lecture_02_graphs-pathfinding.txt

graphs and path-finding

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this is the advanced class

graphs
algorithms

types of graphs
1. directed
2. weighted

algorithms
- traversals/searches/tree-growing
	-bfs, dfs
	-dijkstra's

dijkstra's and bfs

-breadth-first search (bfs)
starting at a single node, search all neighbors
search nodes a distace 2 away
repeat until goal is found
process involves a queue

implementation

storing a graph
-list of edges
	edge[]
	arrayList<edge>
-adjacency list
	list<node>[]
	List<list<node>>

adjacency matrix

adjecency list is preferably in almost every case unless your algorithm depends on a different data structure
easiest way is like so:
arrayList<arrayList<node>> graph = new arrayList<arrayList<node>>
they easily let you find nodes that are connected to a specific node
neighbors are stored directly 
for (node adj : graph...
equivalent ways to represent adjacency lists
	-arrays, hashmaps of lists, using sets instead of list

basic bfs structure:
queue of nodes to process
set of visited nodes
each turn, process one node
	-add neighbors which haven't been visited to the queue
	
queue<node> queue = new arrayDeque<node>();
set<node> visited = new Hashset<Node();
queue.offer(start);

usage in competitive programming:
-what's the runtime of a typical bfs?
-processes each node once for sure
-how about edges?
O(v+E)
V is number of nodes, E is number of edges
sometimes E can be O(v^2), read problem carefully
when do you use it?
looking for shortest paths in an unweighted graph
general graph traversal (dfs also works)
processing levels in increasing distance