Questions tagged [disjoint-sets]

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walk / traverse a disjoint set that has union rank and path compression

I'm studying CLRS section 21.3, which introduces a union rank + path-compressed implementation of disjoint set. The implementations of MAKE-SET, UNION, LINK, and FIND-SET on p 571 of the book all work ...
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Definition of Disjointness for binary strings

Basically, most of the definition for disjointness are such that $DISJ(A, B) = 1$ if $A \cap B = \emptyset $ and $DISJ(A, B) = 0$ for other case. My confusion is how is $0$'s influence in here. For ...
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What's the best non-amortized disjoint set?

In practice, the amortized O(α(n)) data structure is good for every case. But if I want to be pedantic and require each operation to be under a certain time complexity, what's the currently known best ...
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Difficulty in few steps in proof of “Amortized cost of $\text{Find-Set}$ operation is $\Theta(\alpha(n))$”assuming union by rank, path compression

I was reading the section of data structures for disjoint sets from the text Introduction to Algorithms by Cormen et. al .I faced difficulty in understanding few steps in the proof of the lemma as ...
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1answer
308 views

Runtime difference bewteen Union by Rank and Union by Size for union-find

I was studying Union Find, and according to Wikipedia, there are 2 types of union: union by rank and Union by size. My question is, what is the runtime difference between the two (if any)? Intuitively,...
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Amortized analysis for disjoint sets' find-set(x) function (from CLRS)

I start off by apologizing for the fact that I don't really know how to use latex/markdown. My question, however, is directly from the Introduction To Algorithms book by Cormen et al. The topic ...
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Benefits of linked lists over forests for disjoint sets

CLRS discusses two specific data structures for disjoint sets: Single linked lists, where each set is represented by a single linked list, and each node has two pointers, one to the list head and ...