Valid Quick Find implementation of the DisjointSet Graph data structure

graphs/disjointset_quickfind.php

@@ -0,0 +1,77 @@
+<?php
+/**
+ * This is the quick find implementation of the DisjoinSet graph data structure
+ *
+ * DisjointSet's can quickly determine if 2 vertices are connected.
+ * Each index in the root array represents a vert
+ * Each value in the root array represents the value
+ *
+ * QuickFind implementation Time Complexity:
+ * finding the root node is O(1)
+ * unioning 2 vertices is O(N)
+ *
+ * Typically there is a find() method, but we don't need it since we're using $root directly
+ */
+class QuickFind_DisjointSet
+{
+    /**
+     * The root array maintains a pointer to each nodes' root value
+     * Each node is represented as the $root's indexes
+     * e.g. $root[4] = 0 means node 4's root node is 0
+     */
+    public array $root = [];
+
+    /**
+     * @param int $size - The size is the number of nodes in the graph
+     */
+    function __construct(int $size) {
+        for($i = 0; $i < $size; $i++)
+            $this->root [] = $i;
+    }
+
+    /**
+     * Pass in the array's index. The arrays index represents a node in the graph.
+     * Union is how we connect them. We connect them by pointing them to the same root.
+     * @param int $x
+     * @param int $y
+     */
+    public function union(int $x, int $y): void {
+        $root_x = $this->root[$x];
+        $root_y = $this->root[$y];
+        if($root_x != $root_y) {
+            for($i = 0; $i < count($this->root); $i++) {
+                if($this->root[$i] == $root_y) {
+                    $this->root[$i] = $root_x;
+                }
+            }
+        }
+    }
+
+    public function connected(int $x, int $y): string {
+        return ($this->root[$x] == $this->root[$y]) ? 'YES' : 'NO';
+    }
+}
+
+
+function test_one() {
+    # 0, 1, 2, 3, 4
+    $qf = new QuickFind_DisjointSet(5);
+
+    # 1, 4 | 0, 2 | 3
+    # Three disjoint sets (i.e. islands) get created
+    $qf->union(1, 4);
+    $qf->union(0, 2);
+
+    echo "\n";
+    echo 'Are 1 and 4 connected? ' . $qf->connected(1, 4) . "\n";
+    echo 'Are 0 and 4 connected? ' . $qf->connected(0, 4) . "\n";
+    echo 'Are 3 and 4 connected? ' . $qf->connected(3, 4) . "\n";
+}
+
+test_one();
+
+//TODO: create more tests
+
+
+
+// end of file