MPT calculus

src/MaterializedPath/FixedPathCalculator.php

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+<?php
+
+declare(strict_types=1);
+
+namespace Dakujem\Oliva\MaterializedPath;
+
+/**
+ * A calculus for fixed-length materialized path trees.
+ *
+ * It can be used to transform paths to vectors and vice versa.
+ *
+ * Note 💡:
+ *   This calculator is OPINIONATED and assumes a trivial MPT
+ *   where sibling enumerators (sequence numbers) are used to describe a node's position within the tree.
+ *
+ *
+ * The most important setting is the number of characters to store a single position within a path,
+ * a.k.a. the level width.
+ *
+ * Recommended values: 3 and above.
+ * - 3 characters means a maximum of    46_656 siblings per node (36^3)
+ * - 4 characters means a maximum of 1_679_616 siblings per node (36^4)
+ * - 5 characters ~ over 60 million nodes (36^5)
+ * - 6 characters ~ over  2 billion nodes (36^6)
+ *
+ * The number of levels is not limited in theory, but in practice it will be limited by storage restrictions, like column width.
+ * Higher number means that each node can have more children, but takes up more space.
+ *
+ * If IDs are going to be used in the paths, then the length must be used accordingly.
+ * In such a case the delimited variant may be a better choice.
+ * But remember that the delimited variant either requires a storage that supports natural sort (MySQL/MariaDB do not)
+ * and a more convoluted sorting conditions using splits, or requires the use of a second column to store sequence/priority.
+ *
+ * @author Andrej Rypak <xrypak@gmail.com>
+ */
+final class FixedPathCalculator
+{
+    /**
+     * Number of characters to store a single position within a path,
+     * with one position for each level of depth.
+     *
+     * If this value is changed, the tree paths must be recalculated.
+     */
+    private int $charsPerPosition;
+
+    private bool $base36;
+
+    public function __construct(
+        int $charsPerPosition,
+        bool $base36 = true,
+    ) {
+        $this->charsPerPosition = $charsPerPosition;
+        $this->base36 = $base36;
+    }
+
+    /**
+     * Recalculate a path string into a numeric vector.
+     * A vector is a sequence of indexes from the tree's root to a node.
+     * ```
+     * ""        -->       []
+     * "000"     -->      [0]
+     * "00c001"  -->  [12, 1]
+     * ```
+     */
+    public function pathToVector(string $path): array
+    {
+        if ('' === $path) {
+            return [];
+        }
+        return array_map(
+            fn(string $v) => self::posToNum($v),
+            str_split($path, $this->charsPerPosition),
+        );
+    }
+
+    /**
+     * Recalculate a numeric vector into a path string.
+     * ```
+     *      []  -->  ""
+     *     [0]  -->  "000"
+     * [12, 1]  -->  "00c001"
+     * ```
+     */
+    public function vectorToPath(array $vector): string
+    {
+        return implode(
+            '',
+            array_map(fn(int $v) => self::numToPos($v), $vector),
+        );
+    }
+
+    /**
+     * Convert a string of a single position into a vector element.
+     * ```
+     * 000 -->  0
+     * 001 -->  1
+     * 00c --> 12
+     * ```
+     */
+    public function posToNum(string $position): int
+    {
+        if (!$this->base36) {
+            return (int)$position;
+        }
+        return (int)base_convert($position, 36, 10);
+    }
+
+    /**
+     * Convert a numeric vector element to a position string.
+     * ```
+     *  0 --> 000
+     *  1 --> 001
+     * 12 --> 00c
+     * ```
+     */
+    public function numToPos(int $element): string
+    {
+        if (!$this->base36) {
+            return (string)$element;
+        }
+        $x = base_convert((string)$element, 10, 36);
+        return str_pad($x, $this->charsPerPosition, '0', STR_PAD_LEFT);
+    }
+
+    /**
+     * Calculate the depth of a node with the given path.
+     */
+    public function pathToDepth(string $path): int
+    {
+        $depth = strlen($path) / $this->charsPerPosition;
+        if (!is_int($depth)) {
+            throw new InvalidTreePath('The given tree path "' . $path . '" is invalid. The path`s length is expected to be a multiple of ' . $this->charsPerPosition . '.');
+        }
+        return $depth;
+    }
+
+    /**
+     * Calculate the path length for a given depth.
+     *
+     * Note: This method has no equivalent for the delimited MPT variant where the path length is not fixed.
+     */
+    public function depthToPathLength(int $depth): int
+    {
+        return $depth * $this->charsPerPosition;
+    }
+}

src/MaterializedPath/InvalidTreePath.php

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+<?php
+
+declare(strict_types=1);
+
+namespace Dakujem\Oliva\MaterializedPath;
+
+use RuntimeException;
+use Throwable;
+
+/**
+ * @author Andrej Rypak <xrypak@gmail.com>
+ */
+final class InvalidTreePath extends RuntimeException
+{
+    public function __construct($message = null, $code = null, Throwable $previous = null)
+    {
+        parent::__construct($message ?? 'The given string is not a valid tree path.', $code, $previous);
+    }
+}