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# l13-sorting - CS112: Data Structures Lecture 13 CS112:...

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CS112: Slides for Prof. Steinberg ʼ s lecture 1 Lecture 13 CS112: Data Structures CS112: Data Structures Lecture 13

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CS112: Slides for Prof. Steinberg ʼ s lecture 2 Lecture 13 Schedule Schedule Monday, August 8: Work on project 4 Wednesday, August 10: Review Monday August 15: Students present Projects 4 (attendance required) Wednesday, August 17: Final exam
CS112: Slides for Prof. Steinberg ʼ s lecture 3 Lecture 13 Review: Shortest Path Review: Shortest Path Dijkstra’s algorithm: to find shortest path from A to B: Build a tree of shortest paths from A Is set of shortest paths really a tree? Suppose not, then must have two shortest paths converge and then diverge A X B C

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CS112: Slides for Prof. Steinberg ʼ s lecture 4 Lecture 13 Dijkstra Dijkstra s s algorithm algorithm Grow a tree of shortest paths from start grow it one edge / vertex at a time But which? Vertex has to be one edge from tree Of edges for a vertex, has to be edge that gives shortest path to start Of vertices one edge from tree, choose the one with the shortest ‘shortest path via tree’
CS112: Slides for Prof. Steinberg ʼ s lecture 5 Lecture 13 Example Example A B C D E F 5 1 7 4 8 1 2 F E 7 A Fringe D 4 A Fringe C 5 A Fringe B 0 -- Tree A Distance Lin K Status Node

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CS112: Slides for Prof. Steinberg ʼ s lecture 6 Lecture 13 Example Example A B C D E F 5 1 7 4 8 1 2 12 C Fringe F E 7 A Fringe D 4 A Tree C 5 A Fringe B 0 -- Tree A Distance Lin K Status Node
CS112: Slides for Prof. Steinberg ʼ s lecture 7 Lecture 13 Example Example A B C D E F 5 1 7 4 8 1 2 12 C Fringe F E 6 B Fringe D 4 A Tree C 5 A Tree B 0 -- Tree A Distance Lin K Status Node

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CS112: Slides for Prof. Steinberg ʼ s lecture 8 Lecture 13 Example Example A B C D E F 5 1 7 4 8 1 2 12 C Fringe F 7 D Fringe E 6 B Tree D 4 A Tree C 5 A Tree B 0 -- Tree A Distance Lin K Status Node
CS112: Slides for Prof. Steinberg ʼ s lecture 9 Lecture 13 Example Example A B C D E F 5 1 7 4 8 1 2 9 E Fringe F 7 D Tree E 6 B Tree D 4 A Tree C 5 A Tree B 0 -- Tree A Distance Lin K Status Node

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CS112: Slides for Prof. Steinberg ʼ s lecture 10 Lecture 13 Example Example A B C D E F 5 1 7 4 8 1 2 9 E Tree F 7 D Tree E 6 B Tree D 4 A Tree C 5 A Tree B 0 -- Tree A Distance Link Status Node
CS112: Slides for Prof. Steinberg ʼ s lecture 11 Lecture 13 Minimum Spanning Tree Minimum Spanning Tree Spanning Tree: a subgraph with All the nodes Some of the edges A tree, I.E., one path between any pair of nodes Minimum spanning tree A spanning tree With minimum total edge weight

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CS112: Slides for Prof. Steinberg ʼ s lecture 12 Lecture 13 A B C D E F 5 1 7 8 1 Not a tree (has
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## This document was uploaded on 11/01/2011 for the course 198 112 at Rutgers.

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l13-sorting - CS112: Data Structures Lecture 13 CS112:...

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