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Unformatted text preview: 1 CMSC 132: ObjectOriented Programming II Graphs & Graph Traversals Department of Computer Science University of Maryland, College Park Reading Read Chapter 12 in the Koffman text (Chapter 10 in the second edition) 2 3 Graph data structures review A manytomany relationship between elements Each element may have multiple predecessors Each element may have multiple successors many successors many predecessors 3 4 Graph definitions A node or vertex is an element of a graph Its state is a list of the adjacent (neighbor or successor) nodes An edge is a connection between two nodes Its state is the nodes that are its endpoints A 4 A B 5 More graph definitions A directed graph has directed edges An undirected graph has undirected edges 5 A B A B 6 More graph definitions A weighted graph has a weight or cost associated with each edge 6 7 More graph definitions A path is a sequence of nodes n 1 , n 2 , … n k in a graph such that an edge exists between each pair of nodes n i , n i+1 in the path Example: A, B, C is a path A, E, D is not a path 7 8 More graph definitions A cycle is a path that ends back at the starting node Examples: A, E, A A, B, C, D, E, A A simple path is a path that has no cycles An acyclic graph is a graph that has no cycles 8 9 More graph definitions In a connected graph every node in the graph is reachable from every other node in the graph An unconnected graph has several disjoint components 9 10 Some graph operations Adding or removing nodes or edges Traversal (search) of a graph refers to visiting each node in it, usually visiting each node just once Some type of computation is typically performed at each node Two approaches: Breadthfirst search (BFS) Depthfirst search (DFS) 10 11 Breadthfirst search (BFS) Approach visit all neighbors of a node first View as a series of expanding circles Keep the list of nodes to visit in a queue Example traversal: 1. N 2. A, C, B 3. E, G, H, I, J 4. D, F 11 12 Breadthfirst tree traversal Example traversals starting from 1 1 2 3 4 5 6 7 1 3 2 6 5 4 7 1 2 3 5 6 4 7 left to right right to left random 12 13 Traversal orders Order of neighbors For a tree, the children can be ordered from left to right For a graph left to right doesn’t make much sense Each node just has a set of neighbors and predecessors; there is no order among edges For breadthfirst search Visit all nodes at distance k from starting point...
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This note was uploaded on 11/16/2011 for the course CMSC 132 taught by Professor Paduaperez during the Fall '08 term at Maryland.
 Fall '08
 PADUAPEREZ

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