Lec 22 UnionFind & Min Spanning Trees & Priority Queues

Union:

Takes two nodes, and finds their roots

If diff trees, makes the root of one the other one's parent

union(node1, node2):
root1 = find(node1) 
root2 = find(node2)
if root1 != root2:
if root1.rank > root2.rank: # the rank is the height
    root2.parent = root1
else:
    root1.parent = root2
    if root1.rank == root2.rank: # in case they came to be the same rank
    root2.rank++

Priority queue: a list storing things in an order
- Uses comparable protocol, not most recently added
Spanning tree
- Can get from any node to any other node
Kruskal's
- Create a forest, where each vertex is a tree
- Create sorted set S containing all edges in graph
  - Priority Queue
- While S nonempty, f not spanning
  - Pop smallest into spanning tree, unless causes cycle
  - Use Unionfind to see if they're one tree, and if connected
- Just because each node has an edge doesn't mean it's done
Unionfind has directed edges, but MST are weighted and undirected