Up-Trees
• (not as much work as it looks)
• Perform Disjoint Union-Find operations on Up-Tree with
path compression and using weight (# of nodes) in merges.
• Starting with empty tree.
• Keep track of (sub)tree weight, and pointers into tree
(pointers isn’t too hard)
• Vaguely have a sense of # of operations (e.g. edge
traversals)
• For items: a,b,c,d,e,f,g,h,i,j,k
• Union (a,b).  Union (b,c).  Union (d,e).  Union (d,f).
Union (d,j).  Union (d,k).  Union (e,g).  Union (h,i).  Union
(c,h).  Union (c,f).  Find (i).  Find (b).  Find (c).  Find (i).
Find (h).