Section 9 Graph search algorithms. Breadth-first search Idea: Let |n| denote a distance of node n from the initial node. We visit nodes in order: All.

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Presentation transcript:

Section 9 Graph search algorithms

Breadth-first search Idea: Let |n| denote a distance of node n from the initial node. We visit nodes in order: All nodes n such that |n| = 1 All nodes n such that |n| = 2 All nodes n such that |n| = 3 All nodes n such that |n| = 4 All nodes n such that |n| = 5....

BFS: Water analogy BFS is similar to pouring water! We pour the water on the first node. When there is too much water in it, the nodes adjacent to it start to fill. And so on...

BFS

Depth-first search Idea: We go as deep as possible. Visit recursively all the adjacent nodes of the source node.

DFS: Labyrinth analogy DFS is similar to going through labyrinth. We walk leaving a thread behind us. Whenever we have the choice of path, we choose the leftmost one. If we reach a dead-end or the place already marked, we go back to the first unvisited place.

DFS

BFS + DFS Stunning fact - we can implement both of them using the same code, changing only the underlying SequenceStructure.

BFS + DFS initialize toDo with the node we are starting from while (!empty(toDo)) { remove a node n from toDo visit(n) put all unvisited neighbours of n on toDo }

BFS + DFS MethodtoDo implementation DFSStack BFSQueue Best-first searchPriority queue

Best-first search In situation when we have a weight function f on nodes, which tells us which node to visit first. BFS, but visiting neighbours according to the fumction f. Just use priority queue!

WWW as a graph Nodes - Edges -

WWW as a graph Nodes - webpages Edges - links

WWW as a graph How to write a program downloading a whole web page?

WWW as a graph How to write a program downloading a whole web page? Use graph search! Which one?

WWW as a graph How to write a program downloading a whole web page? Use graph search! Which one? BFS!

WWW as a graph Interesting questions: What is the diameter of the graph? (probably about 20) What is its structure? What are the efficient search algorithms? - Google, Altavista What is a „typical” node? Many more...

Bus/train map as a graph Nodes - Edges -

Bus map as a graph Nodes - bus/train stops/stations Edges - there’s an edge from one node to the other if there is a bus/train, which takes you from one stop to the other. How to find how to reach a bus stop/city?

Survival skills How to find a way out in the labyrinth? Optimistic version: With a thread of string. Pessimistic version: Without a thread.

With a thread Use DFS - using a thread to go back to the yet unvisited paths.

Without a thread A heuristics which often works - always turn left.