L18-shortestPaths

1 42 a b a b c 9

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Unformatted text preview: ∅ 9 DE:9:9 ( < , ) ) %&'() < ̸ = ∅ $" % ← F 9E:9:9 ( < ) !"# "%42 v ∈ 7>?A% B $" '! > Av B = ∞ *&)+ > Av B ← > A% B + 5 9 DE:9:9 ( < , v) ) C 5 * Theorem 4 Given any weighted, directed graph G = (V, E ) with non-negative weights and source s, dijkstra(G, s) terminates with du = (s, v ) for all v ⇤ V . J # - 5 88 "8 @ 9 , J J J K%# 12(& *2%* < 4(#101*1 (+ '",*04"1 &0*2 > '%3)"1. 9 • <#3> 5 (, 8 '%3)"1. ;+ 87 $0++", ?> 5 %#$ %33 1-%33"1* %," !,1*. • 9 ... 9 9 + 5 9 + 5 ... 9 + 5 9 !0#4" "%42 '",*"H 6"*1 % !#0*" > '%3)" %* -(1* (#4"7 '%3)"1 %1106#"$ *( '",*04"1 %," -(#(*(#04%33> 0#4,"%10#6 ('", *0-". L4*)%3 G,((+ (+ 4(,,"4*#"11 01 % ?0* *,04I0",. !"" ?((I. @/! -%> #(* ,"%42 %33 '",*04"1. bfs b 8 d 8 g 7 2 5 e 9 3 9 11 3 a 12 c 1 i...
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