E

M

```
package com.thealgorithms.datastructures.disjointsetunion;
/**
* Disjoint Set Union or DSU is useful for solving problems related to connected components,
* cycle detection in graphs, and maintaining relationships in disjoint sets of data.
* It is commonly employed in graph algorithms and problems.
*
* @see <a href="https://en.wikipedia.org/wiki/Disjoint-set_data_structure">Disjoint Set Union</a>
*/
public class DisjointSetUnion<T> {
/**
* Creates a new node of DSU with parent initialised as same node
*/
public Node<T> makeSet(final T x) {
return new Node<T>(x);
}
/**
* Finds and returns the representative (root) element of the set to which a given element belongs.
* This operation uses path compression to optimize future findSet operations.
*/
public Node<T> findSet(Node<T> node) {
while (node != node.parent) {
node = node.parent;
}
return node;
}
/**
* Unions two sets by merging their representative elements. The merge is performed based on the rank of each set
* to ensure efficient merging and path compression to optimize future findSet operations.
*/
public void unionSets(final Node<T> x, final Node<T> y) {
Node<T> nx = findSet(x);
Node<T> ny = findSet(y);
if (nx == ny) {
return; // Both elements already belong to the same set.
}
// Merging happens based on rank of node, this is done to avoid long chaining of nodes and reduce time
// to find root of the component. Idea is to attach small components in big, instead of other way around.
if (nx.rank > ny.rank) {
ny.parent = nx;
} else if (ny.rank > nx.rank) {
nx.parent = ny;
} else {
// Both sets have the same rank; choose one as the parent and increment the rank.
ny.parent = nx;
nx.rank++;
}
}
}
```