Undirected Graphs -- Data structure

1. Undirected Graphs

average degree:

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2. DFS, depth first search

example trace:

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The output is 0-2-1-3-5-4.

DFS implementation:

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Proposition A. DFS marks all the vertices connected to a given source in time proportional to the sum of their degrees.

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Why the preprocessing time is E + V?
For example:

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The source is s. s has adjacent vertices A, C, D.
The trace will be:
Stack: s a b c d
output: s a b c d e v

3. BFS, breadth-first search:
   Depth-first search. Put unvisited vertices on a stack.
   Breadth-first search. Put unvisited vertices on a queue.
   Shortest path. Find path from s to t that uses fewest number of edges.

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