algorithm - Union-Find operations on a tree? -

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can please explain answer in bold? how it's done?

below sequence of 4 union-find operations (with weighted-union , full com- pression) led following up-tree. last 2 operations?

answer: union(d,a), union(b,c), union(d/a,b/c),find(b/c).

enter image description here

the notation used because of sets.

let apply 4 operations:

union(d,a) leads following tree:

   d   /

union(b,c) leads following tree:

   b   /  c

now union(d/a,b/c) means because d , belong same set, not matter first argument is, can d or can a. because b , c belong same set, not matter second argument is, can b or can c, the result same.

the result after third operation:

   d   / \    b       \        c

now because compression allowed, find(c) operation result in tree:

   d   /|\   b c

if fourth operation find(b), tree remain same, because when apply compression after find operation, make nodes encountered in path upto root immediate child of root, since not encounter c, not able make c immediate child of d, in final tree.

correct answer

the correct sequence of 4 operations is:

union(d,a), union(b,c), union(d/a,b/c),find(c).

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