#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Thu Aug 22 11:33:54 2019 @author: adomps """ def trace_Chemin(C, couleur, legende) : ''' Trace un chemin C défini comme une liste de couples de coordonnées. couleur = 'black', ou 'blue', etc legende : chaîne de caractère associée à la courbe ''' plt.xlim(-1, 11) plt.ylim(-1, 11) plt.xticks([i for i in range(11)]) plt.yticks([i for i in range(11)]) plt.grid(b = True) X = [ P[0] for P in C] Y = [ P[1] for P in C] plt.plot(X, Y, color = couleur, label = legende) plt.legend() def dessine_point(P) : plt.plot([P[0]], [P[1]], marker = 'o', color = 'black') def dessine_liste_points(L) : for P in L : dessine_point(P) ## Exemples de points interdits K1 = [1, 3] K2 = [2, 6] K3 = [3, 4] K4 = [4, 6] K5 = [5, 6] K6 = [6, 2] K7 = [7, 8] K8 = [8, 1] K9 = [9, 3] # Exemple de liste de points interdits liste_trous = [K3, K7] # Exemples de chemins C_0 = [[0.0, 0.0], [0.18583042973286876, 0.1447661469933185], [0.3252032520325203, 0.334075723830735], [0.41811846689895477, 0.5122494432071268], [0.4994192799070849, 0.7015590200445435], [0.5691056910569106, 0.913140311804009], [0.6387921022067362, 1.1135857461024499], [0.7084785133565622, 1.3140311804008906], [0.8013937282229964, 1.5144766146993316], [0.9407665505226481, 1.7149220489977728], [1.1265969802555167, 1.8485523385300668], [1.3008130081300813, 1.915367483296214], [1.4866434378629498, 1.937639198218263], [1.6608594657375144, 1.9265033407572383], [1.8466898954703828, 1.915367483296214], [2.0209059233449476, 1.9042316258351895], [2.206736353077816, 1.9042316258351895], [2.380952380952381, 1.9265033407572383], [2.5667828106852495, 2.0044543429844097], [2.706155632984901, 2.1492204899777283], [2.7642276422764223, 2.32739420935412], [2.7642276422764223, 2.527839643652561], [2.7409988385598134, 2.7951002227171493], [2.787456445993031, 3.062360801781737], [2.8687572590011614, 3.2516703786191536], [2.9732868757258997, 3.44097995545657], [3.1126596980255514, 3.6302895322939865], [3.275261324041811, 3.808463251670379], [3.449477351916376, 3.975501113585746], [3.6236933797909407, 4.109131403118041], [3.8095238095238093, 4.198218262806236], [3.983739837398374, 4.242761692650333], [4.13472706155633, 4.164810690423163], [4.204413472706155, 4.031180400890869], [4.192799070847851, 3.8864142538975504], [4.169570267131243, 3.6971046770601337], [4.13472706155633, 3.4966592427616927], [4.088269454123113, 3.262806236080178], [4.088269454123113, 2.9844097995545655], [4.169570267131243, 2.7839643652561246], [4.320557491289199, 2.6391982182628064], [4.506387921022068, 2.5723830734966593], [4.680603948896631, 2.527839643652561], [4.866434378629499, 2.516703786191537], [5.052264808362368, 2.505567928730512], [5.2264808362369335, 2.494432071269488], [5.412311265969802, 2.494432071269488], [5.586527293844367, 2.494432071269488], [5.772357723577235, 2.494432071269488], [5.9465737514517985, 2.494432071269488], [6.1324041811846675, 2.472160356347439], [6.306620209059232, 2.438752783964365], [6.492450638792101, 2.371937639198218], [6.67828106852497, 2.293986636971047], [6.852497096399534, 2.1937639198218264], [7.038327526132404, 2.0712694877505564], [7.224157955865272, 1.948775055679287], [7.398373983739835, 1.8151447661469928], [7.584204413472705, 1.6926503340757237], [7.770034843205573, 1.5701559020044544], [7.944250871080139, 1.4587973273942094], [8.130081300813007, 1.3808463251670378], [8.315911730545874, 1.3140311804008906], [8.49012775842044, 1.269487750556793], [8.67595818815331, 1.2583518930957684], [8.850174216027876, 1.269487750556793], [9.036004645760743, 1.291759465478842], [9.210220673635305, 1.3363028953229399], [9.337979094076655, 1.414253897550111], [9.256678281068524, 1.5701559020044544], [9.117305458768872, 1.7371937639198218], [8.954703832752614, 1.9265033407572383], [8.826945412311265, 2.10467706013363], [8.710801393728222, 2.282850779510022], [8.617886178861788, 2.472160356347439], [8.524970963995354, 2.683741648106904], [8.49012775842044, 2.9844097995545655], [8.62950058072009, 3.2182628062360803], [8.803716608594655, 3.2739420935412022], [8.989547038327526, 3.285077951002227], [9.16376306620209, 3.2739420935412022], [9.349593495934958, 3.2516703786191536], [9.523809523809524, 3.2405345211581293], [9.709639953542393, 3.2405345211581293], [9.883855981416955, 3.3073496659242765], [9.988385598141694, 3.5189309576837418], [9.965156794425086, 3.7193763919821823], [9.825783972125436, 3.8864142538975504], [9.651567944250871, 3.98663697104677], [9.465737514518, 4.031180400890869], [9.279907084785133, 4.064587973273942], [9.105691056910569, 4.086859688195991], [8.919860627177698, 4.097995545657015], [8.75725900116144, 4.175946547884187], [8.919860627177698, 4.342984409799555], [9.094076655052262, 4.443207126948775], [9.245063879210221, 4.576837416481069], [9.140534262485483, 4.710467706013363], [8.966318234610917, 4.755011135857461], [8.780487804878048, 4.766146993318486], [8.606271777003483, 4.7772828507795095], [8.420441347270614, 4.788418708240535], [8.234610917537747, 4.799554565701558], [8.060394889663181, 4.810690423162583], [7.874564459930312, 4.832962138084632], [7.700348432055749, 4.866369710467706], [7.5145180023228795, 4.8997772828507795], [7.340301974448315, 4.9777282850779505], [7.154471544715446, 5.033407572383074], [6.968641114982577, 5.055679287305122], [6.794425087108013, 5.066815144766147], [6.608594657375143, 5.066815144766147], [6.43437862950058, 5.055679287305122], [6.248548199767712, 5.044543429844098], [6.074332171893147, 5.044543429844098], [5.888501742160278, 5.055679287305122], [5.7142857142857135, 5.10022271714922], [5.5284552845528445, 5.200445434298441], [5.365853658536583, 5.389755011135857], [5.284552845528455, 5.6236080178173715], [5.261324041811846, 5.924276169265034], [5.319396051103367, 6.191536748329621], [5.354239256678279, 6.3919821826280625], [5.389082462253194, 6.581291759465478], [5.354239256678279, 6.781737193763919], [5.2264808362369335, 6.948775055679287], [5.0406504065040645, 7.060133630289532], [4.8548199767711955, 7.1158129175946545], [4.680603948896631, 7.171492204899778], [4.494773519163762, 7.2271714922049], [4.320557491289199, 7.30512249443207], [4.13472706155633, 7.438752783964365], [3.983739837398374, 7.605790645879732], [3.890824622531939, 7.861915367483295], [3.9953542392566774, 8.140311804008908], [4.157955865272937, 8.307349665924274], [4.332171893147502, 8.452115812917596], [4.506387921022068, 8.552338530066816], [4.692218350754936, 8.61915367483296], [4.866434378629499, 8.663697104677059], [5.052264808362368, 8.68596881959911], [5.2264808362369335, 8.708240534521156], [5.412311265969802, 8.708240534521156], [5.586527293844367, 8.708240534521156], [5.772357723577235, 8.708240534521156], [5.9465737514517985, 8.68596881959911], [6.1324041811846675, 8.674832962138085], [6.306620209059232, 8.663697104677059], [6.492450638792101, 8.641425389755012], [6.666666666666666, 8.630289532293988], [6.852497096399534, 8.61915367483296], [7.038327526132404, 8.61915367483296], [7.2125435540069684, 8.608017817371937], [7.398373983739835, 8.596881959910913], [7.572590011614399, 8.608017817371937], [7.758420441347269, 8.630289532293988], [7.932636469221833, 8.697104677060132], [8.1068524970964, 8.830734966592429], [8.24622531939605, 9.00890868596882], [8.362369337979093, 9.187082405345212], [8.478513356562136, 9.365256124721602], [8.583042973286876, 9.543429844097995], [8.687572590011614, 9.743875278396436], [8.815331010452962, 9.955456570155903], [8.977932636469221, 10.066815144766146], [9.152148664343786, 10.055679287305123], [9.337979094076655, 10.022271714922049], [9.523809523809524, 9.966592427616925], [9.698025551684086, 9.922048997772828], [9.883855981416955, 9.977728285077951], [10.0, 10.0]] C_1 = [[0.0, 0.0], [0.18079096045197746, 0.14115092290988057], [0.3276836158192091, 0.31487513572204123], [0.44067796610169496, 0.499457111834962], [0.5310734463276837, 0.6948968512486429], [0.5875706214689267, 0.8577633007600435], [0.6327683615819208, 1.0532030401737245], [0.6779661016949153, 1.2703583061889252], [0.6892655367231638, 1.444082519001086], [0.711864406779661, 1.6612377850162865], [0.7231638418079097, 1.9652551574375683], [0.7457627118644069, 2.2801302931596092], [0.7796610169491526, 2.56243213897937], [0.8135593220338985, 2.768729641693812], [0.8700564971751414, 2.9750271444082523], [0.9378531073446327, 3.1704668838219328], [1.0395480225988702, 3.3659066232356136], [1.1977401129943506, 3.550488599348535], [1.378531073446328, 3.702497285559175], [1.5480225988700567, 3.8110749185667756], [1.7288135593220337, 3.908794788273616], [1.9096045197740112, 4.006514657980456], [2.07909604519774, 4.115092290988057], [2.2598870056497176, 4.212812160694898], [2.4293785310734464, 4.321389793702497], [2.610169491525424, 4.429967426710098], [2.790960451977401, 4.5494028230184576], [2.96045197740113, 4.668838219326819], [3.1412429378531073, 4.788273615635179], [3.310734463276836, 4.9185667752443], [3.4915254237288136, 5.070575461454941], [3.672316384180791, 5.2225841476655805], [3.84180790960452, 5.396308360477741], [4.011299435028249, 5.580890336590663], [4.169491525423728, 5.754614549402824], [4.305084745762711, 5.939196525515744], [4.429378531073447, 6.1237785016286646], [4.553672316384182, 6.308360477741585], [4.700564971751413, 6.482084690553746], [4.88135593220339, 6.634093376764387], [5.0508474576271185, 6.731813246471227], [5.231638418079096, 6.807817589576548], [5.4124293785310735, 6.872964169381108], [5.581920903954802, 6.916395222584147], [5.76271186440678, 6.948968512486427], [5.932203389830509, 6.981541802388708], [6.112994350282486, 7.0032573289902285], [6.2824858757062145, 7.035830618892509], [6.463276836158192, 7.057546145494029], [6.632768361581921, 7.10097719869707], [6.813559322033899, 7.133550488599348], [6.994350282485875, 7.187839305103148], [7.163841807909605, 7.25298588490771], [7.344632768361582, 7.339847991313789], [7.514124293785311, 7.4701411509229105], [7.68361581920904, 7.62214983713355], [7.807909604519773, 7.795874049945712], [7.909604519774011, 7.991313789359392], [7.988700564971752, 8.186753528773075], [8.067796610169491, 8.382193268186754], [8.169491525423728, 8.555917480998913], [8.293785310734464, 8.751357220412597], [8.429378531073446, 8.935939196525517], [8.587570621468927, 9.120521172638437], [8.768361581920903, 9.2942453854506], [8.937853107344633, 9.446254071661238], [9.11864406779661, 9.576547231270359], [9.29943502824859, 9.695982627578719], [9.468926553672318, 9.793702497285558], [9.649717514124292, 9.88056460369164], [9.819209039548022, 9.9457111834962], [10.0, 10.0]] C_2 = [[0.0, 0.0], [0.033259423503325974, 0.2069716775599128], [0.06651884700665195, 0.4030501089324619], [0.0997782705099778, 0.6427015250544663], [0.13303769401330376, 0.9150326797385622], [0.16629711751662973, 1.2091503267973853], [0.21064301552106426, 1.5250544662309369], [0.24390243902439024, 1.840958605664488], [0.2771618625277162, 2.10239651416122], [0.2993348115299335, 2.3529411764705883], [0.32150776053215085, 2.549019607843137], [0.34368070953436813, 2.75599128540305], [0.35476718403547663, 2.9629629629629632], [0.37694013303769397, 3.169934640522876], [0.41019955654101997, 3.3986928104575167], [0.46563192904656325, 3.6165577342047928], [0.5210643015521064, 3.8453159041394334], [0.565410199556541, 4.019607843137255], [0.6208425720620844, 4.226579520697168], [0.6873614190687363, 4.433551198257081], [0.7538802660753879, 4.640522875816993], [0.8203991130820399, 4.847494553376905], [0.8758314855875833, 5.043572984749456], [0.9423503325942351, 5.250544662309369], [1.0199556541019956, 5.468409586056644], [1.0864745011086476, 5.675381263616559], [1.1419068736141909, 5.893246187363835], [1.1862527716186255, 6.111111111111111], [1.2305986696230602, 6.339869281045752], [1.2638580931263856, 6.601307189542485], [1.3082039911308203, 6.862745098039217], [1.352549889135255, 7.058823529411766], [1.4301552106430155, 7.276688453159041], [1.5188470066518849, 7.47276688453159], [1.629711751662971, 7.657952069716775], [1.7516629711751666, 7.843137254901961], [1.9179600886917962, 8.039215686274511], [2.0842572062084255, 8.213507625272332], [2.261640798226164, 8.366013071895425], [2.4390243902439024, 8.507625272331156], [2.6164079822616406, 8.627450980392158], [2.7827050997782705, 8.72549019607843], [2.9600886917960088, 8.823529411764707], [3.1374722838137474, 8.910675381263616], [3.3037694013303773, 8.986928104575163], [3.4811529933481156, 9.063180827886711], [3.658536585365854, 9.128540305010894], [3.8248337028824837, 9.193899782135077], [4.002217294900222, 9.248366013071896], [4.17960088691796, 9.302832244008716], [4.3458980044345905, 9.34640522875817], [4.523281596452328, 9.40087145969499], [4.689578713968959, 9.444444444444445], [4.866962305986696, 9.477124183006538], [5.044345898004435, 9.520697167755992], [5.210643015521065, 9.542483660130719], [5.388026607538803, 9.575163398692812], [5.554323725055432, 9.59694989106754], [5.731707317073171, 9.607843137254903], [5.909090909090909, 9.62962962962963], [6.0753880266075395, 9.640522875816993], [6.252771618625277, 9.62962962962963], [6.419068736141907, 9.62962962962963], [6.596452328159645, 9.62962962962963], [6.762749445676275, 9.618736383442267], [6.940133037694013, 9.59694989106754], [7.106430155210643, 9.564270152505449], [7.283813747228382, 9.531590413943356], [7.450110864745012, 9.50980392156863], [7.62749445676275, 9.498910675381264], [7.793791574279379, 9.498910675381264], [7.971175166297119, 9.498910675381264], [8.137472283813748, 9.520697167755992], [8.314855875831485, 9.542483660130719], [8.492239467849224, 9.564270152505449], [8.658536585365855, 9.607843137254903], [8.835920177383592, 9.651416122004358], [9.002217294900221, 9.694989106753813], [9.17960088691796, 9.738562091503269], [9.356984478935697, 9.793028322440088], [9.52328159645233, 9.847494553376908], [9.700665188470067, 9.901960784313726], [9.878048780487804, 9.956427015250545], [10.0, 10.0]] C_3 = [[0.0, 0.0], [0.175054704595186, 0.0335946248600223], [0.35010940919037203, 0.1343784994400896], [0.5032822757111599, 0.29115341545352746], [0.6345733041575494, 0.4703247480403135], [0.7439824945295405, 0.6718924972004477], [0.8424507658643328, 0.8734602463605824], [0.940919037199125, 1.0750279955207167], [1.061269146608315, 1.265397536394177], [1.2144420131291032, 1.433370660694289], [1.389496717724289, 1.5229563269876818], [1.5536105032822758, 1.5453527435610301], [1.728665207877462, 1.5565509518477043], [1.8927789934354489, 1.5565509518477043], [2.067833698030635, 1.5453527435610301], [2.2319474835886215, 1.534154535274356], [2.407002188183808, 1.5117581187010076], [2.5711159737417946, 1.4893617021276597], [2.746170678336981, 1.4557670772676372], [2.9102844638949676, 1.433370660694289], [3.0853391684901537, 1.3885778275475924], [3.2494529540481407, 1.3549832026875699], [3.4245076586433263, 1.3101903695408734], [3.588621444201314, 1.276595744680851], [3.7636761487964994, 1.2318029115341544], [3.927789934354486, 1.1870100783874582], [4.091903719912474, 1.1422172452407615], [4.266958424507659, 1.1086226203807392], [4.431072210065646, 1.0750279955207167], [4.606126914660832, 1.0638297872340425], [4.770240700218819, 1.097424412094065], [4.945295404814005, 1.1422172452407615], [5.12035010940919, 1.2541993281075028], [5.273522975929979, 1.4109742441209407], [5.382932166301971, 1.6013437849944008], [5.4376367614879655, 1.769316909294513], [5.4376367614879655, 1.9820828667413213], [5.404814004376369, 2.161254199328108], [5.339168490153173, 2.3516237402015676], [5.229759299781183, 2.530795072788354], [5.0875273522975935, 2.687569988801792], [4.923413566739606, 2.8219484882418815], [4.75929978118162, 2.9227323628219484], [4.595185995623633, 3.0123180291153413], [4.420131291028447, 3.0795072788353863], [4.25601750547046, 3.135498320268757], 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[9.171210468920393, 7.774193548387096], [9.323882224645583, 7.956989247311827], [9.476553980370774, 8.139784946236558], [9.59651035986914, 8.33333333333333], [9.672846237731736, 8.526881720430104], [9.716466739367503, 8.806451612903226], [9.70556161395856, 8.989247311827958], [9.738276990185387, 9.1505376344086], [9.760087241003273, 9.451612903225806], [9.803707742639041, 9.677419354838708], [9.90185387131952, 9.89247311827957], [10.0, 10.0]] C_6 = [[0.0, 0.0], [0.17601760176017606, 0.03374578177727775], [0.3520352035203521, 0.1012373453318335], [0.517051705170517, 0.202474690663667], [0.6930693069306931, 0.34870641169853767], [0.8470847084708472, 0.5174353205849269], [0.9680968096809682, 0.7086614173228346], [1.067106710671067, 0.8998875140607425], [1.155115511551155, 1.1136107986501689], [1.2211221122112212, 1.327334083239595], [1.2541254125412544, 1.529808773903262], [1.2761276127612762, 1.7322834645669292], [1.2761276127612762, 1.9910011248593928], [1.2651265126512652, 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3.206521739130435], [3.6279069767441867, 3.402173913043478], [3.3953488372093026, 3.5326086956521743], [3.116279069767442, 3.6413043478260874], [2.8255813953488373, 3.6847826086956523], [2.5697674418604652, 3.6847826086956523], [2.302325581395349, 3.7173913043478266], [1.9651162790697674, 3.739130434782609], [1.6744186046511627, 3.804347826086957], [1.4767441860465116, 3.9021739130434785], [1.313953488372093, 4.130434782608696], [1.2790697674418605, 4.391304347826087], [1.5581395348837208, 4.532608695652175], [1.8023255813953494, 4.641304347826087], [2.058139534883721, 4.771739130434783], [2.3953488372093026, 4.923913043478262], [2.674418604651163, 5.086956521739131], [2.965116279069768, 5.25], [3.2209302325581395, 5.380434782608696], [3.476744186046512, 5.554347826086957], [3.686046511627907, 5.717391304347826], [3.9534883720930236, 5.880434782608696], [4.151162790697674, 6.065217391304348], [4.313953488372094, 6.282608695652175], [4.523255813953488, 6.500000000000001], [4.674418604651162, 6.750000000000001], [4.767441860465117, 7.010869565217392], [4.848837209302326, 7.260869565217392], [4.906976744186046, 7.543478260869566], [4.906976744186046, 7.891304347826087], [4.825581395348837, 8.16304347826087], [4.767441860465117, 8.413043478260871], [4.616279069767442, 8.695652173913045], [4.395348837209302, 8.836956521739133], [4.104651162790698, 9.01086956521739], [3.8488372093023258, 9.08695652173913], [3.6279069767441867, 9.130434782608697], [3.3953488372093026, 9.184782608695652], [3.0930232558139537, 9.25], [2.779069767441861, 9.26086956521739], [2.4883720930232562, 9.23913043478261], [2.244186046511628, 9.17391304347826], [2.081395348837209, 9.032608695652176], [2.0697674418604657, 8.73913043478261], [2.2093023255813953, 8.434782608695652], [2.453488372093023, 8.17391304347826], [2.6279069767441863, 7.902173913043478], [2.8372093023255816, 7.75], [3.0348837209302326, 7.641304347826087], [3.1860465116279073, 7.478260869565218], [3.406976744186047, 7.336956521739131], [3.674418604651163, 7.163043478260871], [3.976744186046512, 6.967391304347826], [4.290697674418604, 6.815217391304348], [4.8604651162790695, 6.608695652173913], [5.151162790697675, 6.532608695652174], [5.441860465116279, 6.4565217391304355], [5.767441860465117, 6.380434782608696], [6.093023255813953, 6.347826086956522], [6.441860465116279, 6.336956521739131], [6.790697674418605, 6.369565217391305], [7.151162790697674, 6.423913043478262], [7.488372093023255, 6.500000000000001], [7.790697674418605, 6.630434782608696], [8.023255813953488, 6.793478260869565], [8.313953488372093, 6.989130434782609], [8.430232558139535, 7.271739130434784], [8.651162790697674, 7.565217391304348], [8.80232558139535, 7.91304347826087], [8.906976744186046, 8.271739130434783], [8.988372093023257, 8.521739130434783], [9.08139534883721, 8.880434782608697], [9.19767441860465, 9.17391304347826], [9.325581395348836, 9.434782608695652], [9.5, 9.684782608695652], [9.709302325581396, 9.869565217391305], [10.0, 10.0]] Ensemble_de_chemins = [C_0, C_1, C_2, C_3, C_4, C_5, C_6, C_7, C_8, C_9, C_10, C_11, C_12, C_13, C_14, C_15, C_16]