### FP Graph Algorithms

##### September 4, 2015

Manipulating graphs has traditionally been seen as a place where imperative programming reigns supreme. Tikhon Jelvis begs to differ, and shows a trick where graph traversal can be expressed by a form of pattern matching. After explaining the approach he simulates how it works on a sample graph.

### Summary

- Traditionally graph algorithms are seen as one of the things that are really hard in functional programming
- To some extent it is because the graph algorithms and representations you’ve learned have a very imperative bent
- One insight into making a graph algorithm functional is to find a way to use pattern matching on a graph structure
- What does this even mean?
- Start with what we already know: pattern matching is easy on lists or trees
- Translates to any algebraic data type really
- But there is no algebraic data type for graphs
- Graphs are not inductive — there is more than one way to build them up or take them apart

- But we can pretend! We can treat graphs as if they were inductive
- So how do we break a graph apart in a pattern match?
- We’ll use a a “view”
`match :: Node -> Graph -> Maybe View`

- Depth first search
- We don’t update flags on nodes to say which we have visited
- Our recursion just happens on a subgraph that does not re-visit nodes
- Example of the operation on a specific graph

- You can find the implementation in the Functional Graph Library
- Slides for this talk are available here
- For an example of generating mazes using functional programming, check out this blog post
- Q&A