.. _graph1exoparcourscorrectionrst: ========================================= 1A.algo - Parcours de graphe - correction ========================================= .. only:: html **Links:** :download:`notebook `, :downloadlink:`html `, :download:`python `, :downloadlink:`slides `, :githublink:`GitHub|_doc/notebooks/td1a_algo/graph1exo_parcours_correction.ipynb|*` Algorithme assez simple sur les graphes (correction). .. code:: ipython3 from jyquickhelper import add_notebook_menu add_notebook_menu() .. contents:: :local: .. code:: ipython3 # tutoriel_graphe noeuds = {0: 'le', 1: 'silences', 2: 'quelques', 3: '\xe9crit', 4: 'non-dits.', 5: 'Et', 6: 'risque', 7: '\xe0', 8: "qu'elle,", 9: 'parfois', 10: 'aim\xe9', 11: 'lorsque', 12: 'que', 13: 'plus', 14: 'les', 15: 'Minelli,', 16: "n'oublierai", 17: 'je', 18: 'prises', 19: 'sa', 20: 'la', 21: 'jeune,', 22: "qu'elle,", 23: '\xe0', 24: 'ont', 25: "j'ai", 26: 'chemin', 27: '\xe9tranger', 28: 'lente', 29: 'de', 30: 'voir', 31: 'quand', 32: 'la', 33: 'recul,', 34: 'de', 35: 'trop', 36: 'ce', 37: 'Je', 38: 'Il', 39: "l'extr\xeame", 40: "J'ai", 41: 'silences,', 42: "qu'elle,", 43: 'le', 44: 'trace,', 45: 'avec', 46: 'seras', 47: 'dire,', 48: 'femme', 49: 'soit'} arcs = {(3, 15): None, (46, 47): None, (42, 33): None, (35, 45): None, (1, 14): None, (22, 26): None, (26, 28): None, (43, 29): None, (40, 41): None, (29, 44): None, (17, 3): None, (32, 37): None, (24, 19): None, (46, 34): None, (11, 19): None, (34, 49): None, (22, 2): None, (37, 48): None, (14, 12): None, (3, 10): None, (5, 18): None, (12, 24): None, (34, 32): None, (45, 39): None, (37, 26): None, (33, 45): None, (34, 47): None, (36, 31): None, (29, 47): None, (13, 11): None, (12, 21): None, (2, 16): None, (5, 4): None, (33, 35): None, (28, 49): None, (25, 49): None, (21, 0): None, (3, 13): None, (18, 24): None, (12, 7): None, (13, 15): None, (11, 1): None, (16, 23): None, (37, 45): None, (27, 32): None, (32, 41): None, (8, 24): None, (10, 1): None, (2, 24): None, (24, 11): None, (2, 14): None, (47, 36): None, (48, 39): None, (30, 25): None, (30, 43): None, (15, 14): None, (26, 27): None, (6, 8): None, (20, 10): None, (19, 17): None, (5, 7): None, (44, 25): None, (27, 38): None, (2, 0): None, (3, 18): None, (3, 9): None, (25, 33): None, (42, 48): None, (2, 15): None, (26, 48): None, (26, 38): None, (7, 8): None, (8, 4): None} points = [(0.84737386691659533, 0.95848816613228727), (0.28893525107454354, 0.66073249195336492), (0.60382037086559148, 0.13747945088383384), (0.21951613156582261, 0.040905525433785228), (0.21613062123493632, 0.096875623632852625), (0.99787588721497178, 0.79337171783327132), (0.18576957348508683, 0.78396225027633837), (0.23875443625588322, 0.35497638429086975), (0.8713637939628045, 0.22983756618811024), (0.28301724069085921, 0.99408996134013161), (0.39792684083973429, 0.77105362865540716), (0.75452041353842147, 0.330325155167562), (0.24824845436118537, 0.95998690078041737), (0.92318434139996397, 0.38115765401571988), (0.54660304309415886, 0.62093667623480242), (0.58899996464290505, 0.9017292023892568), (0.60541336358687847, 0.28929082523865812), (0.87925379747840293, 0.94834058131858756), (0.61449632813730748, 0.94264237081849722), (0.13119804743502139, 0.44158556198130949), (0.20660796942108339, 0.915599021810789), (0.3097131996826511, 0.81979953110332837), (0.89711055197298928, 0.7298496710091944), (0.22499060312661545, 0.072786594549671291), (0.012604758185058018, 0.36199484670070914), (0.92050750708863993, 0.91447248587261709), (0.26304069827339327, 0.026058147250910935), (0.59289937178711172, 0.86673111722782969), (0.70640070176443837, 0.64096733852134291), (0.049399266565914535, 0.54027723332288746), (0.26450585597978316, 0.50883097182669357), (0.91987410679455195, 0.97753050553942622), (0.5618293073273094, 0.27688371997865069), (0.91241761244784847, 0.090310675429991605), (0.90925789663628509, 0.40628594240956295), (0.3832814495252409, 0.66221025722485627), (0.74928785967005418, 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-3.5339867923196042), (-3.0906912982614791, -3.8390710019489158), (0.77019164393866146, 4.0099320163703895), (-3.2239134319849398, 2.5227757084315567), (-2.5342615497190861, -4.5402720724503229), (0.52313297572359074, 5.8268409663350287), (-2.0896974241486603, -0.83931337455192145), (5.9824769771009292, 1.8062615072223389), (-1.7151819974072808, -4.6553638508191835), (-0.94296691141453703, -4.3332773280899097), (-2.9080659785364102, 3.8017876981653527), (-4.146797854411842, -2.4943345068020939), (-1.6135304662636716, -4.5968234340599352), (-5.2240732422979015, -0.40050907128273239), (3.0003615064702411, 4.3564534485947091), (1.5251603471425388, 5.3602495377614252), (0.70829180528117897, 4.8705912438690024), (-1.9857439387875215, 4.3495410597763557), (-1.7415118623160484, -2.8482449535792851), (3.1227029816875906, -3.943690794192229), (2.5533372938495322, 0.23654193364300019), (4.9320538122814632, 0.27398085527961841), (3.5379571426787906, 3.5479478416595258), (-3.9952197756192462, 0.9519866242123729), (-0.63418929807710789, 4.9714021509147459), (3.7514419719026835, -3.7952656655539831), (5.8168652955867248, -5.8059389896821614), (-3.86083201462211, 1.6763339473293351), (5.2346287443442741, -2.0049022214331869), (3.0159172780756807, -4.6747832401686313), (1.9625789720275502, 0.21332969214064601), (-5.4459656516053521, 1.8490131071943328), (5.4887755131556295, 1.0537691340713213), (4.1214658457920255, 1.8180419262808878), (1.0417225435808637, 6.4876076903545457), (5.2056831059665383, 3.4403227294912879), (-3.29183542445509, 1.1299087065549616), (-4.6894950904308068, 0.67877427899602139), (-4.2334935303450196, 0.66692066781151726), (6.918359229911677, -0.43825691963852248), (5.0912552685819197, 5.9256467457380193), (3.9995400634925016, -4.2633779062253305), (-1.3270510253578853, -2.8998811026998816), (-3.4372749748248483, -2.800876689538256), (2.5720483206059228, -4.5479241832525954), (3.5107697954439923, -5.6063323885377114), (3.45355690226015, 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-4.6992062016898437), (3.6218017958370492, 2.4171784152426357), (2.1893570148164336, -0.53987360896641756), (-0.62289304323418893, 5.6377915319211773), (0.95656595366184183, -3.5482370903224183), (4.6552715153624238, -0.42419842122106877), (3.9138981541477369, 1.5211086418661788), (-5.7643908686171743, 3.3462875243179644), (4.4001664954474204, 1.8715548148469952), (3.7209034976257116, -4.3132712976844925), (2.0077653108424371, -3.8044349295045858), (-2.7004396541700451, 3.6313151291578776), (2.7805282578575432, -1.3496033840422226), (2.5149407509344646, -4.4491799573779538), (-3.4969549443875327, 0.59052341158001964), (2.5871839418980924, -2.8626995345211439), (4.530084220131168, 0.73947783901217035), (-4.2278934560638541, -1.4480933790189707), (-3.6638968948801822, -1.8603129450393652), (1.0034748779660814, 4.3783603559660618), (-0.24711046251746965, 5.0245225170472958), (-0.75233017871629115, -3.4003624728787472), (-5.3204808270534789, 0.8530050107548528), (-0.66555456366565435, -3.210607962975542), (4.4312598575388913, -1.8510534338146063), (-1.0579141292803367, -3.8599892658343156), (5.1580465239922022, -1.6376354853614972), (-2.6525127599513731, 2.9406618825179196), (3.3353268107001339, 4.5193520805659642), (4.9838132614191322, -4.5937246171656669)] .. code:: ipython3 from mlstatpy.graph.graphviz_helper import draw_graph_graphviz draw_graph_graphviz(noeuds, arcs, "image.png") from IPython.display import Image Image("image.png", width=400) .. image:: graph1exo_parcours_correction_3_0.png :width: 400px .. code:: ipython3 class MonGraphe : def __init__ (self, num, valeur): self.valeur = valeur self.num = num self.arcs = [] # liste d’éléments MonGraphe Q1 -- .. code:: ipython3 def ConstruireMonGraphe(noeuds, arcs) : nodes = {} for i,v in noeuds.items(): nodes [i] = MonGraphe(i,v) for k in arcs: i,j = k nodes[i].arcs.append(nodes[j]) nodes[j].arcs.append(nodes[i]) return nodes[0] .. code:: ipython3 ConstruireMonGraphe(noeuds, arcs) .. parsed-literal:: <__main__.MonGraphe at 0x180b6285518> Q2 -- La fonction est récursive, elle parcourt le graphe en profondeur et peut repasser plusieurs fois par le même noeud. .. code:: ipython3 # déclenche une exception class MonGraphe: def __init__ (self, num, valeur): self.valeur = valeur self.num = num self.arcs = [] # liste d’éléments MonGraphe self.passage = 0 def NombreTotalNoeud(self): self.passage += 1 if self.passage > 3: if self.passage == 10: print("Trop de passages, on s'arrête.") self.passage += 1 return 0 else: r = 1 for a in self.arcs: r += a.NombreTotalNoeud() return r g = ConstruireMonGraphe(noeuds, arcs) g.NombreTotalNoeud() .. parsed-literal:: Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. Trop de passages, on s'arrête. .. parsed-literal:: 150 Q3 -- La fonction retourne le bon résultat pour les graphes orientés et acyclique. C’est la seule façon de ne jamais repasser deux fois par le même noeud. Q4 -- Version non récursive. .. code:: ipython3 def NombreArcsRecursive (r, edges=None, done=None): if edges is None: edges = {} if done is None: done = {} if r.num in done: return 0 done[r.num] = None for node in r.arcs: edges[r.num, node.num] = None NombreArcsRecursive(node, edges, done) final = { } for k in arcs: i,j = k if i != j and (j,i) not in final: final[i,j] = None return len(final) g = ConstruireMonGraphe(noeuds, arcs) NombreArcsRecursive(g) .. parsed-literal:: 73 Version non récursive .. code:: ipython3 def NombreArcs(racine) : edges = {} pile = [ ] done = { } pile.append (racine) while len(pile) > 0 : r = pile.pop () if r.num in done : continue done [r.num] = None for node in r.arcs : if node.num in done : continue edges [ r.num, node.num ] = None pile.append (node) final = { } for k in arcs : i,j = k if i != j and (j,i) not in final: final [i,j] = None return len(final) g = ConstruireMonGraphe(noeuds, arcs) NombreArcs(g) .. parsed-literal:: 73