Professeur_deborde_corrige.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Professeur deborde corrige.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOelqGA7IdzGaB+USq5wluS",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/GeoLabUniLaSalle/Python/blob/main/Professeur_deborde_corrige.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R8kQ2CJh9aDY"
      },
      "source": [
        "## **Professeur débordé ★★★**\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "*Exercice disponible sur la plateforme TOSA : Battle Dev Hello Works - Novembre 2018 : https://www.isograd.com/FR/solutionconcours.php*\n",
        "\n",
        "\n",
        "\n",
        "**Enoncé**\n",
        "\n",
        "\n",
        "Vos élèves sont énervés, ils vous accusent d'annuler des cours en permanence et vous accablent de mauvais commentaires sur internet. Vous allez devoir arrêter d'accepter des étudiants si vous ne pouvez pas donner cours à chacun d'entre eux individuellement. Comme pour l'exercice précédent, tous les étudiants vous donnent deux créneaux de 60 minutes et vous devez leur donner cours sur l'un des deux créneaux. Cette fois-ci, tout ce qui vous intéresse c'est de savoir s'il vous est possible de donner cours à tout le monde et le cas échéant sur quels créneaux.\n",
        "\n",
        "Attention : le nombre d'étudiants est beaucoup plus grand que dans l'exercice précédent, votre solution doit s'exécuter en temps polynomial.\n",
        "\n",
        "**Format des données**\n",
        "\n",
        "*Entrée*\n",
        "\n",
        "\n",
        "\n",
        "Ligne 1 : un entier N entre 3 et 1000 inclus, le nombre d'étudiants.\n",
        "\n",
        "Lignes 2 à N+1 : deux entiers entre 0 et 300.000, les deux débuts de créneaux (en minutes) auxquels un étudiant est disponible, chaque créneau a une durée de 60 minutes à partir des débuts indiqués (vos journées sont très longues).\n",
        "\n",
        "\n",
        "\n",
        "*Sortie*\n",
        "\n",
        "Vous afficherez simplement KO s'il est impossible de donner cours à tout le monde.\n",
        "S'il est possible de donner cours à tout le monde, vous indiquerez, pour chaque étudiant, sur quel créneau vous lui donnerez cours 1 ou 2 dans le même ordre qu'en entrée (on acceptera toutes les solutions possibles). Vous pouvez séparer les étudiant par des sauts de lignes.\n",
        "\n",
        "*Exemple*\n",
        "\n",
        "Pour l'entrée suivante :\n",
        "\n",
        "5\n",
        "\n",
        "205 300\n",
        "\n",
        "210 370\n",
        "\n",
        "290 380\n",
        "\n",
        "120 305\n",
        "\n",
        "390 110\n",
        "\n",
        "La réponse attendue est KO, quel que soit le créneau choisi pour chaque étudiant, il y aura toujours deux créneaux qui se chevauchent.\n",
        "\n",
        "Pour l'entrée suivante :\n",
        "\n",
        "4\n",
        "\n",
        "205 300\n",
        "\n",
        "210 370\n",
        "\n",
        "290 380\n",
        "\n",
        "120 305\n",
        "\n",
        "Il est possible de donner cours à tous :\n",
        "- L'étudiant 1 sur son premier créneau de 205 à 265\n",
        "- L'étudiant 2 sur son second créneau de 370 à 430\n",
        "- L'étudiant 3 sur son premier créneau de 290 à 350\n",
        "- L'étudiant 4 sur son premier créneau de 120 à 180\n",
        "\n",
        "La réponse attendue pour ces 4 étudiants est donc :\n",
        "\n",
        "1\n",
        "\n",
        "2\n",
        "\n",
        "1\n",
        "\n",
        "1"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LaFrvPhE-Ezb"
      },
      "source": [
        "## **Données**\n",
        "\n",
        "*Accès aux données*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2HlpCu_r-aqr",
        "outputId": "04c12672-a529-440c-894a-cd4dc8107e02"
      },
      "source": [
        "import csv\n",
        "filedir = ('https://cours.unilasalle.fr/courses/SG4007/document/Exercices_Python/Professeur_deborde/')\n",
        "\n",
        "import ssl\n",
        "ssl._create_default_https_context = ssl._create_unverified_context\n",
        "\n",
        "import urllib.request\n",
        "\n",
        "for x in range(1,6):\n",
        "  f = urllib.request.urlopen(str(filedir+\"input\"+str(x)+\".txt\"))\n",
        "\n",
        "  data=[]\n",
        "  for i in f:\n",
        "      line=i.decode('utf-8').strip()\n",
        "      data.append(line)\n",
        "  print('Entrée',x,':',data)\n",
        "\n",
        "  f = urllib.request.urlopen(str(filedir+\"output\"+str(x)+\".txt\"))\n",
        "  for i in f:\n",
        "      line=i.decode('utf-8').strip()\n",
        "  print('Sortie',x,':',line,'\\n')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Entrée 1 : ['5', '205 300', '210 370', '290 380', '120 305', '390 110']\n",
            "Sortie 1 : KO \n",
            "\n",
            "Entrée 2 : ['4', '205 300', '210 370', '290 380', '120 305']\n",
            "Sortie 2 : 1 \n",
            "\n",
            "Entrée 3 : ['100', '6969 338', '15605 16525', '10281 6820', '11985 8172', '14092 2699', '7839 9936', '1071 19114', '7185 7483', '1953 1276', '333 10936', '2542 4268', '15370 7340', '786 4676', '8588 6208', '4094 19444', '6722 304', '18946 1884', '9402 3953', '18409 1935', '19347 9852', '6361 15662', '18686 1857', '12526 1460', '12225 3501', '10193 2684', '19446 1696', '1926 3070', '17162 15106', '2841 15895', '5817 18251', '12995 12861', '12991 1781', '13202 9798', '4168 1532', '2365 12525', '11410 8157', '13934 14575', '18067 1109', '10711 1510', '12333 16987', '18835 10340', '7282 15732', '16072 2946', '17202 18089', '9639 15388', '10506 8631', '2301 988', '7003 1871', '13193 18217', '13316 2262', '17065 15612', '6016 8301', '13230 5075', '5056 15330', '4954 11005', '2888 3825', '11278 15577', '5057 17589', '9323 12519', '17090 17052', '10506 11505', '1265 3229', '8880 4149', '14455 16961', '3033 19231', '4928 9934', '13138 18725', '4354 11931', '17243 16553', '8286 12792', '14378 19286', '19367 15461', '17727 10443', '8039 550', '14046 14354', '19206 18512', '111 13864', '14084 8582', '19416 8482', '16459 5745', '10433 9354', '4482 12920', '2207 7320', '3513 8480', '10196 6938', '3687 258', '3006 17418', '3318 19042', '4937 1864', '8665 7156', '377 1712', '1737 4833', '6509 8474', '14928 9404', '15744 19080', '10777 10027', '6096 9997', '9090 6039', '17698 18021', '11963 10244']\n",
            "Sortie 3 : 1 \n",
            "\n",
            "Entrée 4 : ['1000', '55511 160483', '64343 90479', '24119 67860', '206539 21448', '18455 71921', '62681 96411', '180983 184803', '214187 119970', '61124 68220', '48938 114883', '109713 154600', '164603 216012', '99081 130007', '124032 32395', '114987 24211', '50470 203445', '50417 151834', '86422 54914', '47717 143081', '28573 150643', '151718 75394', '151132 66426', '122981 110834', '84734 170473', '32170 150380', '178661 84045', '191358 117763', '51969 52684', '24156 149515', '146641 103096', '131159 198221', '54002 100116', '67655 114234', '48332 60111', '169648 84408', '146984 189621', '18313 212569', '35410 53192', '57546 73972', '15396 9908', '152904 184031', '210876 172565', '158798 122697', '25813 6506', '208028 26994', '103764 191287', '185690 177401', '87758 38045', '56446 194903', '103769 150423', '101979 34706', '19053 10303', '155229 149031', '33991 33713', '63605 86337', '125782 3071', '12858 193066', '20148 91277', '213431 9044', '216270 138158', '202417 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204730', '191133 85136', '207208 206354', '126028 96022', '73407 21535', '144485 68215', '87778 122853', '166064 178641', '211024 141074', '113895 23012', '45429 166309', '37438 144312', '188373 212535', '101069 69133', '103296 61022', '19294 26916', '83227 134486', '139019 1088', '17770 200489', '216760 154491', '25231 216978', '151056 126289', '171736 108109', '188685 21769', '110838 106769', '200040 33837', '67287 185045', '9686 124333', '103503 194428', '142444 6279', '104232 117489', '65919 75560', '172732 148346', '202779 60976', '157654 196849', '4843 34556', '164856 84294', '153398 38024', '118092 27909', '195392 117569', '196140 25890', '72261 169516', '209391 185315', '55088 117194', '73925 79016', '49517 86394', '88703 199114', '92017 19422', '130720 39879', '186939 215829', '67400 190219', '28357 112940', '10238 118407', '40368 135532', '71879 84856', '126075 70084', '21775 155013', '23284 213644', '100447 103470', '201974 80839', '16959 38246', '170997 157753', '131517 214482', '158449 13865', '76384 67771', '163291 121025', '128289 184147', '51101 70626', '88347 114482', '86799 214951', '171038 189281', '87130 160069', '36579 61293', '159095 106601', '189129 31002', '31055 205561', '167035 9795', '104618 44004', '216601 16056', '156038 70851', '182897 187955', '44746 169678', '192934 146909', '98885 164294', '85435 128649', '66156 28583', '142414 164049', '170884 217697', '95361 87288', '68907 97529', '158301 120204', '51937 18479', '204971 195881', '23165 55544', '102046 105983', '20860 134605', '176932 107978', '113334 20164', '137520 144310', '32768 17122', '35464 67413', '165963 33662', '16018 191549', '129802 28757', '8155 18144', '174437 188605', '199840 48715', '114788 62157', '186450 173848', '82887 203896', '107515 14365', '166578 82750', '76068 207568', '136121 69246', '83937 181377', '70438 204483', '116193 66058', '49374 49579', '92799 209345', '194595 16732', '67872 14986', '23118 48910', '61322 104937', '32582 113910', '63971 167780', '98303 104676', '205555 43119', '185041 183072', '52875 2483', '186159 46982', '70531 47437', '217069 195484', '49887 130547', '189243 55867', '96656 45381', '77713 33710', '39686 19811', '73541 114684', '203178 145717', '154300 7822', '156960 123338', '78290 70790', '118474 97040', '204617 108484', '79887 129370', '99161 109909', '195779 13119', '69664 64056', '99309 34251', '80848 215021', '26262 181513', '4093 197323', '128404 123457', '212719 164343', '77732 95175', '92349 210874', '23819 1080', '15689 30488', '49193 4720', '154207 5138', '116220 35873', '214066 78722', '27363 60695', '173478 65046', '116605 125979', '105497 141056', '143694 69074', '166781 175578', '150951 17086', '89552 11014', '186651 69658', '88872 116286', '45795 170002', '95938 171513', '58408 8337', '180346 210776', '171218 214442', '37773 148390', '161755 16535', '214636 145174', '104897 174486', '209558 46078', '86127 138405', '5697 211996', '204422 35582', '134467 16393', '191984 173599', '146682 97101', '24475 148353', '173152 2563', '44737 128289', '131030 23825', '194941 14707', '127152 119151', '92722 58197', '200283 76166', '16254 165860', '118705 106677', '41374 25204', '195200 79418', '88331 212067', '162502 138889', '118956 212341', '106761 33872', '213433 40823', '209335 91262', '66894 14467', '80006 161222', '134289 141936', '85289 130388', '125685 202108', '177374 195992', '13034 143932', '158064 93841', '217414 42114', '72316 11347', '155935 71070', '75016 61250', '173527 212314', '166294 69982', '153905 168046', '41252 194607', '83831 36870', '194800 173439', '52059 175834', '148392 145924', '50567 49627', '40913 208999', '11904 53135', '59557 158315', '77608 67618', '209211 27120', '179537 30923', '26431 93488', '164327 146484', '66708 47260', '146882 21600', '38032 65364', '22773 146518', '52883 50991', '87687 170', '4647 8428', '21681 169622', '106044 168215', '58195 150333', '48272 46722', '186071 165763', '129664 134906', '154899 200972', '68651 126956', '151601 172981', '73681 213366', '66537 60634', '206779 23683', '119622 83958']\n",
            "Sortie 4 : KO \n",
            "\n",
            "Entrée 5 : ['1000', '154303 183783', '200935 2254', '208280 116743', '30779 186454', '51939 200210', '84884 179581', '101871 27515', '163109 48047', '56362 22450', '55680 206807', '41925 11636', '17020 11211', '118700 96291', '85042 79308', '121729 1567', '99864 95602', '35247 185125', '117878 70913', '164527 100828', '111594 78390', '148044 117029', '9589 118331', '179107 200681', '204413 106921', '128675 157252', '10396 183927', '53528 80461', '144350 165739', '191406 210421', '17641 140588', '45508 928', '30938 97817', '124346 127700', '65388 42045', '143844 110737', '108609 14911', '80840 4277', '174496 146275', '133911 132092', '60039 2094', '207295 50661', '75080 93635', '85415 28524', '39277 82472', '37358 59329', '203753 63132', '123735 153893', '9031 41706', '103678 76875', '64387 167074', '42000 4881', '136822 26320', '175105 93858', '173186 49598', '107551 177049', '122106 22880', '18347 130385', '93564 62161', '85235 100075', '65715 133527', '115001 150079', '144938 71632', '31432 96643', '9700 84129', '88819 66611', '120889 189678', '28004 126195', '52781 116568', '208405 106515', '149510 151554', '53011 153877', '3166 191537', '178786 27780', '96743 101026', '70845 140496', '168508 155910', '196441 114799', '18762 182797', '135175 199911', '203293 25935', '8287 207284', '38916 183498', '33014 86759', '15448 15268', '48693 17686', '213879 78880', '112329 131911', '40253 181837', '214768 132272', '143275 122115', '209091 164605', '60402 170962', '57514 41201', '216165 28771', '149128 176697', '202701 73130', '9624 22582', '51778 190029', '10687 122625', '124776 22386', '27690 186229', '155170 113926', '133231 100204', '29691 111498', '73868 117898', '200728 65323', '161887 113843', '81632 193735', '113025 60916', '144379 99435', '122567 110636', '156361 97353', '173426 72691', '177366 31709', '116148 1931', '7624 47263', '133047 40959', '75202 99107', '43032 102592', '174895 75628', '86040 71053', '49438 80708', '216981 10553', '38042 195573', '158491 217254', '55110 4584', '72214 148209', '202277 141504', '87287 80173', '178749 62267', '116991 9336', '173739 195693', '102190 201925', '71266 159032', '203905 99930', '25784 207614', '35764 206586', '145196 172117', '52029 193700', '171312 199615', '67626 125411', '215261 100749', '168813 36936', '191649 87891', '75553 57152', '57535 19732', '117200 129851', '216145 115667', '65085 194171', '215734 32062', '56033 11395', '112573 95592', '131885 102550', '180549 39030', '190751 21206', '72914 172062', '78256 5886', '193092 124143', '128770 151905', '200179 29459', '33799 45632', '208135 198490', '19583 6116', '109669 139958', '88174 120744', '181180 89999', '187785 169601', '73028 39164', '97453 9755', '104933 195607', '177415 121213', '47977 101233', '35931 75295', '203708 146433', '46189 152989', '4119 135304', '46703 18677', '174271 5392', '147535 133515', '28021 30622', '137240 36337', '102163 133995', '60189 199711', '157274 161028', '186258 64505', '185134 112017', '32068 139776', '6751 12571', '42968 53924', '12292 199662', '132153 53266', '129376 24798', '92884 133458', '161115 121242', '132303 103567', '198239 125747', '6052 103599', '92371 151399', '201905 174055', '85496 49791', '43711 207308', '150635 305', '81351 157691', '9887 36591', '57055 58497', '98247 1800', '73746 137433', '30916 83125', '177057 65882', '77449 215959', '101888 146091', '152448 170223', '140641 128361', '104890 150840', '77504 129697', '2483 77850', '105674 140197', '119554 110261', '63470 41784', '95469 48816', '213275 49171', '174860 160381', '212712 59875', '124082 195940', '211796 152653', '182219 61579', '178233 156854', '173121 136024', '134454 210115', '30118 85865', '155458 83170', '206977 194757', '212430 3103', '86526 21791', '130238 181327', '57391 150622', '14329 217224', '204645 54237', '83782 137312', '170367 39940', '33392 34905', '12992 38796', '99618 109758', '118797 143583', '56752 140420', '137484 47557', '23378 137993', '73246 111423', '157071 200459', '209623 5929', '97103 142779', '57364 189082', '89898 66968', '24792 113491', '107620 6864', '45921 96360', '183373 45058', '204604 157304', '144965 37108', '35868 58344', '2538 53427', '204458 67452', '28069 21353', '36868 208982', '203592 29304', '19477 214004', '141026 96678', '133303 29021', '177084 8495', '182742 49382', '122211 194636', '66496 200901', '149631 92334', '23040 204655', '209296 110724', '58993 139830', '75791 63506', '112869 66180', '8774 207949', '182032 51188', '90613 141223', '23421 98136', '68155 68806', '211302 100604', '141525 181767', '29878 58449', '211605 1622', '130374 171691', '129605 124673', '84529 165150', '115159 157351', '185293 177058', '84738 149995', '92001 92480', '186115 21125', '217876 57098', '131243 7974', '15334 4433', '11946 185093', '8396 123876', '47079 7681', '124837 209441', '9572 75859', '116000 31357', '161355 11918', '94819 170023', '144289 200073', '68501 83045', '199062 62315', '40925 113303', '84432 164167', '73074 88822', '209790 44754', '123163 145759', '70195 86663', '76144 137481', '195400 205202', '14702 143', '25207 28600', '143489 33219', '131480 152577', '153249 45555', '189615 12034', '28335 51917', '136491 170994', '22297 202697', '142651 184635', '146323 17608', '142397 107804', '177404 68472', '39809 136467', '61362 59702', '63130 201594', '139441 140672', '112573 16407', '53164 155362', '196063 61553', '164236 144392', '34726 108035', '111610 208428', '13196 144673', '14506 48217', '189431 175458', '137647 120666', '137180 178607', '115875 77847', '156564 143015', '126183 53745', '109922 168694', '53969 54622', '206369 196073', '5555 90264', '145359 89387', '142199 40720', '36532 56440', '133858 201176', '1950 212744', '107946 181463', '151816 159315', '14378 154093', '37214 162093', '206412 87528', '149648 73085', '187695 79553', '79396 197727', '154498 35189', '180425 120287', '217835 68379', '115972 217897', '57575 78963', '44864 44500', '94105 182607', '57202 173046', '8841 152469', '86527 120458', '100567 65689', '64054 137514', '179462 123528', '112714 158348', '146757 2375', '62129 141681', '99065 12841', '217802 74204', '151337 125402', '215418 121935', '207540 18179', '163277 151438', '64498 41995', '187495 179147', '162432 183882', '17853 11425', '86772 2041', '199917 181790', '109881 112320', '93980 46151', '121469 152883', '25806 72596', '60825 160125', '66530 160462', '101982 40707', '79120 187600', '38086 93347', '46713 2991', '108840 188316', '85498 106063', '20703 5128', '169353 7819', '60397 199874', '43597 207143', '120978 116796', '166340 120091', '15763 163731', '159549 103371', '168945 32104', '59773 171997', '216255 107189', '76176 96612', '121664 69251', '160558 99357', '125999 28355', '149010 5516', '23265 85648', '110484 217893', '28080 72833', '126393 78320', '44339 58138', '25217 171315', '213167 126480', '113904 114942', '213535 208935', '82946 149502', '40978 203173', '120167 118698', '16747 114735', '113183 81756', '166586 17352', '100303 9033', '175878 66916', '148225 102133', '1591 214896', '47339 62308', '150632 111266', '95563 215844', '24605 66522', '59406 125439', '135554 12581', '159442 13606', '27745 157935', '49236 40788', '22711 199127', '12795 171336', '7778 127842', '164782 47459', '36281 163614', '48122 128411', '163102 83347', '87025 211061', '74281 132605', '140032 120337', '195194 129141', '31176 101545', '113513 46284', '185367 17805', '7177 83816', '188852 58112', '196441 203071', '156605 197923', '78743 27192', '86018 161992', '94733 195995', '109867 141813', '97812 157964', '86771 108573', '52751 191200', '46290 28182', '202781 95733', '196691 36626', '216645 66158', '186329 41858', '164635 177667', '49514 151542', '213241 196133', '121378 198062', '25894 12687', '96289 74339', '190929 203541', '8140 153104', '143481 176967', '25767 200516', '16333 21387', '42607 55454', '203310 178923', '177151 75730', '58869 157598', '193021 103550', '75877 150615', '46051 6466', '137030 99942', '132131 54294', '65621 98592', '22831 162857', '22018 99613', '76207 185291', '186912 181190', '141865 69899', '24116 94769', '194188 50343', '18133 53697', '114109 165648', '72283 162621', '174613 26961', '69807 38005', '191770 95127', '110254 186744', '10809 165123', '74690 48909', '110139 90010', '117020 77244', '74583 151565', '136712 45784', '112124 152565', '115085 85043', '203449 84674', '73374 19501', '192651 154814', '215633 194130', '177247 131730', '83701 188993', '174419 160571', '167628 20445', '146389 154776', '125138 168100', '194927 74885', '69546 203329', '84950 114711', '107452 22871', '168505 124073', '94937 129307', '129371 38685', '171876 94250', '104215 79448', '78599 162183', '150862 18281', '57017 89785', '13068 100837', '173426 212270', '120876 53138', '204275 125138', '4965 71804', '206607 160130', '52729 68906', '75675 159120', '19824 214558', '74992 119624', '101419 87607', '103336 163925', '164618 179450', '137401 73221', '148399 41867', '217910 194730', '122064 116346', '18963 195239', '10068 65469', '137297 94272', '126266 216870', '58119 152540', '162763 16540', '97388 83649', '122146 99214', '106566 193037', '198283 140449', '122668 12466', '101605 176175', '215802 51608', '197108 72055', '146340 6899', '53596 206865', '166687 150926', '178982 138979', '40812 126561', '112578 17745', '62937 200114', '89481 186414', '147891 50714', '79804 182093', '76237 178593', '21775 183035', '209369 137160', '39721 46532', '170478 71007', '141003 31969', '31304 9866', '118453 132969', '171726 147933', '194502 17176', '91568 18683', '170287 206997', '41099 157758', '6461 64477', '128311 77610', '139032 179387', '148808 90008', '78712 74781', '39499 88059', '20633 197883', '26635 43220', '27929 196480', '118545 122107', '172027 103683', '196870 115679', '22847 196019', '178851 173776', '64300 38807', '92566 200120', '1783 35018', '63384 1030', '103753 109950', '122484 207896', '63844 138572', '335 83367', '156937 166493', '13679 155028', '42610 180196', '30417 100947', '141591 15855', '7865 160416', '137109 18906', '61234 140560', '105422 110854', '167777 113479', '38712 2547', '59390 210754', '155241 207877', '156831 139529', '20997 59284', '7253 148073', '144601 114516', '14451 92192', '201682 50474', '42442 184338', '211299 88484', '40334 131557', '145201 10815', '171652 63730', '34079 79665', '133985 56012', '205035 44648', '41304 29123', '134856 84363', '32660 145880', '31155 215024', '99387 178651', '66759 135693', '74168 26996', '26625 20561', '13180 116736', '13054 187794', '217822 69195', '151378 1940', '186172 200616', '178744 41850', '140329 161723', '160401 150519', '177911 48616', '47881 17200', '194606 7495', '37706 209319', '127745 75832', '206943 138684', '58004 10043', '171965 9174', '57213 44076', '178926 36261', '151123 6742', '148565 205548', '97468 197328', '97613 123941', '50616 55107', '27511 162508', '143732 129842', '156455 152589', '184684 195318', '105525 130308', '107074 72041', '121260 189963', '136973 11680', '177074 42691', '84752 193415', '181608 28983', '142317 125172', '173935 3348', '142997 40430', '194416 205091', '50169 217287', '110453 145272', '196548 8145', '26175 108133', '54155 112885', '42303 105828', '166158 81117', '21742 46015', '126346 198398', '49538 211677', '67314 51026', '139731 16370', '182155 148379', '6986 49411', '89093 94489', '197118 173697', '75553 117573', '3293 126358', '162319 198535', '1815 112041', '151058 70570', '156603 159963', '30789 124429', '162813 25097', '58061 179339', '99746 158296', '84803 102301', '27231 143915', '160746 151807', '9015 138819', '95955 111408', '77517 156523', '110973 3675', '116043 134617', '27478 195261', '49824 152673', '132564 95987', '148510 95466', '8199 178599', '111707 26258', '138008 67419', '118552 110578', '59380 47093', '113420 98033', '190287 64502', '94223 58716', '125874 96274', '89955 38901', '14303 2452', '94244 54604', '189558 90930', '101856 66952', '124608 36902', '126979 52407', '74533 31633', '71238 217896', '159443 106333', '165117 57095', '38944 182255', '100660 172448', '105049 38529', '48028 9964', '99664 111025', '102199 148816', '11184 56248', '118481 85830', '141854 50214', '191800 183402', '84565 91539', '96142 173832', '213395 149025', '50926 18677', '36797 82528', '126418 186911', '47610 162788', '73732 23239', '47505 29577', '57558 112033', '182036 129811', '103003 5556', '15256 128736', '171891 78087', '189951 59181', '7652 200222', '101286 166871', '93968 183524', '193982 59166', '74783 202580', '56034 212075', '110086 54570', '125910 101396', '65649 68303', '87120 168858', '17682 11901', '42550 180351', '12513 44011', '12117 167646', '42696 74723', '15603 196909', '131618 11307', '99988 9028', '172173 55650', '68147 54008', '197710 131413', '17547 154023', '42929 37541', '184925 168336', '4180 167191', '176696 80181', '171943 124862', '16727 133171', '82239 161860', '122812 104955', '48067 125591', '131314 62609', '177782 50775', '11228 66504', '197624 94857', '155059 88542', '63387 114457', '110115 25486', '94448 74630', '165045 6288', '107511 215729', '4244 195772', '203863 19412', '157850 114175', '164438 199917', '213267 76055', '41054 10159', '101168 6902', '121253 185733', '19634 102202', '84896 161379', '200354 15253', '42248 5251', '11664 124513', '202622 61678', '71216 66847', '10194 133721', '44878 211810', '205272 138689', '70550 94792', '30938 103332', '30760 172526', '89375 93461', '184323 175846', '160441 150941', '136687 63288', '69791 67856', '166887 55007', '185009 127661', '146899 207693', '6610 124722', '166925 37234', '198313 55536', '215341 50888', '82558 209924', '3427 10581', '57729 173916', '208184 12745', '175237 72448', '120666 71171', '206423 118371', '51487 95548', '12445 56369', '185646 125575', '141981 206044', '146026 102454', '151074 398', '44063 139308', '150959 187917', '182607 52830', '53295 187206', '131434 86072', '136649 158345', '69893 59808', '54107 150286', '191811 123824', '203144 96903', '138347 172647', '45216 154401', '128640 48732', '160483 205847', '170035 170026', '190221 19954', '47426 198677', '83997 154048', '3396 60333', '157117 176275', '213229 98578', '139731 12080', '4695 175658', '114201 62344', '144342 152327', '141537 29644', '192626 191469', '106269 191636', '138013 74806', '200848 175860', '81083 58068', '101404 71772', '113898 71850', '16503 194975', '50760 181983', '8505 174925', '111542 92662', '111219 8641', '187768 86105', '127032 148730', '74512 130200', '45696 170347', '31542 9822', '141010 24345', '110161 22701', '26136 76616', '125415 30703', '158833 51098', '143280 203107', '192385 44607', '121138 44594', '133332 99986', '32264 93391', '105412 6371', '48505 209027', '107666 19113', '217100 143266', '6916 112671', '59316 199005', '87814 81475', '146188 168698', '25152 179242', '72941 115575', '103673 157684', '123199 111351', '195488 119561', '15177 169843', '199708 7382', '215880 8285', '56781 63662', '95311 134897', '65794 134939', '147093 15329', '110879 87569', '127728 43191', '77981 200320', '186188 48169', '149489 192852', '147722 104305', '150680 215796', '1070 98509', '184377 193630', '186801 26767', '175640 140256', '79439 18865', '189906 126658', '91331 11182', '172693 96466', '29558 84467', '92133 106003', '152850 123489', '168415 183265', '175731 60620', '209562 34819', '102863 98260', '2251 203577', '43953 182969', '153446 60096', '167506 63115', '154151 136487', '74858 207469', '156271 154808', '64501 49985', '131556 58536', '55699 76229', '90507 79565', '140062 71260', '103502 15320', '201280 69463', '49330 158555', '196673 144277', '205319 203158', '98954 212738', '190387 159291', '155495 16236', '1312 17555', '15939 121519', '20188 22685', '75065 153874', '126669 185668', '36955 18619', '15501 114149', '31503 196728', '130930 77793', '46265 53556', '97748 71474', '214741 214764', '8548 195472', '66954 128061', '175434 189622', '34765 35579', '150672 217222', '23802 189560', '140508 128048', '71048 36520', '13932 9814', '101751 139512']\n",
            "Sortie 5 : 1 \n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KIOu5hLwbom8"
      },
      "source": [
        "Nous avons ici à faire à un problème 2-SAT.\n",
        "\n",
        "Commençons par extraire les données dans une liste contenant les paires de créneaux sous la forme de listes d'entiers :"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dQoUe_FxkaGY",
        "outputId": "42f71b6f-4f7e-4144-e72a-995e0b2a1eb1"
      },
      "source": [
        "lines = ['5', '205 300', '210 370', '290 380', '120 305', '390 110']\n",
        "N = int(lines[0])\n",
        "creneaux = [[int(x) for x in x.split()] for x in lines[1:]]\n",
        "print(creneaux)"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[205, 300], [210, 370], [290, 380], [120, 305], [390, 110]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G0OShxmMkktV"
      },
      "source": [
        "Parcourons tous les couples possibles :\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HZE4Ny9anjXs"
      },
      "source": [
        "for c1 in range(2):\n",
        "  for c2 in range(2):\n",
        "    for v1 in range(N):\n",
        "      for v2 in range(N):\n",
        "        print(creneaux[v1][c1],creneaux[v2][c2])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2RrGqOoenyH9"
      },
      "source": [
        "Concentrons nous sur le cas où les couples sont ceux proposés par un même étudiant :"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "61JWx4XpoD7Z",
        "outputId": "00dc6784-348c-47ef-b8cf-5b9d0db947b3"
      },
      "source": [
        "for c1 in range(2):\n",
        "  for c2 in range(2):\n",
        "    for v1 in range(N):\n",
        "      for v2 in range(N):\n",
        "        if v1 == v2:\n",
        "          if c1 != c2:\n",
        "            print(creneaux[v1][c1],creneaux[v2][c2])"
      ],
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "205 300\n",
            "210 370\n",
            "290 380\n",
            "120 305\n",
            "390 110\n",
            "300 205\n",
            "370 210\n",
            "380 290\n",
            "305 120\n",
            "110 390\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5XkwqVb-pPLB"
      },
      "source": [
        "Nous alons ajouter une clause indiquant que les deux propositions ne peuvent être satisfaites. Pour le premier couple, si on a a=205 et b=300, on peut écrire :\n",
        "\n",
        "(a V b) Λ (¬a V ¬b)\n",
        "\n",
        "Mettons que les créneaux soient numérotés 1, 2, 3, etc. Les deux créneaux du premier coule sont donc représentés par 1 et 2. Les clauses correspondantes, dans le module pysat, sont :\n",
        "\n",
        "[1,2]\n",
        "\n",
        "[-1,-2]\n",
        "\n",
        "Pour le couple suivant, nous aurons :\n",
        "\n",
        "[3,4]\n",
        "\n",
        "[-3,-4]\n",
        "\n",
        "En généralisant, nous allons devoir ajouter les clauses :\n",
        "\n",
        "[2*v1+c1+1, 2*v2+c2+1]\n",
        "\n",
        "[-(2*v1+c1+1), -(2*v2+c2+1)]\n",
        "\n",
        "\n",
        "Importont le module nécessaire pour créer une expression dont on souhaite évaluer la satisfaisabilité."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3pMeYmVorSxA"
      },
      "source": [
        "from pysat.solvers import Glucose3"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ih98NplRrTS7"
      },
      "source": [
        "En cas d'erreur sur ce bloc d'instructions, lancez l'installation du module python-sat, redémarrez le noyau, puis re-exécutez la dernière cellule de code.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7z2skB3fkkKN"
      },
      "source": [
        "!pip install python-sat"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0QE6DNoPoS33"
      },
      "source": [
        "Ajoutons ces clauses à notre instruction"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dx0lxPQNcZCf"
      },
      "source": [
        "g = Glucose3()\n",
        "\n",
        "for c1 in range(2):\n",
        "  for c2 in range(2):\n",
        "    for v1 in range(N):\n",
        "      for v2 in range(N):\n",
        "        if v1 == v2:\n",
        "          if c1 != c2:\n",
        "            g.add_clause([2*v1+c1+1, 2*v2+c2+1])\n",
        "            g.add_clause([-(2*v1+c1+1), -(2*v2+c2+1)])"
      ],
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lXw4JnXXqxGP"
      },
      "source": [
        "Il nous reste à traiter le cas où les créneaux du couple sont proposés par 2 étudiants différents.\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Nes-scccrlgD"
      },
      "source": [
        "g = Glucose3()\n",
        "\n",
        "for c1 in range(2):\n",
        "  for c2 in range(2):\n",
        "    for v1 in range(N):\n",
        "      for v2 in range(N):\n",
        "        if v1 == v2:\n",
        "          if c1 != c2:\n",
        "            g.add_clause([2*v1+c1+1, 2*v2+c2+1])\n",
        "            g.add_clause([-(2*v1+c1+1), -(2*v2+c2+1)])\n",
        "        else:\n",
        "          print(creneaux[v1][c1],creneaux[v2][c2])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "txgAGtEOrlxi"
      },
      "source": [
        "\n",
        "Dans ce cas, on ajoute une clause seulement si les créneaux se chevauchent. Ecrivons une fonction qui indiquent si deux créneaux en entrée se chevauchent dans le temps ou non :"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3Wtohwz-rEWc",
        "outputId": "428f3522-fe09-4c46-fe6c-8a6d644d8d0a"
      },
      "source": [
        "def intersect(i1, i2):\n",
        "    return not(i1 + 60 < i2 or i2 + 60 < i1)\n",
        "  \n",
        "g = Glucose3()\n",
        "\n",
        "for c1 in range(2):\n",
        "  for c2 in range(2):\n",
        "    for v1 in range(N):\n",
        "      for v2 in range(N):\n",
        "        if v1 == v2:\n",
        "          if c1 != c2:\n",
        "            g.add_clause([2*v1+c1+1, 2*v2+c2+1])\n",
        "            g.add_clause([-(2*v1+c1+1), -(2*v2+c2+1)])\n",
        "        elif intersect(creneaux[v1][c1], creneaux[v2][c2]):\n",
        "          print(creneaux[v1][c1],creneaux[v2][c2])"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "205 210\n",
            "210 205\n",
            "290 300\n",
            "290 305\n",
            "120 110\n",
            "390 370\n",
            "390 380\n",
            "300 290\n",
            "370 390\n",
            "380 390\n",
            "305 290\n",
            "110 120\n",
            "300 305\n",
            "370 380\n",
            "380 370\n",
            "305 300\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6L5r3txEr9cz"
      },
      "source": [
        "Si les créneaux a et b, proposés par deux étudiants différents, se chevauchent, on doit avoir au moins l'un des deux créneaux qui soit False :\n",
        "\n",
        " (¬a V ¬b)\n",
        "\n",
        "Dans notre exemple, on commence par traiter les créneaux 1 et 3 qui se chevauchent. La clause correspondante dans le module pysat, est :\n",
        "\n",
        "[-1,-3]\n",
        "\n",
        "En généralisant, nous allons devoir ajouter les clauses :\n",
        "\n",
        "[-(2*v1+c1+1), -(2*v2+c2+1)]"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "leYvUuGMqwbY"
      },
      "source": [
        "from pysat.solvers import Glucose3\n",
        "g = Glucose3()\n",
        "\n",
        "for c1 in range(2):\n",
        "  for c2 in range(2):\n",
        "    for v1 in range(N):\n",
        "      for v2 in range(N):\n",
        "        if v1 == v2:\n",
        "          if c1 != c2:\n",
        "            g.add_clause([2*v1+c1+1, 2*v2+c2+1])\n",
        "            g.add_clause([-(2*v1+c1+1), -(2*v2+c2+1)])\n",
        "        elif intersect(creneaux[v1][c1], creneaux[v2][c2]):\n",
        "          g.add_clause([-(2*v1+c1+1), -(2*v2+c2+1)])"
      ],
      "execution_count": 67,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7hQDU-SHtCGM"
      },
      "source": [
        "Résolvons enfin le problème :"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UGqE3uSBtEBq",
        "outputId": "5e4c86b6-0ea9-458e-ab35-a56aa76c86e5"
      },
      "source": [
        "if g.solve():\n",
        "  print('Une solution est :',g.get_model())\n",
        "else:\n",
        "  print('KO')"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "KO\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}