Merge pull request #7 from xi-project/topological-sort

Topological sort

Author: puppe0

.gitignore

@@ -1,5 +1,4 @@
 composer.phar
 composer.lock
-tests/phpunit.xml
 vendor
 .idea

composer.json

@@ -15,11 +15,19 @@
             "name": "Joonas Pajunen",
             "email": "[email protected]",
             "role": "Developer"
+        },
+        {
+            "name": "Martin Pärtel",
+            "email": "[email protected]",
+            "role": "Developer"
         }
     ],
     "require": {
         "php": ">=5.3.3"
     },
+    "require-dev": {
+        "phpunit/phpunit": "3.7.*"
+    },
     "autoload": {
         "psr-0": {
             "Xi\\Algorithm": "library/"

library/Xi/Algorithm/TopologicalSort.php

@@ -0,0 +1,76 @@
+<?php
+namespace Xi\Algorithm;
+
+/**
+ * Implements topological sorting.
+ *
+ * Topological sorting means sorting the nodes in a directed acyclic graph into a list such
+ * that if a node X points to a node Y then Y appears before X in the list.
+ * This is useful for things like resolving dependencies.
+ *
+ * http://en.wikipedia.org/wiki/Topological_sorting
+ */
+class TopologicalSort
+{
+    /**
+     * @param  array                     $edges An array of scalars to arrays of scalars, representing the edges in the graph.
+     * @return array                     An array of nodes in the graph.
+     * @throws \InvalidArgumentException if the graph has a cycle or $deps is in an invalid format
+     */
+    public static function apply(array $edges)
+    {
+        $allNodes = self::allNodes($edges);
+
+        // We do a depth-first search.
+        // A node is marked with 1 when first seen and with 2 when recursion returns from it.
+        // If we meet a node marked 0 then we recursively add its descendants to the list before adding it to the list.
+        // If we meet a node marked 1 then we've found a cycle, which is an error.
+        // If we meet a node marked 2 then it's already on the list and we return.
+        $unmarkedNodes = array_fill_keys($allNodes, null);
+        $marks = array_fill_keys($allNodes, 0);
+        $result = array();
+
+        $visit = function ($node) use ($edges, &$visit, &$marks, &$unmarkedNodes, &$result) {
+            $mark = $marks[$node];
+            if ($mark === 0) {
+                $marks[$node] = 1;
+                unset($unmarkedNodes[$node]);
+
+                foreach ((isset($edges[$node]) ? $edges[$node] : array()) as $next) {
+                    $visit($next);
+                }
+
+                $marks[$node] = 2;
+                $result[] = $node;
+            } elseif ($mark === 1) {
+                throw new \InvalidArgumentException("The graph has a cycle involving node $node");
+            }
+        };
+
+        // We try each node as a starting point since we don't know which node (if any) is the root node.
+        // (if the graph has unconnected subgraphs then their order in the list is undefined).
+        while (!empty($unmarkedNodes)) {
+            $node = key($unmarkedNodes);
+            unset($unmarkedNodes[$node]);
+            $visit($node);
+        }
+
+        return $result;
+    }
+
+    private static function allNodes(array $deps)
+    {
+        $allNodes = array();
+        foreach ($deps as $node => $others) {
+            if (!is_array($others)) {
+                throw new \InvalidArgumentException('Dependencies should be given as arrays, not single elements.');
+            }
+            $allNodes[] = $node;
+            foreach ($others as $other) {
+                $allNodes[] = $other;
+            }
+        }
+
+        return array_unique($allNodes);
+    }
+}

tests/Xi/Tests/Algorithm/TopologicalSortTest.php

@@ -0,0 +1,95 @@
+<?php
+namespace Xi\Algorithm;
+
+class TopologicalSortTest extends \PHPUnit_Framework_TestCase
+{
+    /**
+     * @test
+     */
+    public function simpleCase()
+    {
+        $edges = array(
+            'B' => array('C', 'D'),
+            'A' => array('B'),
+            'C' => array('D'),
+        );
+
+        for ($i = 0; $i < 100; ++$i) {
+            $edges = self::shuffleGraphSpec($edges);
+            $this->assertEquals(array('D', 'C', 'B', 'A'), TopologicalSort::apply($edges));
+        }
+    }
+
+    /**
+     * @test
+     * @dataProvider provider
+     */
+    public function test(array $edges)
+    {
+        for ($i = 0; $i < 100; ++$i) {
+            $edges = self::shuffleGraphSpec($edges);
+            $sorted = TopologicalSort::apply($edges);
+            $this->verify($sorted, $edges);
+        }
+    }
+
+    public function provider()
+    {
+        return array(
+            array(array(
+                'B' => array('C', 'D'),
+                'A' => array('B'),
+                'C' => array('D'),
+            )),
+
+            // Wikipedia's example
+            array(array(
+                7 => array(11, 8),
+                5 => array(11),
+                3 => array(8, 10),
+                11 => array(2, 9, 10),
+                8 => array(9)
+            ))
+        );
+    }
+
+    /**
+     * @test
+     * @expectedException \InvalidArgumentException
+     */
+    public function throwsOnCycle()
+    {
+        $edges = array(
+            'B' => array('C', 'D'),
+            'A' => array('B'),
+            'C' => array('D'),
+            'D' => array('A')
+        );
+
+        TopologicalSort::apply($edges);
+    }
+
+    private function shuffleGraphSpec(array $array)
+    {
+        $keys = array_keys($array);
+        shuffle($keys);
+        $result = array();
+        foreach ($keys as $key) {
+            $result[$key] = $array[$key];
+            shuffle($result[$key]);
+        }
+
+        return $result;
+    }
+
+    private function verify(array $sorted, array $edges)
+    {
+        foreach ($edges as $left => $rights) {
+            foreach ($rights as $right) {
+                $leftIndex = array_search($left, $sorted);
+                $rightIndex = array_search($right, $sorted);
+                $this->assertLessThan($leftIndex, $rightIndex);
+            }
+        }
+    }
+}

tests/bootstrap.php

@@ -5,4 +5,4 @@
 wget http://getcomposer.org/composer.phar
 php composer.phar install --dev
 ");
-}
+}

tests/phpunit.xml.dist renamed to tests/phpunit.xml

@@ -0,0 +1,10 @@
+#!/usr/bin/env watchr
+def run_phpunit
+    system('echo; echo; echo; echo; cd tests/ ; ../vendor/bin/phpunit .')
+end
+
+Dir.chdir(File.dirname(File.dirname(__FILE__)))
+
+watch('.*') { run_phpunit }
+
+run_phpunit