf -->\n<g id=\"edge187\" class=\"edge\">\n<title>cde cbf&#45;&#45;cd cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M432.65,-363.5C402.87,-350.07 354.81,-329.75 323.72,-317.49\"/>\n</g>\n<!-- cd cbf&#45;&#45;cd cb -->\n<g id=\"edge58\" class=\"edge\">\n<title>cd cbf&#45;&#45;cd cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M312.43,-289.98C341.41,-275.4 393.46,-253.86 428.05,-242.55\"/>\n</g>\n<!-- cd cbf&#45;&#45;cd cb -->\n<g id=\"edge113\" class=\"edge\">\n<title>cd cbf&#45;&#45;cd cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M318.91,-292.16C349.01,-278.54 399.19,-257.32 430.72,-244.93\"/>\n</g>\n<!-- cd cbf&#45;&#45;cd cb -->\n<g id=\"edge160\" class=\"edge\">\n<title>cd cbf&#45;&#45;cd cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M323.69,-294.52C355.7,-281.9 405.72,-260.72 435.25,-247.32\"/>\n</g>\n<!-- cd cbf&#45;&#45;cd cb -->\n<g id=\"edge201\" class=\"edge\">\n<title>cd cbf&#45;&#45;cd cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M327.25,-296.7C362.12,-285.11 413.15,-263.9 441.35,-249.63\"/>\n</g>\n<!-- cd cbf&#45;&#45;c cb -->\n<g id=\"edge45\" class=\"edge\">\n<title>cd cbf&#45;&#45;c cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M280.62,-288.99C271.39,-261.42 271.47,-205.38 280.86,-178.31\"/>\n</g>\n<!-- cd cbf&#45;&#45;c cb -->\n<g id=\"edge100\" class=\"edge\">\n<title>cd cbf&#45;&#45;c cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M289.42,-287.87C286.54,-260.58 286.54,-207.52 289.42,-180.19\"/>\n</g>\n<!-- cd cbf&#45;&#45;c cb -->\n<g id=\"edge147\" class=\"edge\">\n<title>cd cbf&#45;&#45;c cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M298.59,-287.87C301.48,-260.58 301.48,-207.52 298.6,-180.19\"/>\n</g>\n<!-- cd cbf&#45;&#45;c cb -->\n<g id=\"edge188\" class=\"edge\">\n<title>cd cbf&#45;&#45;c cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M307.4,-288.99C316.62,-261.42 316.54,-205.38 307.16,-178.31\"/>\n</g>\n<!-- c cbf -->\n<g id=\"node18\" class=\"node\">\n<title>c cbf</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"207.01\" cy=\"-234\" rx=\"32.49\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"207.01\" y=\"-230.3\" font-family=\"Times-Roman\" font-size=\"14.00\">c cbf</text>\n</g>\n<!-- cd cbf&#45;&#45;c cbf -->\n<g id=\"edge50\" class=\"edge\">\n<title>cd cbf&#45;&#45;c cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M265.23,-294.06C245.5,-282.83 222.75,-265.2 210.6,-252.12\"/>\n</g>\n<!-- cd cbf&#45;&#45;c cbf -->\n<g id=\"edge105\" class=\"edge\">\n<title>cd cbf&#45;&#45;c cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M271.32,-291.17C255.17,-279.46 234.24,-262.67 220.56,-250.51\"/>\n</g>\n<!-- cd cbf&#45;&#45;c cbf -->\n<g id=\"edge152\" class=\"edge\">\n<title>cd cbf&#45;&#45;c cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M280.03,-289.12C265.93,-276.61 244.42,-259.41 228.25,-247.78\"/>\n</g>\n<!-- cd cbf&#45;&#45;c cbf -->\n<g id=\"edge193\" class=\"edge\">\n<title>cd cbf&#45;&#45;c cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M290.58,-288.05C278.01,-274.46 253.85,-255.86 233.54,-244.68\"/>\n</g>\n<!-- c cbf&#45;&#45;c cb -->\n<g id=\"edge53\" class=\"edge\">\n<title>c cbf&#45;&#45;c cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M198.43,-216.41C209.08,-201.13 239.33,-179.3 266.82,-168.92\"/>\n</g>\n<!-- c cbf&#45;&#45;c cb -->\n<g id=\"edge108\" class=\"edge\">\n<title>c cbf&#45;&#45;c cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M210.43,-216.05C223.38,-202.05 248.61,-182.75 269.28,-171.7\"/>\n</g>\n<!-- c cbf&#45;&#45;c cb -->\n<g id=\"edge130\" class=\"edge\">\n<title>c cbf&#45;&#45;c cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M220.6,-217.46C234.91,-204.74 257.13,-186.97 273.52,-175.24\"/>\n</g>\n<!-- c cbf&#45;&#45;c cb -->\n<g id=\"edge141\" class=\"edge\">\n<title>c cbf&#45;&#45;c cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M228.33,-220.16C244.78,-208.32 266.75,-190.73 280.8,-178.19\"/>\n</g>\n<!-- c cbf&#45;&#45;c cb -->\n<g id=\"edge155\" class=\"edge\">\n<title>c cbf&#45;&#45;c cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M233.37,-223.41C253.7,-212.26 277.92,-193.62 290.54,-179.99\"/>\n</g>\n<!-- c cbf&#45;&#45;c cb -->\n<g id=\"edge196\" class=\"edge\">\n<title>c cbf&#45;&#45;c cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M236.56,-226.16C263.64,-215.36 292.77,-194.05 302.87,-179.19\"/>\n</g>\n<!-- c cbf&#45;&#45; cb -->\n<g id=\"edge51\" class=\"edge\">\n<title>c cbf&#45;&#45; cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M187.55,-219.38C172.79,-191.34 180.12,-127.62 201.75,-101.98\"/>\n</g>\n<!-- c cbf&#45;&#45; cb -->\n<g id=\"edge106\" class=\"edge\">\n<title>c cbf&#45;&#45; cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M195.31,-216.99C188.93,-189.13 195.12,-132.19 207.63,-105.46\"/>\n</g>\n<!-- c cbf&#45;&#45; cb -->\n<g id=\"edge128\" class=\"edge\">\n<title>c cbf&#45;&#45; cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M204.23,-215.87C204.23,-188.43 209.89,-134.95 215.7,-107.75\"/>\n</g>\n<!-- c cbf&#45;&#45; cb -->\n<g id=\"edge139\" class=\"edge\">\n<title>c cbf&#45;&#45; cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M213.34,-216.15C219.13,-188.97 224.77,-135.72 224.78,-108.27\"/>\n</g>\n<!-- c cbf&#45;&#45; cb -->\n<g id=\"edge153\" class=\"edge\">\n<title>c cbf&#45;&#45; cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M221.72,-217.8C234.08,-190.62 240.1,-133.94 233.59,-106.52\"/>\n</g>\n<!-- c cbf&#45;&#45; cb -->\n<g id=\"edge194\" class=\"edge\">\n<title>c cbf&#45;&#45; cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M228.57,-220.4C249.5,-193.38 256.12,-130.18 240.78,-103.37\"/>\n</g>\n<!--  cbf -->\n<g id=\"node19\" class=\"node\">\n<title> cbf</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"91.01\" cy=\"-162\" rx=\"27.9\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"91.01\" y=\"-158.3\" font-family=\"Times-Roman\" font-size=\"14.00\"> cbf</text>\n</g>\n<!-- c cbf&#45;&#45; cbf -->\n<g id=\"edge52\" class=\"edge\">\n<title>c cbf&#45;&#45; cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M176.85,-226.91C145.57,-216.6 107.2,-195.34 89.96,-180.18\"/>\n</g>\n<!-- c cbf&#45;&#45; cbf -->\n<g id=\"edge107\" class=\"edge\">\n<title>c cbf&#45;&#45; cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M179.26,-224.56C153.5,-213.36 119.14,-193.36 100.46,-179.2\"/>\n</g>\n<!-- c cbf&#45;&#45; cbf -->\n<g id=\"edge129\" class=\"edge\">\n<title>c cbf&#45;&#45; cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M182.97,-221.6C160.53,-209.28 127.9,-189.66 108.01,-176.56\"/>\n</g>\n<!-- c cbf&#45;&#45; cbf -->\n<g id=\"edge140\" class=\"edge\">\n<title>c cbf&#45;&#45; cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M189.08,-218.83C168.49,-205.33 135.13,-185.32 113,-173.28\"/>\n</g>\n<!-- c cbf&#45;&#45; cbf -->\n<g id=\"edge154\" class=\"edge\">\n<title>c cbf&#45;&#45; cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M197.51,-216.76C178.2,-202.14 142.24,-181.32 116.26,-170.38\"/>\n</g>\n<!-- c cbf&#45;&#45; cbf -->\n<g id=\"edge195\" class=\"edge\">\n<title>c cbf&#45;&#45; cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M207.91,-215.7C189.98,-199.99 149.56,-177.83 117.79,-168.01\"/>\n</g>\n<!-- cde cbfr&#45;&#45;cde cbf -->\n<g id=\"edge173\" class=\"edge\">\n<title>cde cbfr&#45;&#45;cde cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M429.45,-432.05C435.58,-421.05 443.54,-406.76 449.65,-395.79\"/>\n</g>\n<!-- cde cbfr&#45;&#45;cd cbf -->\n<g id=\"edge99\" class=\"edge\">\n<title>cde cbfr&#45;&#45;cd cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M405.55,-432.71C381.25,-405.32 332.49,-350.36 308.29,-323.1\"/>\n</g>\n<!-- cd cbfr -->\n<g id=\"node21\" class=\"node\">\n<title>cd cbfr</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"256.01\" cy=\"-378\" rx=\"42.49\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"256.01\" y=\"-374.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cd cbfr</text>\n</g>\n<!-- cde cbfr&#45;&#45;cd cbfr -->\n<g id=\"edge126\" class=\"edge\">\n<title>cde cbfr&#45;&#45;cd cbfr</title>\n<path fill=\"none\" stroke=\"black\" d=\"M389.55,-436C359.53,-423.19 314.03,-403.77 284.66,-391.23\"/>\n</g>\n<!-- cd cbfr&#45;&#45;cd cbf -->\n<g id=\"edge146\" class=\"edge\">\n<title>cd cbfr&#45;&#45;cd cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M265.01,-360.41C270.98,-349.41 278.79,-335.03 284.8,-323.96\"/>\n</g>\n<!-- cd cbfr&#45;&#45;c cbf -->\n<g id=\"edge127\" class=\"edge\">\n<title>cd cbfr&#45;&#45;c cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M250.2,-360.15C240.76,-332.82 222.24,-279.14 212.81,-251.82\"/>\n</g>\n<!-- c cbfr -->\n<g id=\"node22\" class=\"node\">\n<title>c cbfr</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"135.01\" cy=\"-306\" rx=\"36.29\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"135.01\" y=\"-302.3\" font-family=\"Times-Roman\" font-size=\"14.00\">c cbfr</text>\n</g>\n<!-- cd cbfr&#45;&#45;c cbfr -->\n<g id=\"edge135\" class=\"edge\">\n<title>cd cbfr&#45;&#45;c cbfr</title>\n<path fill=\"none\" stroke=\"black\" d=\"M231.81,-363C210.3,-350.55 179.06,-332.48 157.93,-320.26\"/>\n</g>\n<!-- c cbfr&#45;&#45;c cbf -->\n<g id=\"edge138\" class=\"edge\">\n<title>c cbfr&#45;&#45;c cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M150.99,-289.46C163.08,-277.7 179.6,-261.64 191.57,-250.01\"/>\n</g>\n<!-- c cbfr&#45;&#45; cbf -->\n<g id=\"edge136\" class=\"edge\">\n<title>c cbfr&#45;&#45; cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M115.14,-290.75C103.67,-281.24 90.31,-267.63 84.01,-252 74.45,-228.28 80.12,-198.16 85.36,-179.75\"/>\n</g>\n<!--  cbfr -->\n<g id=\"node23\" class=\"node\">\n<title> cbfr</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"125.01\" cy=\"-234\" rx=\"31.7\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"125.01\" y=\"-230.3\" font-family=\"Times-Roman\" font-size=\"14.00\"> cbfr</text>\n</g>\n<!-- c cbfr&#45;&#45; cbfr -->\n<g id=\"edge137\" class=\"edge\">\n<title>c cbfr&#45;&#45; cbfr</title>\n<path fill=\"none\" stroke=\"black\" d=\"M132.54,-287.7C130.99,-276.85 129,-262.92 127.45,-252.1\"/>\n</g>\n<!-- cdefg cbf&#45;&#45;cdef cbf -->\n<g id=\"edge317\" class=\"edge\">\n<title>cdefg cbf&#45;&#45;cdef cbf</title>\n<path fill=\"none\" stroke=\"black\" d=\"M688.95,-505.12C675.2,-493.66 656.72,-478.26 642.99,-466.82\"/>\n</g>\n<!-- cdef cb -->\n<g id=\"node25\" class=\"node\">\n<title>cdef cb</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"789.01\" cy=\"-378\" rx=\"44.39\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"789.01\" y=\"-374.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cdef cb</text>\n</g>\n<!-- cdefg cbf&#45;&#45;cdef cb -->\n<g id=\"edge270\" class=\"edge\">\n<title>cdefg cbf&#45;&#45;cdef cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M717.62,-504.15C733.21,-476.82 763.83,-423.14 779.41,-395.82\"/>\n</g>\n<!-- cdefg cb -->\n<g id=\"node28\" class=\"node\">\n<title>cdefg cb</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"825.01\" cy=\"-450\" rx=\"50.09\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"825.01\" y=\"-446.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cdefg cb</text>\n</g>\n<!-- cdefg cbf&#45;&#45;cdefg cb -->\n<g id=\"edge345\" class=\"edge\">\n<title>cdefg cbf&#45;&#45;cdefg cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M733.11,-505.98C752.98,-494.09 780.59,-477.57 800.35,-465.75\"/>\n</g>\n<!-- cdef cb&#45;&#45;cde cb -->\n<g id=\"edge279\" class=\"edge\">\n<title>cdef cb&#45;&#45;cde cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M756.6,-365.44C725.19,-352.98 678.42,-333.17 649.54,-320.13\"/>\n</g>\n<!-- cdef cb&#45;&#45;cde cb -->\n<g id=\"edge366\" class=\"edge\">\n<title>cdef cb&#45;&#45;cde cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M762.65,-363.5C733.22,-350.23 685.94,-330.23 654.83,-317.93\"/>\n</g>\n<!-- cdef cb&#45;&#45;cde c -->\n<g id=\"edge271\" class=\"edge\">\n<title>cdef cb&#45;&#45;cde c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M784.42,-359.87C781.54,-332.58 781.54,-279.52 784.42,-252.19\"/>\n</g>\n<!-- cdef cb&#45;&#45;cde c -->\n<g id=\"edge358\" class=\"edge\">\n<title>cdef cb&#45;&#45;cde c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M793.59,-359.87C796.48,-332.58 796.48,-279.52 793.6,-252.19\"/>\n</g>\n<!-- cdef c -->\n<g id=\"node26\" class=\"node\">\n<title>cdef c</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"864.01\" cy=\"-306\" rx=\"38.19\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"864.01\" y=\"-302.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cdef c</text>\n</g>\n<!-- cdef cb&#45;&#45;cdef c -->\n<g id=\"edge306\" class=\"edge\">\n<title>cdef cb&#45;&#45;cdef c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M800.94,-360.41C812.38,-348.52 829.45,-332.68 843.07,-321.34\"/>\n</g>\n<!-- cdef cb&#45;&#45;cdef c -->\n<g id=\"edge393\" class=\"edge\">\n<title>cdef cb&#45;&#45;cdef c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M810.55,-362.15C824.19,-350.76 841.09,-335.03 852.36,-323.29\"/>\n</g>\n<!-- cdef c&#45;&#45;cde c -->\n<g id=\"edge308\" class=\"edge\">\n<title>cdef c&#45;&#45;cde c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M836.12,-293.44C818.56,-282.18 799.35,-264.93 789.63,-252.08\"/>\n</g>\n<!-- cdef c&#45;&#45;cde c -->\n<g id=\"edge348\" class=\"edge\">\n<title>cdef c&#45;&#45;cde c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M843.28,-290.83C829.44,-279.33 811.97,-263.1 800.48,-251.1\"/>\n</g>\n<!-- cdef c&#45;&#45;cde c -->\n<g id=\"edge395\" class=\"edge\">\n<title>cdef c&#45;&#45;cde c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M852.41,-288.76C840.79,-276.65 823.15,-260.27 809.28,-248.79\"/>\n</g>\n<!-- cdef c&#45;&#45;cde c -->\n<g id=\"edge408\" class=\"edge\">\n<title>cdef c&#45;&#45;cde c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M863.22,-287.7C853.22,-274.58 833.47,-256.96 815.68,-245.79\"/>\n</g>\n<!-- cdef c&#45;&#45;cde  -->\n<g id=\"edge307\" class=\"edge\">\n<title>cdef c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M861.35,-287.87C870.92,-258.96 908.93,-201.12 935.71,-175.6\"/>\n</g>\n<!-- cdef c&#45;&#45;cde  -->\n<g id=\"edge347\" class=\"edge\">\n<title>cdef c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M870.37,-288.15C885.46,-260.24 921.43,-204.82 941.87,-178.1\"/>\n</g>\n<!-- cdef c&#45;&#45;cde  -->\n<g id=\"edge394\" class=\"edge\">\n<title>cdef c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M878.64,-289.26C899.19,-262.25 934.81,-207.33 949.73,-179.69\"/>\n</g>\n<!-- cdef c&#45;&#45;cde  -->\n<g id=\"edge407\" class=\"edge\">\n<title>cdef c&#45;&#45;cde </title>\n<path fill=\"none\" stroke=\"black\" d=\"M885.63,-291.13C912.3,-265.03 949.18,-208.69 958.63,-180.22\"/>\n</g>\n<!-- cdef  -->\n<g id=\"node27\" class=\"node\">\n<title>cdef </title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"968.01\" cy=\"-234\" rx=\"33.6\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"968.01\" y=\"-230.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cdef </text>\n</g>\n<!-- cdef c&#45;&#45;cdef  -->\n<g id=\"edge316\" class=\"edge\">\n<title>cdef c&#45;&#45;cdef </title>\n<path fill=\"none\" stroke=\"black\" d=\"M871.55,-288.05C887.61,-274.3 916.78,-255.42 939.95,-244.28\"/>\n</g>\n<!-- cdef c&#45;&#45;cdef  -->\n<g id=\"edge356\" class=\"edge\">\n<title>cdef c&#45;&#45;cdef </title>\n<path fill=\"none\" stroke=\"black\" d=\"M880.9,-289.81C898.34,-277.02 925.29,-258.98 944.72,-247.14\"/>\n</g>\n<!-- cdef c&#45;&#45;cdef  -->\n<g id=\"edge403\" class=\"edge\">\n<title>cdef c&#45;&#45;cdef </title>\n<path fill=\"none\" stroke=\"black\" d=\"M888.71,-292C908.18,-280.06 934.54,-262.37 951.55,-249.87\"/>\n</g>\n<!-- cdef c&#45;&#45;cdef  -->\n<g id=\"edge416\" class=\"edge\">\n<title>cdef c&#45;&#45;cdef </title>\n<path fill=\"none\" stroke=\"black\" d=\"M894.22,-294.67C917.2,-283.34 945.36,-264.98 960.85,-251.62\"/>\n</g>\n<!-- cdefg cb&#45;&#45;cdef cb -->\n<g id=\"edge357\" class=\"edge\">\n<title>cdefg cb&#45;&#45;cdef cb</title>\n<path fill=\"none\" stroke=\"black\" d=\"M816.29,-432.05C810.63,-421.05 803.29,-406.76 797.64,-395.79\"/>\n</g>\n<!-- cdefg cb&#45;&#45;cdef c -->\n<g id=\"edge346\" class=\"edge\">\n<title>cdefg cb&#45;&#45;cdef c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M830.82,-431.9C834.25,-421.56 838.58,-408.09 842.01,-396 849.04,-371.19 855.99,-342.14 860.13,-324.15\"/>\n</g>\n<!-- cdefg c -->\n<g id=\"node29\" class=\"node\">\n<title>cdefg c</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"947.01\" cy=\"-378\" rx=\"44.39\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"947.01\" y=\"-374.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cdefg c</text>\n</g>\n<!-- cdefg cb&#45;&#45;cdefg c -->\n<g id=\"edge404\" class=\"edge\">\n<title>cdefg cb&#45;&#45;cdefg c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M850.58,-434.33C871.68,-422.22 901.44,-405.15 922.3,-393.18\"/>\n</g>\n<!-- cdefg c&#45;&#45;cdef c -->\n<g id=\"edge406\" class=\"edge\">\n<title>cdefg c&#45;&#45;cdef c</title>\n<path fill=\"none\" stroke=\"black\" d=\"M928.59,-361.46C914.64,-349.7 895.6,-333.64 881.81,-322.01\"/>\n</g>\n<!-- cdefg c&#45;&#45;cdef  -->\n<g id=\"edge405\" class=\"edge\">\n<title>cdefg c&#45;&#45;cdef </title>\n<path fill=\"none\" stroke=\"black\" d=\"M972,-363.06C985.68,-353.92 1001.36,-340.59 1009.01,-324 1015.7,-309.47 1014.18,-303.14 1009.01,-288 1004.04,-273.47 993.3,-259.83 984.05,-250.03\"/>\n</g>\n<!-- cdefg  -->\n<g id=\"node30\" class=\"node\">\n<title>cdefg </title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"960.01\" cy=\"-306\" rx=\"39.79\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"960.01\" y=\"-302.3\" font-family=\"Times-Roman\" font-size=\"14.00\">cdefg </text>\n</g>\n<!-- cdefg c&#45;&#45;cdefg  -->\n<g id=\"edge417\" class=\"edge\">\n<title>cdefg c&#45;&#45;cdefg </title>\n<path fill=\"none\" stroke=\"black\" d=\"M950.22,-359.7C952.24,-348.85 954.82,-334.92 956.83,-324.1\"/>\n</g>\n</g>\n</svg>\n"},"metadata":{}}]},{"cell_type":"markdown","source":"## 2.6. Mémoïser la fonction","metadata":{}},{"cell_type":"code","source":"# votre code  les cle du memo m1+\" \"+m2\n\ndef distance_graph_memo(m1, m2, cs, ci, cd, dot= Graph()):\n    dot.node(m1+\" \"+m2)\n    if len(m2) == 0 :\n        return len(m1)*ci, [\"i 0 \" + m1[k] for k in range(len(m1)-1, -1, -1)] , dot\n    elif len(m1) == 0 :\n        return len(m2)*cd, [\"d 0 \"  for k in m2] , dot\n    elif m1[-1] == m2[-1]:\n        dot.node(m1[:-1]+\" \"+m2[:-1])\n        dot.edge(m1+\" \"+m2,m1[:-1]+\" \"+m2[:-1])\n        \n        d, op = distance_graph(m1[:-1], m2[:-1], cs, ci, cd, dot)\n        # return d, [\"s\"+ m1[-1] + \" \"+ str(len(m2)-1)]+ op\n        return d, op, dot\n    else :\n        dot.node(m1[:-1]+\" \"+m2[:-1])\n        dot.edge(m1+\" \"+m2,m1[:-1]+\" \"+m2[:-1])\n        \n        vs ,op_s = distance_graph(m1[:-1], m2[:-1], cs, ci, cd,dot)\n        vs += cs\n        op_s = [\"s\"+ m1[-1] + \" \"+ str(len(m2)-1)]+ op_s\n        \n        \n        dot.node(m1[:-1]+\" \"+m2)\n        dot.edge(m1+\" \"+m2,m1[:-1]+\" \"+m2)\n        \n        vi, op_i =distance_graph(m1[:-1], m2, cs, ci, cd, dot)\n        vi +=  ci\n        op_i = [\"i \"+m1[-1]+ \" \"+str(len(m2)-1)] +op_i\n        \n        \n        dot.node(m1[:-1]+\" \"+m2[:-1])\n        dot.edge(m1+\" \"+m2,m1+\" \"+m2[:-1])\n        \n        vd, op_d = distance_graph(m1, m2[:-1], cs, ci, cd, dot)\n        vd += cd \n        op_d = [\"d \"+m1[-1] +str(len(m2)-1)] + op_d\n        \n        tab_v = [vs, vi, vd]\n        tab_op = [op_s, op_i, op_d]\n        \n        return min(tab_v), tab_op[np.argmin(tab_v)], dot","metadata":{"trusted":true},"execution_count":416,"outputs":[]},{"cell_type":"markdown","source":"## 2.7. Représenter le graphe des appels de la fonction mémoïsée","metadata":{}},{"cell_type":"code","source":"# votre code","metadata":{"trusted":true},"execution_count":417,"outputs":[]},{"cell_type":"markdown","source":"## 2.8. Mettre en oeuvre la programmation dynamique","metadata":{}},{"cell_type":"code","source":"# votre code","metadata":{"trusted":true},"execution_count":418,"outputs":[]},{"cell_type":"markdown","source":"*** vos explications","metadata":{}},{"cell_type":"markdown","source":"## 2.9. Trouver une/des mesures vous permettant d'estimer le gain par rapport à la version récursive du début\nCette question n'est pas triviale, les deux chaînes ne sont pas nécessairement de la même longueur, le nombre d'appels dépend des lettres utilisées,... A vous de trouver une mesure satisfaisante qui permettra une représentation graphique mettant en évidence le gain obtenu par la programmation dynamique.","metadata":{}},{"cell_type":"markdown","source":"*** vos explications...","metadata":{}},{"cell_type":"code","source":"# votre code","metadata":{"trusted":true},"execution_count":419,"outputs":[]},{"cell_type":"markdown","source":"*** vos commentaires...","metadata":{}},{"cell_type":"markdown","source":"---\n# 3. Problème du compte exact\n---\n\n![compte_bon.jpeg](attachment:compte_bon.jpeg)\n\nVous disposez de pièces dont les valeurs sont dans un ensemble E d'entiers strictement positifs (par exemple $E = \\{500, 200, 100, 50, 20, 10, 5, 2, 1\\}$) (en quantité suffisante pour la suite, on en a autant qu'on le désire). Ecrire un programme qui calcule le nombre de façon de payer une somme N passée en argument comme somme d'éléments de E (l'ordre ne compte pas). \n\nExemple pour N = 5 avec l'ensemble E = {500, 200, 100, 50, 20, 10, 5, 2, 1} :\n\n| Combinaison | Nombre de façons |\n|:----------------|-------------:|\n| 1 pièce de 5 | --> 1  façon |\n| 3 pièces de 1, une pièce de 2 | --> 1  façon |\n| 1 pièce de 1, deux pièce de 2 | --> 1  façon |\n| 5 pièces de 1  | --> 1  façon |\n| TOTAL | --> 4 façons |\n\nLes questions suivantes décomposent et précisent le problème.\n","metadata":{},"attachments":{"compte_bon.jpeg":{"image/jpeg":"/9j/4AAQSkZJRgABAQAAAQABAAD/2wCEAAkGBxISEhUTExMWFRUVFx0aFxgYFhoXFxcYGB0YGBgYHRcYHyggGB0lGxgXITEhJSkrLi4uFx8zODMtNygtLisBCgoKDg0OGxAQGislICUtLS0tLS0tNS0tLS0tLS0tLS8rLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLf/AABEIAL4BCQMBIgACEQEDEQH/xAAcAAABBQEBAQAAAAAAAAAAAAAFAgMEBgcBAAj/xABIEAACAQIDBAYFCAcGBwEBAAABAgMAEQQSIQUGMUETIlFhcYEykZKhsQcUFiNCUlTRM2Jyk8Hh8CRTc4KishVDRGPC0vE0F//EABoBAAIDAQEAAAAAAAAAAAAAAAMEAQIFAAb/xAAzEQABBAEDAgQEBQMFAAAAAAABAAIDEQQSITEUUQUTQWEVIjJxM0JSgaEjNLEkYpHR4f/aAAwDAQACEQMRAD8ADT4li5L3LZjcHWxubi1RwKL4xFnmdogD0jXCgHqk2+Jrm1NiS4cKXykMbXVgwDDiptwPdW4yRjdLSaJ9F5aSKQlzgLA9UMVNPPt/hXcnDtqVs/BPM4RBcnyGmpJPKjB3Xm/vIdP+6nD110uTFEae4AqsOJNMNTGkhV0xka8q6VA7DfsPCpuPwEkD5HAuRcWNwR2gjjTWEwrytlRczHQAf140QSNLdQOyGY3h2ijfZRjHw4a//Na4ymrCd0sRw+rLfcEi5/Vfj3VBwWxZpXZFQ3X0r6BfEnQUNuTE4Ehw2RXYk7SAWHdG9kbltLh0mLMGdxdR/dE2LePPwotifk/QswWVtAtswFtS1xcC3AE6c6Bw7KxMF5BaUKuU5JcxQceCm4APlULZkGInLBJGAXUlpCqre4GpNhxPrNKmQut7ZBQT4iayo3RHUUcbcI/2izHqNaL9fQMxPrt41Jk3AiGZmldgL2CgFrBQStvvXv6xVTxkk8TlHZg6n7xuNLaG/MW4d1S/m+NSPpwzgHrEiQ57Hq5yt76gWv3VznPABLxvwoY2IkgRkkc+yjbS2Ay4s4WM5iQCubqnrLms3YRR2Tcl2V2zNdYUYC3GQrdl8gB5mhuB2JimdZiupOYEuoYm2jdY31qPilxvShHabpCbqMx1J0uCDY6c64y2aa8bcrmwaQXOjdROyMSbhHo8+c3MaG1hfOSMw8ADTsnyegN+lOXPYaC5TLf2r3FDf+FbR/vGv/jr2Afe7AB5VCmwuO6QREyljqBnJFgS2YEG1gSTftoYmviQIxxw3mFyKvuxhlUuzzqOiMgUgB1VTYgg876igO7uyBii6Bysgylb8Ct7OfEDWpc+xcexZmzEsMrEygll7Cc2o7qCTRywOVOaNxobGxsdCLjkRV43h4IDwShTRmMhzoyArS+6ULC6zSNcdIrkfVlM2Wxb71qWm5MdyrPLe7gC1r5WspudBca68areAhxUyGKIuYxqVzWQHlxNqmvs/aQJa8t8ttJbkr2aNc+FUdJpNF4Ro4w9upsRpNbv7EjnWZppTGIja9xYceN/DhRmfcyBQrBpWAQsVWxZ7AGy9h14VVMFgJ5QyoDl0z3bKlxwzE6XvwpWJwOKiZL9Jct1GViQW4dVlNr20qHyDVQeF0cZ0WYyfdWHF7pYdI3ZpmQ3suYgWJAIRhzbXlSxudCXUHpgAxUgj9JZc2dba5b8TQKXYGKOjMvG5DTp6XAkgtx5VE2lBiYchkduBCMsmYDkQrA6eFUbIHHSHi0V0RY3U6IgInvLu5Hh8OHUPmL2JJuoF242FuQqpNU7DRyzERqWa9zYscotqWNzYc9akvu5N9kxOfurKpJ8BfU0Qysj+V7haCIXzfNGw0gbU2aeaFy4jVSXJta2t/Cpy7Bk4GSIN90uL+F+F/OokyI2bOKtFiyyfS0lCGptqmvs+QSiIqQ5NgD39/Z309idiSKyAFXDtlDKbgNzBvwtVXTRit+URmPIbIadkFemaLbU2YYrHMrK1wGW/FeI1prZuzOlDMXCKtrkgnU8BYUMzM0672RmwSa9FbqDE1jy8+HnVu6/6nvqqY7DGKRkbipsbfGrT0f65qrjdEKQCNlZ92m/tOH436Rb6WHHsort5/7L4zt8KBbDxSxzxSP6KMpNuNhVqgxsSgqMRh2XMW66sdT4rU+Iao8iN4aSAqeF6JcSWIuAJPqg+6P6STuhk/2mrPg+hKKDA7HmwQkHXjUBtpYUOBnjDNG6M8akIM3o3FrnvsKlRbWCqFGKgsBYaPw9ms3PL55RJoIFdlqeHCPHgMXmAkHvSq+8rlsQ6sVtH1Rl0AUch30Y3ZiywAqbNNJ0ZbmFFrjzJ9QoLvFNE0xMVrWGYqCFLcyAeVPbC2oqK0UtwjEMrDUow0zW5gjQitfIie/BDYxv2WFjTRM8Sc6U2O6nYvbwikZEgX6tiFLE5rg+keXLhRUt1FDXKiIzOBxkY9b+Nu7WuHHw3zSS4Z1PpHKTIw7LWvehuz9sRtlUv0TxkiNyLqUN7K1uFr2vWW+PXF/TjIrn3W4yXy5j5soN3p9k/szanSrI6oInhUMCt7FSQCpvz/nT00Kr85yiwdYXtyGY3It40jEYyJV68sOW9ykAuZCOFyBYedQ8FtVJWnzyLGZchXMDlUIfRuL8qoYXvD3RtIbXCI3IjjfG2V4c6+VNk2ek+V5eq0Gkl+LRjVD3n7PqpErlxiGYWzQkgdi6ZQO6wp/E4/DTMXMgUIcrA3BkRQMpUczy9VNbR2lE8ckodBnhCCMemG0FsvZpxoPlznS1wNN4RhLjN1uaRbhunJehE7GUEjIlrC+uROw9lQ8bi+giVwOEpMKvx6Mgh9Pum486dx20kRJJo5lu8aBAp+sDAKGuv2bWNU7F4p5GzOxY9pNzTeFgOkeXO2FpLxLxRkMYYzckD7BW7CwRS9A4jCiQOWUEn0Cba+VRNn7S6YyAIESOBgqg3OrAsSaf2Nio+hhcyIvQrIHUmzXa5Wy/avflQTdqZQ8iswUyRlVLGy3uCATyqG4lCU6eOFd+aSYAXbHlHcOmEKqCpzkAN1WtmOh4cqqm8kzNO4YAFDkABuAE6o158KuUe0JI1Vc2H6osD06g6c9DVM3iEfTN0RBWwvYllzEdaxPEXvrVvCW1LuPRV8edcOx2vuiGyAPmuvDpxfwy6+6iwGGBLQrd0BdQ2YDqdbj5XoTsCQNAUDIHWUPZ2C3FuROh1o3NjS91lMAjb07Ti+XnYKbnwpbLYepdY9U7gPHRso+ndCsFMskUTsCyBnMoXiHYkgkDy9RpO1sT0USvhwMnSqxNycrr6Iyn0b9vOvbFxcSJaFow+ZswkORnW/VsxsOHK9RdvYxRHIpZDJMykqhDKgXXUjS5J5VLYj1NaSRfqofMOjJLgCB6H1UvCmOdYZOjCZ5SrAE2Iuvbw4mq/t7aJc9EECJGzWAvqb2JJPgKLbvYmPoow0qIYpS7BjYlTY9XTrHS1qrGMfNI7DgWJHgTTmHjBuQ/5eOFmeIZjnYcY1bnlT92/wBJJ/gSfAUXlePoQBGwfTr6gXvqb+FBNgTqkpztlVo3TMeALCwvblRuTHL0YjfExdGAAcuZmIBvYC1LeJxPdNYHonvBZo241OcBv3ScfEM8726xaKPN2ZlJZh42GvjQyXEhMR0HRArmC63zm/2gaQ+3FM0hZSYpAFK/aAT0WH6w/ianf8Sjtpik0FgTGelA7OH8aG6B7DcjSbGyNHkRyNqJ4bRs+670QLRE6mKfIp7VIJt5EX86bwbdH9YwvGXIb9Vl1VvfQyfbCCSLIG6KNs2vpOx0LHy4CnZ9tRJlRCZELMZOrl6r2FgDzGW96o7GlpoIKI3Ngt+4/wC1C29+gj/xX+C1G2FKmSSNnCFirAte2nHgONL21jImRI4yWAYsWK5eIAAt5caY2LjkhL5swzAWZQCy2N+fbTjIndNpI3SEk7Ot1tIruoe3cQsk8jrqpOnfbS9T/nC/fb2TQ3as4lldwuUMbgf1zNJ6Ze33H86bYNLAEjI63kjuryDS0NIIpS1vgLyBKWK9euCuqe4Hx+NSQoBK5XRSak4LByTOEjUux4Af1oKg0OVIBJoJgGnoIHY9VSx7AL/Cr1svcmGFRJjHBP3QbKO6/Fj4UWO3IYhlw8IAHA2yj1DX11l5PisEO1rZxfB55hZ2VAi3Zxj6jDv5gL/uIp76IY7+4b2k/wDakbG+UnG4gSk9GuSQqMqch3k0RG+GM/vF9gUP4g7sE23wZvOoqEd1cb+Hb1r+dNNuvjPw7/6fzoqu+OL++vsCvHfLF9qewK7rndgp+Dt/UUFbdrGfh5PUPzpo7uYv8PL7NWAb44r9T2a8d8cT+p7P86nrz2UfBx+oqttu9i/w8nsGmzu/ivw8vsmrKd8sTfgns/zrh3yxPYnsn867rj+ld8Ir8xVWk3fxR/6eT2DSBsDFD/p5fYNWs744nsT2f50ht8MT2J7J/Oo62vyq3wm/zFVU7AxX4eX2DSDsDFfh5PYNWh98cT2J7J/Oo7b5Yn/t+z/OqnOv0Vh4UR+YqunYGK/DyezSfo7i/wAPJ7NHpN8cV/2/Z/nTB3xxf6nsVHW+ysPCv9xQkbt4z8PJ6h+de+jGM/Dv/p/OiZ3xxfansU02+WL+8nsCo609lPwsd0IxGwsUnpQSD/Lf4XoZJGQbEEHv0q2Rb74oekI2H7JHvFPHfLCTOkWJgsZNA1g637/tD31IzAeQqu8Nc0fKVR3FOYXAyTHLGjOe4fE8BV5n3Ow7MJUlIi4sL3Fh2NyqHtPeNIB0WHUIo7B1j3k8vjXSZbRQbuT6KIsB5svNAeqFRbl4gi7mOPuLXPu099Im3Km+zLGx7LkVEkx2IluQCe+xPvPOoSbTlB0N/L8qFqyjvQ/5RwzEG2o/ek3tHY88P6SMgfeHWX1ihpNWzZ29DejJqp4g6g+Z1FNbb2EjqZ8MNOLR9neB/V6hmT82iQUVL8Wm64zYVVakW7qcIpOtHPulwr+TSlNJa2tqcVe+tteXK9XSKX0XG5Aty/8AlK6HS9x767ZVop3Zez3xEixxi7N6gOZPYBWlxxwbNiyIA8zDU8z3nsHYKY3awK4HCGdxeSQDTnr6K/xNAsRK0jF2NyTc15jxjxMs+Ri9l4F4SCPMkTmJxbytmdiT7h3AUgt8KbApvGYlYo3dzZVUkk+FeRJc91nleuLWsZss+3O9Gbvmb4CrCDVd3IN4Hb70pPrAqxV6wLAtOLXSaQrV0mpUWlg12kqa6TULrXozx8fyqG+1kBIKvobaAW086kIeP7X5Ua2Q+HmighgGFfFZHMiSxuSWBJtnAsp8as0Woc6kCn2ii2urm4voL2v266U2NoqVLWewNrW19V6c2dtRow4yhekyAzFC/Q9Y3svA9lqK7WEK7UyyoqQ9ImYfZN10Y24Am1SWhQHoFHjlc2AYHvFh6701Met5VY94YFECSFYw/wA4dVaPLYx2YqDl04Wqsv6XlQ3CiiMNpDGmjTjmmSaoiJLUy4p1jTd9a5QmHqAYS+Lwqgas9veKJSLUzc6APtGC/wBlJG8wBb41I32VXn5bVh3y2iIUECaBRr3sdfdx8TVQwCxnMzgu/JbHUm1mvwtx4kWsON6m72S5pzc6XJ7eJte3gKanx0EQtCt30Ja918PcDw0J46U1hxgR6wNz/hZ2fKTJo9G/5KfyyyRqGboUUa3sCdTr28CNTzuaHTY6KK4hW5tq5t3cOZ0HcDrUvDTpMM02aWQt1UXt4AZbi4538RUn6PqS02ItEquFaNSCRe2rNey3vewvTFgcpUAu+lVWOFpGsqlmY8AOZ+FHNg414JTHJpl0I46dl+duNHMdPhcMrQoSGDBlEXWkz81JPLhYnkTVe3gxbPiIyQAAqgEX1zanrH0rXtSuR/VaaH2TmN/SeLPOxH3UbevZ4hmOX0HGZe7tHr+NCOgPZVp3t62Gw7HiNPd/Kqv05/oUSB+qMFCyIwyQtV4HGlCvNxror0IXkiug0Z3VwHT4qKM+jfM37K6n12A86DCrx8lkF5pX+6gA/wAx1+FCyHaYyUbEZ5kzW+6c+UzdnaGOljGGxEcMUa+iXdSzHiTlB4CwFUwfJhtgf9dF+8k/9a2eQ3J8a5evLucHHcBe0a5zRQKxz/8Ame2fx0X7yT/0oNvVuBtSCFpZZBiI0F2ySMxUD7RRgLgdovW/A03jADG45FGv6jUtDb4CsZHkcrANy2/s5tzdv4UeUUA3IW2Ht+u38KPg1cqRwlE0kmosm0kUkHNobHTSjEeyp3jEix3DIXVcyh2QcWCE3IrqK4kKEppd6GJtSM8M3qo1iNmYiNM7RNYZb8Cy5/RzKDdb3HGppRqCiIePj+Vcwm3MRBkKYOJpIhIsUucqcrk6sg0cgW405tLYmIiDSSLJGq6tZ00/y3JoPDOrsFWWbMTYDTUngOFWAKqSCpSY3FQrkiRJUkVekSRQy511Btca3pJ2jjC3zpgrYnpQ4BUZSBpbLwtbSn8bsjEQoZJenRF4schAPZoKHYWUSOsaTTM7GygKLk9lstQSVYAKQ20cRLaN8PHBCHeUhLnNI/EksTbidBSHtm8qXtXBy4cAzPMga4BshBI4i4BF+6ouzm6Z8kReVyOGXUAak6AADvNUIJKI2gEpzTDU9tMNhyBMpQsLrcXBHaCNDTGDRpyRCrSFdSFBNr11FTqC41INcx7GBgswaNiLgMpBt203HOrC6m9VIpcCCuu1SN18WI9o4YnQPnT2gLe+ozmh0x/tOF/xR8VqG8rn/SrJvlg2WfQE3Yj1m6/E0xgt22Zc0rdH1wiplLM7EBrdX0dCNTV33s2V06Z09JeNuOmoYd4rPosfiYGZEkZS5119InQG5+NM4kp0eUORx9ln5sI1+cRsefYqyvPhMIuRcxZhmAABchierfmyMvO1CMbM8zzGVuhVggdb5gQBe/DS/HxNtam/RwRyO4dk6GNGLlQ4kkbNmIBI6tDsTHh1WLEyGTECRmBFhGqldWFtTpe4HOjCr5soBviqC5sTAo06yRFgqXszei7jQAE9vE+6m9uTzPLHDKqAoc/UJOh9EEH0dANO+pOO3hEYkw6JHIhI6LKOoFaxylRzHdrek7u7Ny3nmOg1Yk34crn+uVK5EhA9zsE3jRgn2G5UffRskcEXMDMfVb4k1Van7c2gZ5mkPDgo7FHDz5+dDb0zBGWRhqXmf5khcr/ShXLV0V6ALyRSxWhfJSP0/wDl/wDKs8rRPkp9GfxX4Glc38Epzw0f6hqtJNevXrV21eVB3Xrl4Gm8Y31cn7DfA0B2tvxgcOcry5mHERqXt4kaVAxnyh7PaBiJTd1YBchzXsRqOQ76O0bqCsx3QFsMtiDck3HfbTxFG81At1YiuHCniCeffRhnsL9nZRCFccIFjGJZvE/GtVjwyyrhSYyFXZzH5yjMrIRb6vMDlseJBHKs5McJJP1muvon/wBaQZYgCnTShfu5mC66+ja1WvZU0obh2OhHG+njyrQdpDE4PDAOrzYzGGN55GBKRRoQI0ZgLX0AJ5a9mtLC4ccHb3/lTr4wMCrYmdlOhBZiCPAirWo0q27bwrzw4+fGYWODERFMrx5rMWUC2Ym0gy24cPKs8Q2F78j8KLTYwOoVsRM6j7LFiOzgRUSRYAL5n8LcfDSu1ALtJRzeEnDYHC4I36SVTiJ9dRmH1am/d8Kr2xExHziMYUkTk2jI5E8Tc8Ba9+6pEGAxeLbpRHK9xbOxLErawAJ4+VdfZM8BEjrLDY2DjTKT3jh2VXzGonlOpFN9pRDEmARXZYWLyzMpAknc3fLcWtcnh+dMfJhb53KCM18LLoNLiwuB4ih2JnEgyy4qVwOAds1j26jjTEMUcbB452VhwZTYjzFTqC7QaRHfSDLh8Aw6RFeI5YJGz9Db7IJUNbxoRuvs98RioYUZlDveQqxFo0GZibdwt50rGkSm8uIZzyLG5A7Na9hT0RJixDIWBUlbAlTxXw0rtQpdp2SN8Nq/OsXJIPQU5Ix+omg9difOm9keg37X5UycFENBLbyFP4FFUFVbNrc93AVRxsKzGqSxofiT/aMN/ir8Vqc1DMUfr8P/AIq/7loYG6u/6VtzSlWJFB9rbBhxAJFlbmDwJ8vR8qLTjU1Eeky7dSDSqcu72MiuI5JACLEXzAjXT3nlzocm6uIICEtlBva2gJ0J1Ohq79MwI1NVzf8Ax8sTRCORlDK17G17EW+NNQPlkOlrv4S8ohYNTmfyo8WxoMKM87qO692Pd/IVX94N4Gn+rQZIhwXm3eezwoTM5Y3YkntJufWaaIp2PFDTqcbKVkyy8aWih2XDXK6aTTCWWiYmbOxbKq35IuVfVTYpyQcb8RzHOm62m8LzDuUoVo3yVDqT/tL8KzgVpHyV/op/2h/tpXO/BKd8NH+oH7qzA1SPlP3gOHhWFWytNfMRxEY5DsufcDVj3h2uuEws2JZcwiTNlvbMbhQL8rkisD3h23PjZRNLlzFBoNFUX0A7h299ebibZtesKnR4mAjr6G3ADjSMRhY+rlN83OhIwrWzAZhbl9q3G16s25O7TYlWln6URg2VALFj3DTTlTD3tYLKuxhcapI2dGq3CgjXUngSOIA7tD51NXjRLa2HdMOlsP0UYkYKSSX1FrtyGb/xFCIzQ2O1C10jdBpS8PhhITnJKjTLewJ7TbiO6p8OzYSbdGg0+6PVw/o1FwDaHxNS83KirIllcXndNnAQn/lJ4ZRpXF2XC1wIkv8AsgaczTxck3PPjXBIRw014+HAVKHrN8lRG2dBfSNbfsig204oOlSELlYsvo6XueflrVglYXuBa/Ecr87d3OguJwQ+dRzE8Ctu8gm49VvVVXmmlNYbiZgCVoezNqQK6xdKgcD0L66crVA3oxUckUq9IrjK2YAgkeVKnmwSMs5hsytcyBL2Nuwa916r+0tm4NIJJYVYSSKdLkXL87HxrIFd16bTvdIBsHDpPF0kkS3vxt3Cwqa2y4P7pff+dRN1YXSM5ySDpl5dXQMO+il+J7Be/wAB5mtS15yZx1mioh2NBbN0a27ifS5Dj5+FMNsuD7g9bfnRGVrWUXK2N7DQ35jtt/CmJIyADzPK2tu/srih63d0PfZcPJSPBmH8ahzRZDYm45E8fA250XCE35WF9dPAWodtiMqVB8a48I0Er9VFJ2Ts9sTKIwbcSzfdUak1bMBsSLq5YQwBvmaxY24Nc8DfXShu6sRWHESczHlFuOpB99qLQ7RdoyY4zYWADAqSeYsezurOyJCTQ9FtwsBG6fMxJIzspHDXMD3eNSkckdYAMDYjiPHzFVXGYlyyyZWjCN9oWJ7Tb+uFENoY2R4XdGKO8RdbcQQNOPhS7QQaKtNHtsizHWqx8pI1g/z/APjVIw2+GNDqTOzC4uCFIIvw4VevlH1WA97e8Ka18SIsk3WPkuDoyqI9INOPTVahWcFw0nLXSK5VCrhaAK8KUuhvXCK215derSfktH1M37Y/21m1aT8mLWw8xP3/AILSmd+CU/4Z/cBRvlPky7KxR4nKnfe8sYtWETYeeZMyoxC6MQp0PHKe+2tq+hcW4mXI9jG9uAuupGVu+zZTfupW5+70SpLGRoJS1uGjgE37dcwrz7QWherWRbltJEuWWFWUXMbNfMjHja3FT2GrxhMa2nRuQOfO3gKf29sNMM7prkOsZ7FPLyOnqqq7PmZ5LAnJcqGHMjx0tcWpWRutxC043tYwEotvRtskdEjtlOjqUXK3Ywa1xr+dV2NqMb1bMMeWbOGBsp0UEEDq3CcfHjQONr01FHobSz55Nb7CJYF+r5mpGfWoWEOnnUgGjLEk+sp9WroamFaou08Z0cZYceA8akC1UC1NZ6jdIHljhUgySNZFvrfjfu4GqviNqStxcgHs0+FJ3fn6PG4WTsmX1Mcp9zUUwmt0zFEWuBKusc2HmjCyusciXU58yk2PC6EHTvoTtXER5b6th4yFaQlmuzejqTcjSjfyhwQtiSsSEyW+tI0XN2cNWA427Reou8UmHbYskcQCvFLGJVvfrE3zX5g/yrMbC0SabXoJJ3mHVXO1qDBOjAZGBHcdKfSXqNdtARZSLgEn0rHhYXrP06oHI93Gp2H2pLGQwc6G9jqLedaJgNWsMxkG1cJlOdgpOg42toACdBw8KaYvZcpa561rg6Dnfjx7aaR89ipHWI5kHXnc+vjXJcOS2UHlpc9nhypcqlJTIxuSwJIFxpmtf+WtC9snUC1sunG/DvqeHIQnMCNBlIv7vf5UJ2lKSRzJNrAcewAD4VBRYvrCtG7mHDYY3+1mIPeDZfhTGI2hOwVi2UDUjq9e1wAvYRz4cRRzDRDC4EFxYxoWbtuetb1kCqys2IwsUd2t0ydIbgHKzknKL8Bb4VlaS5zne634pAKCH7w4+Rv0nEDQcTryPlVi2whEXVB0h0A8DQjdnDCd5Z5SSI2VF53ZrsxPkAPOr08K2Jte6gW7tarJTSB+6vI+9/ThfPVa18oH6HDnvPvUVTN7t2fm5MiG8bG6g8bH41ct+dcLhz3j3pWzA8PcC1YeQwtaQVRXpoinWpDVolZwSLV61dNcvVFdaBXCKWa5W0vLWk2rRPk+a2DxJ729yVnhrQ9xHC4DEt2Zz6kpTO/C/daPhf8AcD7FV3dnaDMXw5YlejDx6k6EhSunLreGtHId4MTDCVgjSSYKBlkYqLLmGmnHxrPt2ZCuLjVQWGRzGQM3UNmAtY6qwt51cdp4MnJIv1bC+pKrwN+du2sUtsr1IOyRsneJtpqI8XlidCc4FlC8QWDEm69oJ5CoU+8kUtsHgYk+bKygynV3ysCWXsF+fOoGL2YJmbgSG69rsCjdbMTzsQ2l+VHdk4KOKNMihLgff+FqGIgDauXkgBQ95Xth8hP2x2/ZueZt2VU4DR3eXEBpliuCBe9r6luHHsAv51X4Ta47KJ6IZKJYQ6edPXqJhW6v9d9PBqlZUn1FPXqv7zTHMi3toT58vgaNZqqG35fr2JNhoB3WF/43q7OUSEW5RxJckcOz+udcMpDK3AqwI7iCCDUfMVb+rd9qU5LaAXJ5AXPupjVYTi1zbOVcLBIpJYhzqSxZmN2JPEkvf10E3kRBsi1rSCZS+v2nN2/LXsruzMTI8USTRMDHbIdcuQrnubjRsxI7iKib2K5wzKqk5mW4AudCeQrHkkLcse61442vw/cKl37aZ6S5PjTww01tIpPYb8qhJEVv0isvMgixPdrrWs597LJIVt2HOrQG9uag6E6Hstfzqc8KHqqeLgA27aC7syWz38bcQLjS45juo7gpY8yqA1yVuQTyN+HCxNqUeN0La00uHPWB6wHo2PE+AN9dBVh3K2XGZ3mZOtGtkB1ys3FtedhYW4XNVf50mgJFuQK2sLWI7zzv3VY918UFR3HAEA2uQfSsNPAUJ3CJGBqXd4sWpd4ZDlRuN+4g37+FS9s7PGKQOCOhEFgAPTsb3ueFtLd96d2/sFcUBKvpFer4G2vjajUMSIFjXgiAW5Aagesg0qyHSSU8ZbA2VV2Xs9MLC8Y7Q5ub9YgC1zxsNPKgW097SrEX63R5VA+8WOp7LCrZjMHK4LEZ1Ooy+la/3eZqj7N2D02PmtrGpzXIsbHQeB4+qhiHU8lyZ80BgA5Vp2KJlivPZ8yC3A8fs69g4mou/o/s0VuTj/aanbbmEcZynKoFr6WHdc8+4a0N3ubNgYW4m6H1g01i0JAAkMo6mEqhNSDS2ptq1yskLxNJrxNevVVdaDXa4FPZ7q5lPf6q2dbe68xpcvE1oXycuGw2Ij53P+pbVnpU9h9VWv5NcdkxLRk6Srp+0uo9YvS2XT4jSdwDonaSs5wk6/OEZeqqi2U8Ab3Ya6WuK0BZiY11GrNwt2J9yqtvbu7Jh9oS5YiY2YuhFrWbUga30JNGsIymFAJFXj1WLk6nha1+AFYxXqQhO8W05sNiY2RAySKVcFA2a1zbr68CTRTFYlliDrkUquZicoAst+VEZt3JFBubP1SFKDKQWXMDe2mW57dKib1bqviIbCbISL2J+rdhwBkF8vLQ0J0zQaJRWxuIsBVXZzXHSuQS+umtr6m/9cqQ2jEd9RcHs6bDt0RRlcAFizdTXgVP2ge0UWn2TiipmERZRa5UfBeJ8hVy4Vdoek8UvYZhanc1DcJixwJt48PPsqT84X76+v8AlXWs+SN2o7KTeqjtSUmaQXsM2nZoALEVZukH309qqhjLNK9zfrHQHT186JHyrxMIO4USZrHW1+BtS8LigvWPLQ/wpOJjNtALePCpg3exCYZ8RJGBG6XQkjMRcWcKDcA62Y1Z7qTTRafXa2F59MNBcBVOvnTjY/Ccfrz29RaDbEwvTSBMwWwJue7sHM3I0ojtLB9E+VVvoGD8EIPMk8NePOlwASiaiAnf+J4QG/13eCq2PqoZPjA7XF9BwIuaYxbRg9XrHnyUHu7fdXNnuLuOZXQ9hBBqw2KqTaMbBchmvxIvRjpCDcEjwJHwqvbHmAm1I1U6k2HKjUki/eX2hUScpdzTdpyXaEg/5jHxN/jerxsiLJh4yVBzRqxsAt2JJ5aDiKzqZx99faq/7Gx5mwkagEPGtrnQOAOXPs40CRwaEeBjieEe2DOGjNtArlR3DkPfaqpvFve+HxMqoiuq2DEkgjKNRfzPrqDhd8zF00JQNzAvbjoTfnrVfgAkdxYOWuSC1i3dftqBZ5TFALVcHKcqIb+gDfS2oBtpTWFwaxtM1wWkcOe21gq39Te+gLbaZ2SPDLd8qks2qxiw5Dj/ACp5se0CO0j9MzMqkgBbMA1wtuIAPlrQyVKD79yqgBN2c8LknKo4kDgtybaU9vmcmEgj53X/AErrUKOL53i14MCwa41XImoHr99658oGMDTrGOEa6/tNqfUAPXR8VtvQMp1MVTakGltTbVplZjUmuXrl69eqIlLXJsa6skccjBz0ShdclmRdQAbA3JJqbtDCTOZZEmmAW5yJfhYFcuutwQT2XNSf+ExyFbXEjKBmXiPq1Bufsi17c+ND5dgRBihklvmCEkm17XIBA1GXkNe6ubkw2AHUQN9rQfJfW4sfdQMaJY5SnTz5VAIYlgrEkWAN+BB49tRvnDRzmRdGWUsPEMaORbtoWUdJI2VwAC5svW0FiNOF7dlVqV7sx7WPvJp3HnjmNNN0N9qWfmRvjAJFbrRt68MuOwa4qEXeNSxAFyV+2niDqBWbbvibE2liTNGrgE5kAJFiR1iDwqybmbyHCvle5hf0h90/eH8RTu/e5kovjNmO2V+vJFGfSvxkReDd4/8AlITwmN1enotjEyRMy/UcqxbcRp5S6cCq6dXkNRa9QDs6VNUQqTxMdlv3FCbH41kP0nxqE3kBI060aX87AGpQ33xmmbIwHcRf31mPxgSStmPKIaG7LTMXsQFg8zRAL1kjd8pJIswY8lvY2HMVHk2wqTk9PF0aqqIiXa8khsZHIHBQLAA86zWbed2bMYlBHA9g4m1xzqXFvVGAxZGBIANiCLg6G3bUOiptAKzZQ42SEU3pxGHmaM4eIiWRmBspQFUuouDYF2YFiRytQWeF0bIw146EHj4UjHbYEpB9EcQLc7WJqPi9sIzlnk6xAvoeAAUcB2AUeJpA3SsrgSaUhs1tAT4Cq1Phpc7ZUe1z9k0fw+8AQWScqDqbXF/dXF3umDH+0MVv98ii3XCGN+UEi2bipL5YJn7csTtx8BV331xWIeCXpMP0SBIwC1wNAFCrmAvYDhVWxW38Q7E/PJBc8BIbD31HxOIeRGD4wsNOqxLZte3uqHfNyrNOkmlJ3Yx6gZZHiRU9EMAGJOpbNU7F7TUSNHJIBe+oTMEPFSc3E+Wl6q3zVf7xa6+HBNzMpPeSTpoPdUNGl1rnPLmhp9FJ22bPcFCORQDKfVz7dBUHDAkkKCSVNgBcnyFdaAf3i+v+VPbPcxyB1lCsuoYEgjwI51x5sKo909s2FlfrqwJGlxbTmdaKRws7ZRbzIHxIqP8A8VLMDLMz2BtmZmtfx4UvD7WjVwysQQdCAb/1aoO4VmkAqVsvZbTTBDkVQQXLyKoK3FwDzJF9K0WSAqLQywAAgj60Dhw4jsGXwrLl2uqHqZhpbs0qU+9vVAEZJ0uSRr28qXkj1eiNG/SSrZtndhZysr4yGFgpDAEuONxY3Gnd3VWcfs2KElkxSTtyVIjlv3sWtQbE7eka/UQA8soNqh/P5T9o0QNIFIbnAm1atm729BDl6A9IWIdhopA4W7wNKF7Q2+076rlRfRTkO89pOtBhiJWsgZyCdFBOpPYo51oW5+5YhHzrG2XL1lRvs/rP39gqdAUakX3fwy4LCtPJcMwFlPFR9lfEk3qjYuYyOztxYknxNGN6NuHEyWW4iX0R2n7x/rSgTU9jxaBZWdkza3UOE2RTT061IYUUoTU1auV01zNVERb5dmEaC6rmAJvlJFgb5uIXvHfS48KgsXNhckFWJbMCcvDUG3PnzNUXEakt20loiONuFVf4U9w+V9ft/wCpP4o0csv91eIjLmizG13YsQVsoXMVDa9tjfvNUQmumPwpfRk2Hqp3DxPIJJN37UkszK88AVSZvrVg3a3olwhy+nETqhPDvU8vhQ+TZEgXNdOI7SddeyobxEU49rJBRSzHvicHNNK+bS2Fsva4zK3RT8ytlk/zIdH8ao+1vkmx0RJhaPEL3EI/ssbHyNcWIixBsfVbzo9g9v42HQTZhcCz9b3kXrOkwq+krZg8UvaQb+yoM2520UNmwU3kpPvW4pr6MY78FiP3TGtch3uxAyZ1jOckCwPEWtz4XNNy78YkMV6OLQkcW5G1L9O/sneuiq7WTrutjeeDxH7pvyqFtLdHHsRlwWI7/qm/KtkO/OJ0HRxa97VzEb74lSbxxad7c6jpX9lHXw9/4WIfQzaP4LE/um/Ku/Q3aP4LEfum/KtqO/eJtfo4vW1cG/OJP/Li9bV3Sv7Luuh7/wALFvoZtH8FiP3TflXvoZtH8FiP3TflW77L3ixk8hjVYFtxJz/wqDtTe3FwsVKxGxI0zcjao6d10rdZHV2sW+he0fwWI/dtXvoXtH8FiP3bVr433xJUsEisDb7XOm333xWnUi17jXdM/so62Lusj+he0fwc/wC7Ne+hW0fwc/7s1rP00xdvRi/1U3Lvlixrli9Rrumf2XdbF3/hZUdy9o/g5/YNdTc3aA/6Ob2DWnPvni7A5Yte40y2+eKuRli9RqOmeu6yLus5+h+0fwk3sV07m7R/CS+zWjQ724tzYCLzBpWL3mxkbFWENx2A1HTuVusj7rPMPuDtJz/+ZlHa5VR7zRzZ3yU4gm88sca9iXdv4Ae+jb74Ys8OjWw5L+dCMftnEyjrytY8gco91WGM5VOaz0R7D4XZ2zB1PrJu3039fBKrW3tvS4o9bqoOCA6eJ7TUHoTSTDRmQNbuUs/Jc/b0UY0hqkmCkfNz3UQoYKjNTTVKMBsT2Uh8MdOGtUJRGqI1JvTpSk9HVCihf//Z"}}},{"cell_type":"markdown","source":"## 3.1. Dénombrer 'à  la main' le nombre de façons pour différentes valeurs de votre choix\nConseils :\n- Pour votre réflexion, il n'est pas nécessaire de faire varier E\n- Chercher une présentation systématique de vos calculs (ce n'est pas le cas dans l'exemple ci-dessus, j'ai mélangé les lignes). Tant que vous n'avez pas une façon mécanique d'énumérer sur des exemples, il y a peu de chances que vous trouviez un algorithme\n- il y a une et une seule façon de payer 0, c'est de ne rien donner (c'est une des conséquences du fait que E ne contient que des éléments strictement positifs)\n\n","metadata":{}},{"cell_type":"markdown","source":"*** votre énumération sur des exemples, présentée de façon à voir apparaitre un schéma récursif","metadata":{}},{"cell_type":"markdown","source":"## 3.2. Equation de récurrence\n1. Ecrire l'équation de récurrence qui généralise votre travail dans la question précédente sur des exemples partticuliers\n1. Vérifier sur les cas traités à la main la validité de votre équation de récurrence.\n1. Justifier votre équation (ébauche de preuve de la correction de votre algorithme)","metadata":{}},{"cell_type":"markdown","source":"*** votre équation, justifications, ...","metadata":{}},{"cell_type":"markdown","source":"## 3.3. Ecrire une fonction récursive résolvant le problème posé","metadata":{}},{"cell_type":"code","source":"# votre code","metadata":{"trusted":true},"execution_count":420,"outputs":[]},{"cell_type":"markdown","source":"## 3.4. Représenter le multi-graphe des appels","metadata":{}},{"cell_type":"code","source":"# votre code","metadata":{"trusted":true},"execution_count":421,"outputs":[]},{"cell_type":"markdown","source":"*** vos explications","metadata":{}},{"cell_type":"markdown","source":"## 3.5. Etude de complexité empirique de la solution purement récursive\n1. Représenter en fonction de $N$ le nombre d'appels à votre fonction\n1. Déterminer par essai/erreur une fonction qui approche au mieux le tracé précédent","metadata":{}},{"cell_type":"code","source":"# Votre code pour la représentation graphique","metadata":{"trusted":true},"execution_count":422,"outputs":[]},{"cell_type":"code","source":"# votre code pour la recherche d'une fonction approchante","metadata":{"trusted":true},"execution_count":423,"outputs":[]},{"cell_type":"markdown","source":"## 3.6. Mémoïser la fonction récursive","metadata":{}},{"cell_type":"code","source":"# votre code","metadata":{"trusted":true},"execution_count":424,"outputs":[]},{"cell_type":"markdown","source":"## 3.7. Représenter le graphe des appels de la fonction mémoïsée","metadata":{}},{"cell_type":"code","source":"# votre code","metadata":{"trusted":true},"execution_count":425,"outputs":[]},{"cell_type":"markdown","source":"## 3.8. Résoudre le problème en appliquant les principes de la programmation dynamique","metadata":{}},{"cell_type":"code","source":"# votre code","metadata":{"trusted":true},"execution_count":426,"outputs":[]},{"cell_type":"markdown","source":"*** vos explications...","metadata":{}},{"cell_type":"markdown","source":"## 3.9. Etude de complexité empirique de la solution par programmation dynamique\n1. Représenter en fonction de $N$ le nombre d'appels à votre fonction\n1. Déterminer par essai/erreur une fonction qui approche au mieux le tracé précédent","metadata":{}},{"cell_type":"code","source":"# votre code","metadata":{"trusted":true},"execution_count":427,"outputs":[]},{"cell_type":"markdown","source":"*** vos conclusions...","metadata":{"trusted":true}}]}