Added-> DisjointUnion Set by Size (#6514)

* Added-> DisjointUnion Set by Size

* Add tests for DisjointSetUnionBySize

---------

Co-authored-by: Deniz Altunkapan <93663085+DenizAltunkapan@users.noreply.github.com>

src/main/java/com/thealgorithms/datastructures/disjointsetunion/DisjointSetUnionBySize.java

@@ -0,0 +1,83 @@
+package com.thealgorithms.datastructures.disjointsetunion;
+
+/**
+ * Disjoint Set Union (DSU) with Union by Size.
+ * This data structure tracks a set of elements partitioned into disjoint (non-overlapping) subsets.
+ * It supports two primary operations efficiently:
+ *
+ * <ul>
+ *     <li>Find: Determine which subset a particular element belongs to.</li>
+ *     <li>Union: Merge two subsets into a single subset using union by size.</li>
+ * </ul>
+ *
+ * Union by size always attaches the smaller tree under the root of the larger tree.
+ * This helps keep the tree shallow, improving the efficiency of find operations.
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Disjoint-set_data_structure">Disjoint Set Union (Wikipedia)</a>
+ */
+public class DisjointSetUnionBySize<T> {
+    /**
+     * Node class for DSU by size.
+     * Each node keeps track of its parent and the size of the set it represents.
+     */
+    public static class Node<T> {
+        public T value;
+        public Node<T> parent;
+        public int size; // size of the set
+
+        public Node(T value) {
+            this.value = value;
+            this.parent = this;
+            this.size = 1; // initially, the set size is 1
+        }
+    }
+
+    /**
+     * Creates a new disjoint set containing the single specified element.
+     * @param value the element to be placed in a new singleton set
+     * @return a node representing the new set
+     */
+    public Node<T> makeSet(final T value) {
+        return new Node<>(value);
+    }
+
+    /**
+     * Finds and returns the representative (root) of the set containing the given node.
+     * This method applies path compression to flatten the tree structure for future efficiency.
+     * @param node the node whose set representative is to be found
+     * @return the representative (root) node of the set
+     */
+    public Node<T> findSet(Node<T> node) {
+        if (node != node.parent) {
+            node.parent = findSet(node.parent); // path compression
+        }
+        return node.parent;
+    }
+
+    /**
+     * Merges the sets containing the two given nodes using union by size.
+     * The root of the smaller set is attached to the root of the larger set.
+     * @param x a node in the first set
+     * @param y a node in the second set
+     */
+    public void unionSets(Node<T> x, Node<T> y) {
+        Node<T> rootX = findSet(x);
+        Node<T> rootY = findSet(y);
+
+        if (rootX == rootY) {
+            return; // They are already in the same set
+        }
+        // Union by size: attach smaller tree under the larger one
+        if (rootX.size < rootY.size) {
+            rootX.parent = rootY;
+            rootY.size += rootX.size; // update size
+        } else {
+            rootY.parent = rootX;
+            rootX.size += rootY.size; // update size
+        }
+    }
+}
+// This implementation uses union by size instead of union by rank.
+// The size field tracks the number of elements in each set.
+// When two sets are merged, the smaller set is always attached to the larger set's root.
+// This helps keep the tree shallow and improves the efficiency of find operations.