Disjoint Set Data Structures

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A disjoint-set data structure is defined as one that keeps track of a set of elements partitioned into a number of disjoint (non-overlapping) subsets.

A union-find algorithm is an algorithm that performs two useful operations on such a data structure:

Find: Determine which subset a particular element is in. This can determine if two elements are in the same subset.
Union: Join two subsets into a single subset. Here first we have to check if the two subsets belong to the same set. If not, then we cannot perform union.

Applications of Disjoint set Union:

S. No.	Problem	Practice link
1	Kruskal’s Minimum Spanning Tree Algorithm.	solve
2	Job Sequencing Problem.	solve
3	Cycle Detection	solve
4	Number of pairs	solve
5	City With the Smallest Number of Neighbors at a Threshold Distance	solve

Practice problems for DSU:

Problem	Difficulty
Difference between Smallest and Largest Component of the graph after each Query	Easy
Equation satisfiability check	Easy
Evaluate the Fractions	Medium
Substring segment query & modification	Medium
Maximum number of soldier in a team	Medium
Minimum difference between components of the Graph after each query	Hard
Minimum cost to provide water	Hard
Minimum operations for adjacent E and E+1 pairing	Hard

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