# Disjoint Set Data Structures

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 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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