{"id":911,"date":"2015-05-07T21:10:44","date_gmt":"2015-05-07T19:10:44","guid":{"rendered":"http:\/\/revista.newprojects.org\/?p=911"},"modified":"2017-05-07T21:17:40","modified_gmt":"2017-05-07T19:17:40","slug":"911","status":"publish","type":"post","link":"https:\/\/revista.newprojects.org\/?p=911","title":{"rendered":"Proiect didactic &#8211; Grafuri euleriene"},"content":{"rendered":"<h5>Angelica \u2013 Ioana T\u0102B\u00ceRC\u0102 \u2013 Liceul Teoretic \u201cIon Heliade R\u0103dulescu\u201d T\u00e2rgovi\u0219te<br \/>\nNicolae \u2013 Radu T\u0102B\u00ceRC\u0102 &#8211; Liceul Teoretic \u201cIon Heliade R\u0103dulescu\u201d T\u00e2rgovi\u0219te<\/h5>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: center;\">PROIECT DIDACTIC<\/h2>\n<p><strong>Unitatea \u0219colar\u0103: <\/strong>Liceul Teoretic \u201cIon Heliade R\u0103dulescu\u201d T\u00e2rgovi\u0219te<\/p>\n<p><strong>Profesori propun\u0103tori<\/strong>: Angelica \u2013 Ioana T\u0102B\u00ceRC\u0102, Nicolae &#8211; Radu T\u0102B\u00ceRC\u0102<\/p>\n<p><strong>Disciplina<\/strong>:\u00a0 INFORMATIC\u0102<\/p>\n<p><strong>Clasa<\/strong>: a XI-a<\/p>\n<p>Data: ____________________<\/p>\n<p><strong>Unitatea de \u00eenv\u0103\u0163are<\/strong>: Grafuri neorientate<\/p>\n<p><strong>Tema lec\u021biei<\/strong>: Grafuri euleriene<\/p>\n<p><strong>Tipul lec\u0163iei <\/strong>\u2013 mixt\u0103 ( lec\u021bie care urm\u0103re\u0219te at\u00e2t predarea, c\u00e2t \u0219i fixarea, verificarea \u0219i aplicarea cuno\u0219tin\u021belor )<\/p>\n<p><strong>Locul de desf\u0103\u015furare<\/strong>: Laboratorul de informatic\u0103<\/p>\n<p><strong>Durata: <\/strong>50 min.<\/p>\n<p><strong>Nivelul ini\u0163ial al clasei:<\/strong><\/p>\n<p>&#8211; elevii \u015fi-au \u00eensu\u015fit no\u0163iunile teoretice legate de grafurile neorientate: terminologie, reprezentare, memorare;<\/p>\n<p>&#8211; elevii rezolv\u0103 corect probleme simple cu grafuri, scriu programele surs\u0103, le ruleaz\u0103 \u015fi depaneaz\u0103.<\/p>\n<p><strong>Competen\u0163\u0103 general\u0103 : <\/strong><\/p>\n<ul>\n<li>Identificarea datelor care intervin \u00eentr-o problem\u0103 \u015fi aplicarea algoritmilor fundamentali de<\/li>\n<\/ul>\n<p>prelucrare a acestora<\/p>\n<p><strong>Competen\u0163e specifice:<\/strong><\/p>\n<ul>\n<li>Analizarea unei probleme \u00een scopul identific\u0103rii datelor necesare \u015fi alegerea modalit\u0103\u0163ilor adecvate de structurare a datelor care intervin \u00eentr-o problem\u0103<\/li>\n<li>Transpunerea unei probleme din limbaj natural \u00een limbaj de grafuri, folosind corect terminologia specific\u0103<\/li>\n<li>Descrierea unor algoritmi simpli de verificare a unor propriet\u0103\u0163i specifice grafurilor<\/li>\n<\/ul>\n<p><strong>Obiective educa\u0163ionale<\/strong>:<\/p>\n<ul>\n<li><strong>Obiective cognitive<\/strong><\/li>\n<li><em>explicarea \u0219i exemplificarea no\u0163iunilor legate de grafuri euleriene;<\/em><\/li>\n<li><em>aplicarea no\u0163iunilor studiate, \u00een aplica\u0163ii concrete;<\/em><\/li>\n<li><em>emiterea de ipoteze pentru rezolvarea unor probleme;<\/em><\/li>\n<li><strong>Obiective afective<\/strong><\/li>\n<li><em>formarea convingerii c\u0103 teoria grafurilor are aplica\u021bii \u00een multe domenii ale \u0219tiin\u021bei \u0219i tehnicii, c\u00e2t \u0219i \u00een via\u021ba real\u0103; <\/em><\/li>\n<li><em>manifestarea ini\u0163iativei \u015fi disponibilit\u0103\u0163ii de a aborda sarcini variate<\/em>;<\/li>\n<li><strong>Obiective psihomotorii<\/strong><\/li>\n<li><em>utilizarea corect\u0103 a mediului de programare Code::Blocks pentru a realiza programe \u00een C++;<\/em><\/li>\n<li><em>formarea deprinderii de a depana \u00een timp util erorile ce apar \u00een programele surs\u0103;<\/em><\/li>\n<li><strong>Obiective opera\u0163ionale<\/strong><\/li>\n<\/ul>\n<p><strong>La sf\u00e2r\u0219itul lec\u021biei, elevii vor fi capabili:<\/strong><\/p>\n<ul>\n<li><em>s\u0103 analizeze dac\u0103 un graf neorientat este eulerian sau con\u021bine un lan\u021b eulerian;<\/em><\/li>\n<li><em>s\u0103 verifice, utiliz\u00e2nd programarea \u00een C++, dac\u0103 un graf este eulerian.<\/em><\/li>\n<\/ul>\n<p><strong>STRATEGIA DIDACTIC\u0102<\/strong><\/p>\n<ul>\n<li><strong>Metode de \u00eenv\u0103\u0163\u0103m\u00e2nt<\/strong><\/li>\n<li>expunere, conversa\u0163ie, problematizare;<\/li>\n<li>observarea independent\u0103, exerci\u0163iul euristic, rezolvarea de probleme;<\/li>\n<li><strong>Procedee de instruire:<\/strong><\/li>\n<li><strong>\u00a0<\/strong>&#8211; expunere \u00een etapa de comunicare;<\/li>\n<li>&#8211; \u00eenv\u0103\u0163area prin descoperire, observarea independent\u0103, exerci\u0163iul euristic, rezolvarea de probleme;<\/li>\n<li>&#8211; problematizarea prin crearea situa\u0163iilor problem\u0103;<\/li>\n<li>&#8211; conversa\u0163ia de consolidare \u00een etapa de fixare a cuno\u015ftin\u0163elor;<\/li>\n<li><strong>Forme de organizare a activit\u0103\u0163ii<\/strong>: frontal \u015fi individual;<\/li>\n<li><strong>Forme de dirijare a activit\u0103\u0163ii: <\/strong>dirijat\u0103 de profesor \u0219i independent\u0103;<\/li>\n<li><strong>Material bibliografic:<\/strong><\/li>\n<li><strong>Manual de informatic\u0103<\/strong> Vlad Hu\u021ban, Tudor Sorin, \u2013 <em>Aprobat prin Ordinul MEdC nr. 4446 din 19.06.2006<\/em> \u2013 editura L&amp;S Soft Bucure\u0219ti<\/li>\n<li><strong>Ghid de evaluare \u2013 Informatic\u0103 \u0219i Tehnologia informa\u021biei, S.N.E.E., Bucure\u0219ti 2001<\/strong><\/li>\n<li><strong>Mijloace de \u00eenv\u0103\u021b\u0103m\u00e2nt: <\/strong><a href=\"http:\/\/informat21.wikispaces.com\/\" target=\"_blank\" rel=\"noopener noreferrer\">http:\/\/informat21.wikispaces.com\/<\/a><\/li>\n<li><strong>Metode de evaluare <\/strong>:<\/li>\n<li>evaluare ini\u0163ial\u0103: \u00eentreb\u0103ri orale, observarea sistematic\u0103 a activit\u0103\u021bii \u0219i comportamentului elevilor<\/li>\n<li>evaluare formativ\u0103: observarea sistematic\u0103 a activit\u0103\u021bii \u0219i comportamentului elevilor, set de aplica\u021bii poste pe site-ul wiki<\/li>\n<li>evaluarea final\u0103 ( sumativ\u0103 ): \u00eentreb\u0103ri orale, set de aplica\u021bii poste pe site-ul wiki<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul>\n<li><strong>Desf\u0103\u015furarea activit\u0103\u0163ii<\/strong><\/li>\n<\/ul>\n<table>\n<tbody>\n<tr>\n<td rowspan=\"2\" width=\"251\"><strong>Momentele lec\u021biei<\/strong><\/td>\n<td colspan=\"2\" width=\"502\"><strong>Activitatea de predare &#8211; \u00eenv\u0103\u021bare<\/strong><\/td>\n<td rowspan=\"2\" width=\"251\"><strong>Metode de \u00eenv\u0103\u021b\u0103m\u00e2nt<\/strong><\/p>\n<p><strong>(<\/strong><strong><em>Metode \u015fi mijloace de \u00eenv\u0103\u0163\u0103m\u00e2nt utilizate)<\/em><\/strong><\/td>\n<td rowspan=\"2\" width=\"251\"><strong>Modalit\u0103\u021bi de evaluare <\/strong><\/p>\n<p><strong>( instrument de evaluare )<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"251\"><strong>Activitatea profesorului<\/strong><\/td>\n<td width=\"251\"><strong>Activitatea elevilor<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"251\">1. Moment organizatoric<\/td>\n<td width=\"251\">Asigur\u0103 cadrul necesar \u00eenceperii orei:<\/p>\n<p>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 amplasarea elevilor la calculatoare;<\/p>\n<p>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 notarea absen\u021bilor etc.<\/td>\n<td width=\"251\">Elevii se preg\u0103tesc pentru or\u0103:<\/p>\n<p>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 verific\u0103 func\u021bionarea calculatoarelor;<\/p>\n<p>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00ee\u0219i organizeaz\u0103 masa de lucru etc.<\/td>\n<td width=\"251\">&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 conversa\u021bia<\/td>\n<td width=\"251\">&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 observarea sistematic\u0103 a activit\u0103\u021bii \u0219i comportamentului elevilor ( list\u0103 de verificare );<\/p>\n<p>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td width=\"251\">2. Reactualizarea cuno\u0219tin\u021belor<\/td>\n<td width=\"251\">&#8211; Verific\u0103 tema pentru acas\u0103<\/p>\n<p>&#8211; Prezint\u0103 elevilor modalitatea prin care li se vor verifica cuno\u0219tin\u021bele referitoare la grafurile neorientate ( <strong>fi\u0219a nr. 1<\/strong> )<\/td>\n<td width=\"251\">Elevii adreseaz\u0103 \u00eentreb\u0103ri \u0219i r\u0103spund la \u00eentreb\u0103ri referitoare la no\u021biuni specifice teoriei grafurilor <em>neorientate<\/em> ( conform informa\u021biilor primite de la profesor )<\/td>\n<td width=\"251\">&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 explica\u021bia<\/p>\n<p>&nbsp;<\/td>\n<td width=\"251\">&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 observarea sistematic\u0103 a activit\u0103\u021bii \u0219i comportamentului elevilor (list\u0103 de verificare);<\/p>\n<p>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 prob\u0103 oral\u0103;<\/td>\n<\/tr>\n<tr>\n<td width=\"251\">3. Anun\u021barea temei \u0219i a obiectivelor lec\u021biei<\/td>\n<td width=\"251\">Prezint\u0103 tema lec\u021biei \u0219i obiectivele acesteia ( expuse pe flipchart )<\/td>\n<td width=\"251\">Noteaz\u0103 tema \u0219i obiectivele lec\u021biei<\/td>\n<td width=\"251\">&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 conversa\u021bia<\/td>\n<td width=\"251\">&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 observarea sistematic\u0103 a activit\u0103\u021bii \u0219i comportamentului elevilor (list\u0103 de verificare);<\/td>\n<\/tr>\n<tr>\n<td width=\"251\">4. Parcurgerea secven\u021bial\u0103 a materialelor postate pe site-ul wiki<\/td>\n<td width=\"251\">Prezint\u0103, secven\u021bial, con\u021binutul site-ului wiki:<\/p>\n<p><em>informat21.wikispaces.com<\/em>, coordon\u00e2nd atent ac\u021biunile elevilor spre atingerea obiectivelor lec\u021biei<\/p>\n<p>( <strong>fi\u0219a nr. 2<\/strong> )<\/td>\n<td width=\"251\">Parcurg, sub \u00eendrumarea profesorului, materialele postate pe site-ul wiki. Noteaz\u0103 informa\u021biile importante, rezolv\u0103 exerci\u021biile \u0219i problemele propuse.<\/td>\n<td width=\"251\">&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 expunerea,<\/p>\n<p>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 conversa\u0163ia euristic\u0103,<\/p>\n<p>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 explica\u021bia,<\/p>\n<p>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 problematizarea,<\/p>\n<p>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 rezolvarea de probleme.<\/td>\n<td width=\"251\">&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 observarea sistematic\u0103 a activit\u0103\u021bii \u0219i comportamentului elevilor (list\u0103 de verificare);<\/p>\n<p>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td width=\"251\">5. Ob\u021binerea performan\u021bei \u0219i realizarea feed-back-ului<\/td>\n<td width=\"251\">Verific\u0103 atingerea obiectivelor propuse prin intermediul:<\/p>\n<p>&#8211; gradului de realizare de c\u0103tre elevi a aplica\u021biilor propuse pentru rezolvare \u00een clas\u0103;<\/p>\n<p>&#8211; \u00eentreb\u0103rilor finale referitoare la con\u021binuturile lec\u021biei.<\/p>\n<p>Discut\u0103 \u0219i analizeaz\u0103 cu elevii tema propus\u0103 pentru acas\u0103<\/td>\n<td width=\"251\">&#8211; R\u0103spund la \u00eentreb\u0103ri<\/p>\n<p>&#8211; Rezolv\u0103 individual aplica\u021biile propuse \u0219i realizeaz\u0103 programul \u00een C++ utiliz\u00e2nd mediul de programare Code::Blocks<\/p>\n<p>&#8211; Particip\u0103 la discu\u021biile referitoare la modalitatea de realizare a temei pentru acas\u0103, argumenteaz\u0103<\/td>\n<td width=\"251\">&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 conversa\u0163ia euristic\u0103,<\/p>\n<p>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 explica\u021bia,<\/p>\n<p>&#8211; rezolvarea de probleme.<\/td>\n<td width=\"251\">&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 observarea sistematic\u0103 a activit\u0103\u021bii \u0219i comportamentului elevilor (list\u0103 de verificare);<\/p>\n<p>&#8211; prob\u0103 oral\u0103;<\/p>\n<p>&#8211; prob\u0103 practic\u0103.<\/td>\n<\/tr>\n<tr>\n<td width=\"251\">6. \u00cencheierea activit\u0103\u021bii<\/td>\n<td width=\"251\">Apreciaz\u0103 participarea elevilor la lec\u021bie, dovedit\u0103 \u0219i prin manifestarea ini\u0163iativei \u015fi disponibilit\u0103\u0163ii lor de a aborda sarcini variate<\/p>\n<p>( <strong>fi\u0219a nr. 3<\/strong> )<\/td>\n<td width=\"251\">Ascult\u0103 observa\u021biile profesorului, argument\u00e2nd, manifest\u00e2nd opinii pro \u0219i contra.<\/p>\n<p>Completeaz\u0103 scara de clasificare.<\/td>\n<td width=\"251\">&#8211; conversa\u021bia<\/td>\n<td width=\"251\">&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 observarea sistematic\u0103 a activit\u0103\u021bii \u0219i comportamentului elevilor (list\u0103 de verificare);<\/p>\n<p>&nbsp;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Evaluare ini\u021bial\u0103 \u2013 Grafuri neorientate<\/strong><strong>:<\/strong><\/p>\n<p><strong>\u00a0<\/strong><strong>Fi\u0219a nr. 1 &#8211; <u>VERIFICAREA CUNO\u0218TIN\u021aELE REFERITOARE LA GRAFURILE NEORIENTATE<\/u><\/strong><\/p>\n<p><strong><em>Joc didactic desf\u0103\u0219urat de elevi <\/em><\/strong>r<strong><em>eferitor la tema studiat\u0103 ( 3 min. )<\/em><\/strong> \u2013 care presupune, <strong><u>pentru elevi,<\/u><\/strong> formularea de \u00eentreb\u0103ri \u0219i evaluarea r\u0103spunsurilor primite<\/p>\n<p><strong>\u00a0<\/strong><strong>Reguli:<\/strong><\/p>\n<ul>\n<li>Elevii au primit ca tem\u0103 pentru acas\u0103 recapitularea\/ reactualizarea no\u021biunilor referitoare la grafuri neorientate ( defini\u021bii, teoreme, probleme specifice etc. ) ;<\/li>\n<li>Profesorul \u00eemparte cartona\u0219e cu numere tuturor elevilor, astfel \u00eenc\u00e2t fiecare elev prime\u0219te un cartona\u0219 cu un num\u0103r cuprins \u00eentre 1 \u0219i num\u0103rul total al elevilor din clas\u0103 ( <strong>num\u0103rul nu trebuie cunoscut dec\u00e2t de elevul respectiv<\/strong> );<\/li>\n<li>Profesorul adreseaz\u0103 prima \u00eentrebare \u0219i solicit\u0103 r\u0103spuns elevului cu num\u0103rul x;<\/li>\n<li>Dac\u0103 elevul r\u0103spunde corect <strong><em>este notat cu + \u00een fi\u0219a de evaluare<\/em><\/strong> \u0219i este rugat s\u0103 adreseze urm\u0103toarea \u00eentrebare ( din domeniul studiat ) elevului cu num\u0103rul y ( ales la \u00eent\u00e2mplare );<\/li>\n<li>Dac\u0103 elevul nu r\u0103spunde corect sau nu \u0219tie s\u0103 formuleze o \u00eentrebare <strong><em>este notat cu &#8211; \u00een fi\u0219a de evaluare<\/em><\/strong> \u0219i profesorul nominalizeaz\u0103 alt elev \/ num\u0103r \u0219.a.m.d.<\/li>\n<li>Jocul se deruleaz\u0103 \u00eentr-un timp finit.<\/li>\n<\/ul>\n<p><strong>\u00a0<\/strong><strong><em><u>\u00centreb\u0103ri \u2013 R\u0103spunsuri a\u0219teptate<\/u><\/em><\/strong><\/p>\n<p><strong>\u00a0<\/strong><strong>Ce este un graf neorientat ?<\/strong> ( defini\u021bie )<\/p>\n<p><strong>R: <\/strong>Un graf neorientat este o pereche ordonat\u0103 G=( V, E ), unde:<\/p>\n<ul>\n<li>V = {v1, v2, \u2026, vn} este o mul\u021bime finit\u0103 \u0219i nevid\u0103. Elementele mul\u021bimii V se numesc noduri ( v\u00e2rfuri )<\/li>\n<li>E este o mul\u021bime finit\u0103 de perechi neordonate de forma (vi, vj), unde i \u2260 j \u0219i vi, vj \u0454 V. Elementele mul\u021bimii E se numesc muchii.<\/li>\n<li>Orice muchie une\u0219te 2 noduri distincte.<\/li>\n<\/ul>\n<ol start=\"2\">\n<li><strong> C\u00e2nd sunt 2 noduri adiacente ?<\/strong><\/li>\n<\/ol>\n<p><strong>R: <\/strong>C\u00e2nd reprezint\u0103 extremit\u0103\u021bile unei muchii. \/ C\u00e2nd sunt unite de o muchie.<\/p>\n<ol start=\"3\">\n<li><strong> Ce reprezint\u0103 gradul unui nod ?<\/strong><\/li>\n<\/ol>\n<p>R: Num\u0103rul muchiilor <strong>incidente<\/strong> cu nodul respectiv. ( Not: d( v ) )<\/p>\n<p><strong>Observa\u021bii<\/strong><strong>: <\/strong><\/p>\n<ul>\n<li>Dac\u0103 d(v) = 0, nodul v este <strong>nod izolat<\/strong><\/li>\n<li>Dac\u0103 d(v) = 1, nodul v este <strong>nod terminal<\/strong><\/li>\n<\/ul>\n<p><strong>\u00a0<\/strong><strong>Care este suma gradelor unui graf neorientat cu n noduri \u0219i m muchii ?<\/strong><\/p>\n<p><strong>R<\/strong><strong>: <\/strong>S = d1+d2+\u2026dn= 2m<\/p>\n<ol start=\"5\">\n<li><strong> Care sunt metodele ( studiate ) de memorare a grafurilor ?<\/strong><\/li>\n<\/ol>\n<p>R: Utiliz\u00e2nd:<\/p>\n<ul>\n<li>Matricea de adiacen\u021b\u0103 ( matrice p\u0103tratic\u0103, simetric\u0103 fa\u021b\u0103 de diagonala principal\u0103 )<\/li>\n<li>Listele de adiacen\u021b\u0103 ( prin utilizarea aloc\u0103rii statice )<\/li>\n<\/ul>\n<ol start=\"6\">\n<li><strong> Ce este un graf complet ?<\/strong><\/li>\n<\/ol>\n<p><strong>R: <\/strong>Un graf neorientat \u00een care oricare 2 noduri sunt sunt adiacente ( Not: <strong>Kn <\/strong>)<\/p>\n<p>Observa\u021bii:<\/p>\n<ul>\n<li>\u00centr-un graf complet, <strong>gradul oric\u0103rui nod este n-1<\/strong> ( din fiecare nod pleac\u0103 \/ sosesc n-1 muchii )<\/li>\n<li>\u00centr-un graf complet exist\u0103 rela\u021bia <strong>m = n(n-1) \/ 2<\/strong>, unde <strong>m<\/strong> este num\u0103rul de muchii, iar <strong>n <\/strong>este num\u0103rul de noduri. ( C<sup>2<\/sup><sub>n<\/sub> = n(n-1)\/2 )<\/li>\n<li>Exist\u0103 un num\u0103r de 2<sup>n(n-1)\/2<\/sup> grafuri neorientate cu n noduri.<\/li>\n<\/ul>\n<ol start=\"7\">\n<li><strong> Ce este un graf par\u021bial al unui graf neorientat ?<\/strong><\/li>\n<\/ol>\n<p><strong>R<\/strong><strong>: <\/strong>Un graf par\u021bial al unui graf neorientat dat G=(V,E) este un graf G1=(V, E1), unde E1\u00a0E<\/p>\n<p>( Un graf par\u021bial al unui graf dat este el \u00eensu\u0219i sau se ob\u021bine prin suprimarea anumitor muchii.)<\/p>\n<ol start=\"8\">\n<li><strong> Ce este un subgraf al unui graf neorientat ?<\/strong><\/li>\n<\/ol>\n<p><strong>R<\/strong><strong>: <\/strong>Un graf par\u021bial al unui graf neorientat dat G=(V,E) este un graf G1=(V1, E1),<\/p>\n<p>unde E1E, V1V, iar muchiile din E1 sunt toate muchiile din E care sunt incidente numai la noduri din mul\u021bimea V1.<\/p>\n<p>( Un subgraf par\u021bial al unui graf dat G este el \u00eensu\u0219i sau se ob\u021bine din G prin suprimarea anumitor noduri \u0219i a tuturor muchiilor incidente cu acestea.)<\/p>\n<ol start=\"9\">\n<li><strong> Ce reprezint\u0103 parcurgerea grafurilor ?<\/strong><\/li>\n<\/ol>\n<p><strong>R<\/strong><strong>: <\/strong>Prin parcurgerea grafurilor \u00een\u021belegem o modalitate de vizitare a nodurilor acestuia, cu scopul prelucr\u0103rii informa\u021biilor asociate nodurilor.<\/p>\n<ol start=\"10\">\n<li><strong> Ce este un lan\u021b ?<\/strong><\/li>\n<\/ol>\n<p><strong>R<\/strong><strong>: <\/strong>Un lan\u021b\u00a0 L=[v1, v2, \u2026, vp ] este o succesiune de noduri cu proprietatea c\u0103 oricare dou\u0103 noduri vecine sunt adiacente.<\/p>\n<ol start=\"11\">\n<li><strong>Ce reprezint\u0103 lungimea unui lan\u021b ?<\/strong><\/li>\n<\/ol>\n<p><strong>R<\/strong><strong>: <\/strong>Num\u0103rul de muchii ce unesc nodurile lan\u021bului.<\/p>\n<ol start=\"12\">\n<li><strong> Ce este un lan\u021b elementar ?<\/strong><\/li>\n<\/ol>\n<p><strong>R<\/strong><strong>: <\/strong>Un lan\u021b elementar este un lan\u021b care con\u021bine numai noduri distincte.<\/p>\n<ol start=\"13\">\n<li><strong> Ce este un graf conex ?<\/strong><\/li>\n<\/ol>\n<p><strong>R<\/strong><strong>: <\/strong>Un graf \u00een care exist\u0103 un lan\u021b \u00eentre oricare dou\u0103 noduri ale acestuia.<\/p>\n<p><strong>Observa\u021bie<\/strong><strong>:<\/strong> Graful conex admite o singur\u0103 component\u0103 conex\u0103.<\/p>\n<ol start=\"14\">\n<li><strong> Ce este un ciclu ?<\/strong><\/li>\n<\/ol>\n<p><strong>R<\/strong><strong>: <\/strong>Un lan\u021b pentru care nodul ini\u021bial coincide cu nodul final.<\/p>\n<ol start=\"15\">\n<li><strong> Ce este un ciclu elementar ?<\/strong><\/li>\n<\/ol>\n<p><strong>R<\/strong><strong>: <\/strong>Un ciclu care con\u021bine numai noduri distincte, cu excep\u021bia ultimului nod, care coincide cu primul.<\/p>\n<p><strong>Fi\u0219a nr. 2 &#8211; <\/strong><strong><u>CON\u021aINUTUL SITE-ULUI WIKI<\/u><\/strong><strong>: <em><a href=\"http:\/\/informat21.wikispaces.com\/\">informat21.wikispaces.com<\/a><\/em><\/strong><\/p>\n<p><strong>Fi\u0219a nr. 3<\/strong> \u2013 Verificarea, utiliz\u00e2nd mediul de programare C++, a faptului c\u0103 un graf este sau nu eulerian<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"560\"><strong>G2.in<\/strong><\/td>\n<td width=\"563\"><strong>G2.out<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"560\">5<\/p>\n<p>1 2<\/p>\n<p>1 3<\/p>\n<p>1 4<\/p>\n<p>1 5<\/p>\n<p>2 3<\/p>\n<p>2 4<\/p>\n<p>2 5<\/p>\n<p>3 4<\/p>\n<p>3 5<\/p>\n<p>4 5<\/td>\n<td width=\"563\">Graful este eulerian<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>#include &lt;iostream&gt;<br \/>\n#include &lt;fstream&gt;<br \/>\nusing namespace std;<br \/>\nint main ()<br \/>\n{<br \/>\nunsigned int i,j, n, s, a[10][10],ok=1;<\/p>\n<p>ifstream f( &#8222;G2.in&#8221;);<\/p>\n<p>ofstream g ( &#8222;G2.out&#8221;);<\/p>\n<p>f&gt;&gt;n;<\/p>\n<p>for(i=1;i&lt;=n;i++)<\/p>\n<p>for (j=1;j&lt;=n;j++)<\/p>\n<p>a[i][j]=0;<\/p>\n<p>while (f&gt;&gt;i&gt;&gt;j)<\/p>\n<p>a[i][j]=a[j][i]=1;<\/p>\n<p>for(i=1;i&lt;=n;i++)<\/p>\n<p>{<\/p>\n<p>s=0;<\/p>\n<p>for(j=1;j&lt;=n;j++)<\/p>\n<p>s=s+a[i][j];<\/p>\n<p>if(s%2!=0) ok=0;<\/p>\n<p>}<\/p>\n<p>if(ok==1)<\/p>\n<p>g&lt;&lt;&#8222;Graful este eulerian&#8221;;<\/p>\n<p>else<\/p>\n<p>g&lt;&lt;&#8222;Graful nu este eulerian&#8221;;<\/p>\n<p>f.close();<\/p>\n<p>g.close();<\/p>\n<p>}<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Fi\u0219a nr. 4<\/strong> &#8211; <strong>SCAR\u0102 DE CLASIFICARE <\/strong>completat\u0103 de elevi la finalul lec\u021biei<\/p>\n<p><strong>Tema lec\u021biei<\/strong><strong>: GRAFURI EULERIENE\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 DATA: _______________<\/strong><\/p>\n<p><strong>\u00a0<\/strong><strong><em>Bifeaz\u0103, pentru fiecare \u00eentrebare, ceea ce consideri c\u0103 te reprezint\u0103.<\/em><\/strong><\/p>\n<ol>\n<li><strong>No\u021biunile prezentate \u00een lec\u021bie sunt importante pentru activitatea mea viitoare.<\/strong><\/li>\n<\/ol>\n<p><strong>\u00a0puternic dezacord\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><strong>\u00a0dezacord\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><strong>\u00a0neutru\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><strong>\u00a0acord \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><strong>\u00a0puternic acord<\/strong><\/p>\n<ol start=\"2\">\n<li><strong>Sunt interesat s\u0103 aprofundez no\u021biunile prezentate la lec\u021bie \u0219i s\u0103 rezolv tema pentru acas\u0103.<\/strong><\/li>\n<\/ol>\n<p><strong>\u00a0puternic dezacord\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><strong>\u00a0dezacord\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><strong>\u00a0neutru\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><strong>\u00a0acord \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><strong>\u00a0puternic acord<\/strong><\/p>\n<ol start=\"3\">\n<li><strong>Am participat cu pl\u0103cere la lec\u021bie<\/strong><\/li>\n<\/ol>\n<p><strong>\u00a0puternic dezacord\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><strong>\u00a0dezacord\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><strong>\u00a0neutru\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><strong>\u00a0acord \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><strong>\u00a0puternic acord<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Angelica \u2013 Ioana T\u0102B\u00ceRC\u0102 \u2013 Liceul Teoretic \u201cIon Heliade R\u0103dulescu\u201d T\u00e2rgovi\u0219te Nicolae \u2013 Radu T\u0102B\u00ceRC\u0102 &#8211; Liceul Teoretic \u201cIon Heliade R\u0103dulescu\u201d T\u00e2rgovi\u0219te &nbsp; PROIECT DIDACTIC Unitatea \u0219colar\u0103: Liceul Teoretic \u201cIon Heliade R\u0103dulescu\u201d T\u00e2rgovi\u0219te Profesori propun\u0103tori: Angelica \u2013 Ioana T\u0102B\u00ceRC\u0102, Nicolae &#8211; Radu T\u0102B\u00ceRC\u0102 Disciplina:\u00a0 INFORMATIC\u0102 Clasa: a XI-a Data: ____________________ Unitatea de \u00eenv\u0103\u0163are: Grafuri neorientate&#8230;<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-911","post","type-post","status-publish","format-standard","hentry","category-infogates"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=\/wp\/v2\/posts\/911","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=911"}],"version-history":[{"count":5,"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=\/wp\/v2\/posts\/911\/revisions"}],"predecessor-version":[{"id":918,"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=\/wp\/v2\/posts\/911\/revisions\/918"}],"wp:attachment":[{"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=911"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=911"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=911"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}