Implemented Disjoint Set (Union-Find) Data Structure

DIRECTORY.md

@@ -22,6 +22,7 @@
   * [Queue](./DataStructures/Queue.php)
   * [Singlylinkedlist](./DataStructures/SinglyLinkedList.php)
   * [Stack](./DataStructures/Stack.php)
+  * [DisjointSets](./DataStructures/DisjointSets/DisjointSet.php)
 
 ## Graphs
   * [Bellmanford](./Graphs/BellmanFord.php)

DataStructures/DisjointSets/DisjointSet.php

@@ -0,0 +1,40 @@
+<?php
+
+use DataStructures\DisjointSets\DisjointSetNode;
+
+class DisjointSet
+{
+    /**
+     * Finds the representative of the set that contains the node.
+     */
+    public function findSet(DisjointSetNode $node): DisjointSetNode
+    {
+        if ($node !== $node->parent) {
+            $node->parent = $this->findSet($node->parent);    // Path compression: make the parent point directly to the root
+        }
+        return $node->parent;
+    }
+
+    /**
+     * Unites the sets that contain x and y.
+     */
+    public function unionSet(DisjointSetNode $nodeX, DisjointSetNode $nodeY): void
+    {
+        $rootX = $this->findSet($nodeX);
+        $rootY = $this->findSet($nodeY);
+
+        if ($rootX === $rootY) {
+            return; // They are already in the same set
+        }
+
+        // Union by rank: attach the smaller tree under the larger tree
+        if ($rootX->rank > $rootY->rank) {
+            $rootY->parent = $rootX;
+        } else {
+            $rootX->parent = $rootY;
+            if ($rootX->rank === $rootY->rank) {
+                $rootY->rank += 1;
+            }
+        }
+    }
+}

DataStructures/DisjointSets/DisjointSetNode.php

@@ -0,0 +1,16 @@
+<?php
+
+namespace DataStructures\DisjointSets;
+
+class DisjointSetNode
+{
+    public mixed $data;     # PHP 8.0^ . Otherwise, define with annotations:  @var int|string|float|null
+    public int $rank;
+    public DisjointSetNode $parent;
+
+    public function __construct(mixed $data = NULL) {
+        $this->data = $data;
+        $this->rank = 0;
+        $this->parent = $this;  // Initialize parent to itself
+    }
+}

tests/DataStructures/DisjointSetTest.php

@@ -0,0 +1,85 @@
+<?php
+
+namespace DataStructures;
+
+use DataStructures\DisjointSets\DisjointSetNode;
+use DisjointSet;
+use PHPUnit\Framework\TestCase;
+
+class DisjointSetTest extends TestCase
+{
+    private DisjointSet $ds;
+    private array $nodes;
+
+    protected function setUp(): void
+    {
+        $this->ds = new DisjointSet();
+        $this->nodes = [];
+
+        // Create 20 nodes
+        for ($i = 0; $i < 20; $i++) {
+            $this->nodes[$i] = new DisjointSetNode($i);
+        }
+
+        // Perform union operations to form several disjoint sets
+        $this->ds->unionSet($this->nodes[0], $this->nodes[1]);
+        $this->ds->unionSet($this->nodes[1], $this->nodes[2]);
+
+        $this->ds->unionSet($this->nodes[3], $this->nodes[4]);
+        $this->ds->unionSet($this->nodes[4], $this->nodes[5]);
+
+        $this->ds->unionSet($this->nodes[6], $this->nodes[7]);
+        $this->ds->unionSet($this->nodes[7], $this->nodes[8]);
+
+        $this->ds->unionSet($this->nodes[9], $this->nodes[10]);
+        $this->ds->unionSet($this->nodes[10], $this->nodes[11]);
+
+        $this->ds->unionSet($this->nodes[12], $this->nodes[13]);
+        $this->ds->unionSet($this->nodes[13], $this->nodes[14]);
+
+        $this->ds->unionSet($this->nodes[15], $this->nodes[16]);
+        $this->ds->unionSet($this->nodes[16], $this->nodes[17]);
+
+        $this->ds->unionSet($this->nodes[18], $this->nodes[19]);
+
+    }
+
+    public function testFindSet(): void
+    {
+        // Nodes in the same sets should have the same root
+        for ($i = 0; $i < 6; $i++) {
+            for ($j = 0; $j < 6; $j++) {
+                $setI = $this->ds->findSet($this->nodes[$i]);
+                $setJ = $this->ds->findSet($this->nodes[$j]);
+
+                if ($this->inSameSet($i, $j)) {
+                    $this->assertSame($setI, $setJ, "Nodes $i and $j should be in the same set");
+                } else {
+                    $this->assertNotSame($setI, $setJ, "Nodes $i and $j should be in different sets");
+                }
+            }
+        }
+    }
+
+    private function inSameSet(int $i, int $j): bool
+    {
+        // Define which nodes should be in the same set based on union operations
+        $sets = [
+            [0, 1, 2],      // Set A
+            [3, 4, 5],      // Set B
+            [6, 7, 8],      // Set C
+            [9, 10, 11],    // Set D
+            [12, 13, 14],   // Set E
+            [15, 16, 17],   // Set F
+            [18, 19]        // Set G
+        ];
+
+        foreach ($sets as $set) {
+            if (in_array($i, $set) && in_array($j, $set))
+                return true;
+        }
+
+        return false;
+    }
+
+}