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17-50: Dijkstra Running TimeTotal running time:Sum <strong>of</strong>:Time for initializationTime for executing all calls tominUnknownVertexTime for executing all distance / path updates= Θ(V + V 2 + (V + E)) = Θ(V 2 )
17-51: Improving DijkstraCan we do better than Θ(V 2 )For dense graphs, we can’t do betterTo ensure that the shortest path to all verticesis computed, need to look at all edges in thegraphA dense graph can have Θ(V 2 ) edgesFor sparse graphs, we can do betterWhere should we focus our attention?
Page 3 and 4: 17-1: Shortest Path ExampleShortest
Page 5: 17-3: Single Source Shortest PathTo
Page 8 and 9: 17-6: Single Source Shortest PathIf
Page 10 and 11: 17-8: Single Source Shortest Path2A
Page 12 and 13: 17-10: Single Source Shortest PathN
Page 14 and 15: 17-12: Single Source Shortest PathA
Page 16 and 17: 17-14: Single Source Shortest PathA
Page 18 and 19: 17-16: Single Source Shortest Path2
Page 24 and 25: 17-22: Dijkstra’s Algorithm Examp
Page 32 and 33: 17-30: Dijkstra’s AlgorithmAfter
Page 42 and 43: 17-40: Dijkstra Codevoid Dijkstra(E
Page 44 and 45: 17-42: Dijkstra Running TimeTime fo
Page 46 and 47: 17-44: Dijkstra Running TimeTotal t
Page 48 and 49: 17-46: Dijkstra Running TimeTotal #
Page 50 and 51: 17-48: Dijkstra Running TimeTotal r
Page 54 and 55: 17-52: Improving DijkstraCan we do
Page 56 and 57: 17-54: Improving DijkstraTo improve
Page 58 and 59: 17-56: Rearranging the heapTotal ti
Page 60 and 61: 17-58: Improving DijkstraCreate a n
Page 62 and 63: 17-60: Improved? Dijkstra TimeDon
Page 64 and 65: 17-62: All-Source Shortest PathWhat
Page 66 and 67: 17-64: All-Source Shortest PathWhat
Page 68 and 69: 17-66: Floyd’s AlgorithmVertices
Page 70 and 71: 17-68: k-path Examples0115 357211Sh
Page 72 and 73: 17-70: Floyd’s AlgorithmShortest
Page 74 and 75: 17-72: Floyd’s AlgorithmIf we had
Page 76 and 77: 17-74: Floyd’s AlgorithmUse a dou
Page 78: 17-76: Floyd’s AlgorithmWe’ve o

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