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Drumuri minime si drumuri maxime intr -un graf

Drumuri minime si drumuri maxime intr -un graf. Consideram un graf orientat G=(V,U) cu n varfuri,in care fiecarui arc, ii asociem un cost (nr. intreg ) , semnificatia acestui cost poate fi de exemplu : costul deplasarii unui autoturism ..;

iphigenie-kadin
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Drumuri minime si drumuri maxime intr -un graf

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  1. Drumuriminimesidrumurimaximeintr-un graf

  2. Consideram un graforientat G=(V,U) cu n varfuri,in care fiecarui arc, ii asociem un cost (nr. intreg) , semnificatiaacestui cost poatefi de exemplu: costuldeplasariiunuiautoturism..; Matriceacosturiloreste o matrice A cu n liniisi m coloane care poateavea 2 forme: c, dacaexista arc de cost c>0 de la i la j; A= 0, dacai=j; +∞,daca nu exista arc; F1

  3. F2 c, dacaexista arc de cost de la i la j; A= 0, dacai=j; -∞, daca nu exista arc de cost de la i la j;

  4. V={(1,2) (1,4) (2,4) (3,2) (3,4)} u1 u2 u3 u4 u5 u1=7; u3=4; u5=2; u2=3; u4=6; 0 7 +∞ 3 A= +∞ 0 +∞ 4 +∞ 6 0 2 +∞ +∞ +∞ 0 1 2 3 4

  5. Un drum este minim atuncicandlungimealuiesteceamaimica si se numeste drum de cost minim. Un drum este maxim candlungimealuiesteceamai mare si se numeste drum de cost maxim. Exista 3 posibilitati de a determinadrumuloptim: -sursasigura, destinatieunica (intre 2 noduri date); -sursaunica , destinatiemultipla (Dijkstra); -sursamultipla, destinatiemultipla (Roy-Floyd);

  6. V={(1,2)(1,4)(2,3)(3,2)(4,3)(5,1)} u1 u2 u3 u4 u5 u6 u1= 4; u2=6; u3=9; u4=1 ; u5=7; u6=3; 1 2 5 4 3

  7. 0 4 +∞ 6 +∞ +∞ 0 1 +∞ +∞pentrudrumuri A= +∞ 9 0 7 +∞ minime +∞ +∞ +∞ 0 +∞ 3 +∞ +∞ +∞ 0 0 4 -∞ 6 -∞ pentrudrumuri -∞ 0 1 -∞ -∞ maxime A= -∞ 9 0 7 -∞ -∞ -∞ -∞ 0 -∞ 3 -∞ -∞ -∞ 0

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