From 65d76e11ea1ecc19585b2fdb00cd5d4c13cf3a52 Mon Sep 17 00:00:00 2001
From: Dennis Eichhorn <spl1nes.com@googlemail.com>
Date: Sun, 26 Jan 2020 12:06:11 +0100
Subject: [PATCH] continue graph implementation

---
 Stdlib/Graph/BinaryTree.php      | 226 ---------------------------
 Stdlib/Graph/Graph.php           | 231 +++++++++++++++++++++++++--
 Stdlib/Graph/Tree.php            | 257 -------------------------------
 tests/Stdlib/Graph/GraphTest.php |   1 -
 4 files changed, 215 insertions(+), 500 deletions(-)
 delete mode 100644 Stdlib/Graph/BinaryTree.php
 delete mode 100644 Stdlib/Graph/Tree.php

diff --git a/Stdlib/Graph/BinaryTree.php b/Stdlib/Graph/BinaryTree.php
deleted file mode 100644
index e615644d8..000000000
--- a/Stdlib/Graph/BinaryTree.php
+++ /dev/null
@@ -1,226 +0,0 @@
-<?php
-/**
- * Orange Management
- *
- * PHP Version 7.4
- *
- * @package   phpOMS\Stdlib\Graph
- * @copyright Dennis Eichhorn
- * @license   OMS License 1.0
- * @version   1.0.0
- * @link      https://orange-management.org
- */
-declare(strict_types=1);
-
-namespace phpOMS\Stdlib\Graph;
-
-/**
- * Tree class.
- *
- * @package phpOMS\Stdlib\Graph
- * @license OMS License 1.0
- * @link    https://orange-management.org
- * @since   1.0.0
- */
-class BinaryTree extends Tree
-{
-    /**
-     * Invert the tree
-     *
-     * @return BinaryTree
-     *
-     * @since 1.0.0
-     */
-    public static function invert($list) : self
-    {
-        if (empty($list->getNodes())) {
-            return $list;
-        }
-
-        $left = $list->getLeft();
-        $list->setLeft($list->invert($list->nodes[1]));
-        $list->setRight($list->invert($left));
-
-        return $list;
-    }
-
-    /**
-     * Get left node of a node.
-     *
-     * @param Node $base Tree node
-     *
-     * @return null|Node Left node
-     *
-     * @since 1.0.0
-     */
-    public function getLeft(Node $base) : ?Node
-    {
-        $neighbors = $base->getNeighbors($base);
-
-        // todo: index can be wrong, see setLeft/setRight
-        return $neighbors[0] ?? null;
-    }
-
-    /**
-     * Get right node of a node.
-     *
-     * @param Node $base Tree node
-     *
-     * @return null|Node Right node
-     *
-     * @since 1.0.0
-     */
-    public function getRight(Node $base) : ?Node
-    {
-        $neighbors = $this->getNeighbors($base);
-
-        // todo: index can be wrong, see setLeft/setRight
-        return $neighbors[1] ?? null;
-    }
-
-    /**
-     * Set left node of node.
-     *
-     * @param Node $base Base node
-     * @param Node $left Left node
-     *
-     * @return BinaryTree
-     *
-     * @since 1.0.0
-     */
-    public function setLeft(Node $base, Node $left) : self
-    {
-        if ($this->getLeft($base) === null) {
-            $this->addNodeRelative($base, $left);
-            // todo: doesn't know that this is left
-            // todo: maybe need to add numerics to edges?
-        } else {
-            // todo: replace node
-            $a = 2;
-        }
-
-        return $this;
-    }
-
-    /**
-     * Set right node of node.
-     *
-     * @param Node $base  Base node
-     * @param Node $right Right node
-     *
-     * @return BinaryTree
-     *
-     * @since 1.0.0
-     */
-    public function setRight(Node $base, Node $right)  : self
-    {
-        if ($this->getRight($base) === null) {
-            $this->addNodeRelative($base, $right);
-            // todo: doesn't know that this is right
-            // todo: maybe need to add numerics to edges?
-        } else {
-            // todo: replace node
-            $a = 2;
-        }
-
-        return $this;
-    }
-
-    /**
-     * Perform action on tree in in-order.
-     *
-     * @param Node     $node     Tree node
-     * @param \Closure $callback Task to perform on node
-     *
-     * @return void
-     *
-     * @since 1.0.0
-     */
-    public function inOrder(Node $node, \Closure $callback) : void
-    {
-        $this->inOrder($this->getLeft($node), $callback);
-        $callback($node);
-        $this->inOrder($this->getRight($node), $callback);
-    }
-
-    /**
-     * Get nodes in vertical order.
-     *
-     * @param Node   $node               Tree node
-     * @param int    $horizontalDistance Horizontal distance
-     * @param Node[] $order              Ordered nodes by horizontal distance
-     *
-     * @return void
-     *
-     * @since 1.0.0
-     */
-    private function getVerticalOrder(Node $node, int $horizontalDistance, array &$order) : void
-    {
-        if (!isset($order[$horizontalDistance])) {
-            $order[$horizontalDistance] = [];
-        }
-
-        $order[$horizontalDistance][] = $node;
-        $left                         = $this->getLeft($node);
-        $right                        = $this->getRight($node);
-
-        if ($left !== null) {
-            $this->getVerticalOrder($left, $horizontalDistance - 1, $order);
-        }
-
-        if ($right !== null) {
-            $this->getVerticalOrder($right, $horizontalDistance + 1, $order);
-        }
-    }
-
-    /**
-     * Perform action on tree in vertical-order.
-     *
-     * @param Node     $node     Tree node
-     * @param \Closure $callback Task to perform on node
-     *
-     * @return void
-     *
-     * @since 1.0.0
-     */
-    public function verticalOrder(Node $node, \Closure $callback) : void
-    {
-        $order = [];
-        $this->getVerticalOrder($node, 0, $order);
-
-        foreach ($order as $level) {
-            foreach ($level as $node) {
-                $callback($node);
-            }
-        }
-    }
-
-    /**
-     * Check if tree is symmetric.
-     *
-     * @param null|Node $node1 Tree node1
-     * @param null|Node $node2 Tree node2 (optional, can be different tree)
-     *
-     * @return bool True if tree is symmetric, false if tree is not symmetric
-     *
-     * @since 1.0.0
-     */
-    public function isSymmetric(Node $node1 = null, Node $node2 = null) : bool
-    {
-        if (($node1 === null && $node2 === null)
-            || $node1->isEqual($node2)
-        ) {
-            return true;
-        } elseif ($node1 === null || $node2 === null) {
-            return false;
-        }
-
-        $left1  = $this->getLeft($node1);
-        $right1 = $this->getRight($node1);
-
-        $left2  = $node2 !== null ? $this->getLeft($node1) : null;
-        $right2 = $node2 !== null ? $this->getRight($node1) : null;
-
-        return $this->isSymmetric($left1, $right2) && $this->isSymmetric($right1, $left2);
-    }
-}
diff --git a/Stdlib/Graph/Graph.php b/Stdlib/Graph/Graph.php
index a4d9763ef..ddb3078fb 100644
--- a/Stdlib/Graph/Graph.php
+++ b/Stdlib/Graph/Graph.php
@@ -21,6 +21,19 @@ namespace phpOMS\Stdlib\Graph;
  * @license OMS License 1.0
  * @link    https://orange-management.org
  * @since   1.0.0
+ *
+ * @todo Orange-Management/phpOMS#10
+ *      * Count all paths between 2 nodes
+ *      * Return all paths between 2 nodes
+ *      * Find cycles using graph coloring
+ *      * Find a negative cycle
+ *      * Find cycles with n length
+ *      * Find cycles with odd length
+ *      * Find shortest path between 2 nodes
+ *      * Find longest path between 2 nodes
+ *      * Find islands
+ *      * Find all unreachable nodes
+ *      * Check if strongly connected
  */
 class Graph
 {
@@ -32,6 +45,14 @@ class Graph
      */
     protected $nodes = [];
 
+    /**
+     * Directed
+     *
+     * @var   bool
+     * @since 1.0.0
+     */
+    protected $isDirected = false;
+
     /**
      * Set node to graph.
      *
@@ -62,6 +83,20 @@ class Graph
         return $this->nodes[$key] ?? null;
     }
 
+    /**
+     * Graph has node
+     *
+     * @param mixed $key Node key
+     *
+     * @return bool
+     *
+     * @since 1.0.0
+     */
+    public function hasNode($key) : bool
+    {
+        return isset($this->nodes[$key]);
+    }
+
     /**
      * Get graph nodes
      *
@@ -74,6 +109,51 @@ class Graph
         return $this->nodes;
     }
 
+    /**
+     * Is directed graph
+     *
+     * @return bool
+     *
+     * @since 1.0.0
+     */
+    public function isDirected() : bool
+    {
+        return $this->isDirected;
+    }
+
+    /**
+     * Set graph directed
+     *
+     * @param bool $directed Is directed?
+     *
+     * @return void
+     *
+     * @since 1.0.0
+     */
+    public function setDirected(bool $directed) : void
+    {
+        $this->isDirected = $directed;
+    }
+
+    /**
+     * Get graph/edge costs
+     *
+     * @return int|float
+     *
+     * @since 1.0.0
+     */
+    public function getCost()
+    {
+        $edges = $this->getEdges();
+        $costs = 0;
+
+        foreach ($edges as $edge) {
+            $costs += $edge->getWeight();
+        }
+
+        return $costs;
+    }
+
     /**
      * Get graph edges
      *
@@ -180,37 +260,161 @@ class Graph
     /**
      * Get minimal spanning tree using Kruskal's algorithm.
      *
-     * @return Tree
+     * @return Graph
      *
      * @since 1.0.0
      */
-    public function getKruskalMinimalSpanningTree() : Tree
+    public function getKruskalMinimalSpanningTree() : self
     {
-        return new Tree();
+        $graph = new self();
+        $edges = $this->getEdges();
+
+        \usort($edges, Edge::class . '::compare');
+
+        foreach ($edges as $edge) {
+            if ($graph->hasNode($edge->getNode1()->getId())
+                && $graph->hasNode($edge->getNode2()->getId())
+            ) {
+                continue;
+            }
+
+            /** @var Node $node1 */
+            $node1 = $graph->hasNode($edge->getNode1()->getId()) ? $graph->getNode($edge->getNode1()->getId()) : clone $edge->getNode1();
+            /** @var Node $node2 */
+            $node2 = $graph->hasNode($edge->getNode2()->getId()) ? $graph->getNode($edge->getNode2()->getId()) : clone $edge->getNode2();
+
+            $node1->setNodeRelative($node2);
+
+            if (!$graph->hasNode($edge->getNode1()->getId())) {
+                $graph->setNode($node1);
+            }
+
+            if (!$graph->hasNode($edge->getNode2()->getId())) {
+                $graph->setNode($node2);
+            }
+        }
+
+        return $graph;
     }
 
     /**
-     * Get minimal spanning tree using Prim's algorithm
+     * Has cycle in graph.
      *
-     * @return Tree
+     * @return bool
      *
      * @since 1.0.0
      */
-    public function getPrimMinimalSpanningTree() : Tree
+    public function hasCycle() : bool
     {
-        return new Tree();
+        return $this->isDirected ? $this->hasCycleDirected() : $this->hasCycleUndirected();
     }
 
     /**
-     * Get circles in graph.
+     * Has cycle in directed graph.
      *
-     * @return array
+     * @return bool
      *
      * @since 1.0.0
      */
-    public function getCircle() : array
+    private function hasCycleDirected() : bool
     {
-        return [];
+        $visited  = [];
+        $recStack = [];
+
+        foreach ($this->nodes as $node) {
+            if ($this->hasDirectedCyclicUtil($node->getId(), $visited, $recStack)) {
+                return true;
+            }
+        }
+
+        return false;
+    }
+
+    /**
+     * Has cycle in directed graph.
+     *
+     * @param string $node    Node name
+     * @param array  $visited Visited nodes
+     * @param array  $stack   Recursion stack
+     *
+     * @return bool
+     *
+     * @since 1.0.0
+     */
+    private function hasDirectedCyclicUtil(string $node, array &$visited, array &$stack) : bool
+    {
+        if (isset($visited[$node]) && $visited[$node]) {
+            $stack[$node] = false;
+
+            return false;
+        }
+
+        $visited[$node]  = true;
+        $stack[$node]    = true;
+
+        $neighbors = $this->nodes[$node]->getNeighbors();
+        foreach ($neighbors as $neighbor) {
+            if ((!isset($visited[$neighbor->getId()]) || !$visited[$neighbor->getId()])
+                && $this->hasDirectedCyclicUtil($neighbor->getId(), $visited, $stack)
+            ) {
+                return true;
+            } elseif (isset($stack[$neighbor->getId()]) && $stack[$neighbor->getId()]) {
+                return true;
+            }
+        }
+
+        $stack[$node] = false;
+
+        return false;
+    }
+
+    /**
+     * Has cycle in undirected graph.
+     *
+     * @return bool
+     *
+     * @since 1.0.0
+     */
+    private function hasCycleUndirected() : bool
+    {
+        $visited = [];
+
+        foreach ($this->nodes as $node) {
+            if (!isset($visited[$node->getId()]) && $this->hasUndirectedCyclicUtil($node->getId(), $visited, null)) {
+                return true;
+            }
+        }
+
+        return false;
+    }
+
+    /**
+     * Has cycle in undirected graph.
+     *
+     * @param string      $node    Node name
+     * @param array       $visited Visited nodes
+     * @param null|string $parent  Parent node
+     *
+     * @return bool
+     *
+     * @since 1.0.0
+     */
+    private function hasUndirectedCyclicUtil(string $node, array &$visited, ?string $parent) : bool
+    {
+        $visited[$node] = true;
+
+        $neighbors = $this->nodes[$node]->getNeighbors();
+        foreach ($neighbors as $neighbor) {
+            if (!isset($visited[$neighbor->getId()])) {
+                if ($this->hasUndirectedCyclicUtil($neighbor->getId(), $visited, $node)) {
+                    return true;
+                }
+            } elseif ($neighbor->getId() !== $parent) {
+                return true;
+            }
+        }
+
+        return false;
     }
 
     /**
@@ -411,7 +615,6 @@ class Graph
      */
     public function isConnected() : bool
     {
-        // todo: implement
         return true;
     }
 
@@ -424,7 +627,6 @@ class Graph
      */
     public function getUnconnected() : array
     {
-        // todo: implement
         // get all unconnected sub graphs
 
         return [];
@@ -439,7 +641,6 @@ class Graph
      */
     public function isBipartite() : bool
     {
-        // todo: implement
         return true;
     }
 
@@ -452,7 +653,6 @@ class Graph
      */
     public function isTriangleFree() : bool
     {
-        // todo: implement
         return true;
     }
 
@@ -465,7 +665,6 @@ class Graph
      */
     public function isCircleFree() : bool
     {
-        // todo: implement
         return true;
     }
 }
diff --git a/Stdlib/Graph/Tree.php b/Stdlib/Graph/Tree.php
deleted file mode 100644
index dc67718e4..000000000
--- a/Stdlib/Graph/Tree.php
+++ /dev/null
@@ -1,257 +0,0 @@
-<?php
-/**
- * Orange Management
- *
- * PHP Version 7.4
- *
- * @package   phpOMS\Stdlib\Graph
- * @copyright Dennis Eichhorn
- * @license   OMS License 1.0
- * @version   1.0.0
- * @link      https://orange-management.org
- */
-declare(strict_types=1);
-
-namespace phpOMS\Stdlib\Graph;
-
-/**
- * Tree class.
- *
- * @package phpOMS\Stdlib\Graph
- * @license OMS License 1.0
- * @link    https://orange-management.org
- * @since   1.0.0
- */
-class Tree extends Graph
-{
-    /**
-     * Root node.
-     *
-     * @var   Node
-     * @since 1.0.0
-     */
-    private $root = null;
-
-    /**
-     * Constructor.
-     *
-     * @since 1.0.0
-     */
-    public function __construct()
-    {
-        $root = new Node();
-        parent::addNode($root);
-    }
-
-    /**
-     * Add a note relative to a node.
-     *
-     * @param Node $base Base node
-     * @param Node $node Node to add
-     *
-     * @return Tree
-     *
-     * @since 1.0.0
-     */
-    public function addRelativeNode(Node $base, Node $node) : self
-    {
-        parent::addNode($node);
-        parent::addEdge(new Edge($base, $node));
-
-        return $this;
-    }
-
-    /**
-     * Get maximum tree depth.
-     *
-     * @param Node $node Tree node
-     *
-     * @return int
-     *
-     * @since 1.0.0
-     */
-    public function getMaxDepth(Node $node = null) : int
-    {
-        $currentNode = $node ?? $this->root;
-
-        if ($currentNode === null) {
-            return 0;
-        }
-
-        $depth     = 1;
-        $neighbors = $this->getNeighbors($currentNode);
-
-        foreach ($neighbors as $neighbor) {
-            $depth = \max($depth, $depth + $this->getMaxDepth($neighbor));
-        }
-
-        return $depth;
-    }
-
-    /**
-     * Get minimum tree path.
-     *
-     * @param Node $node Tree node
-     *
-     * @return int
-     *
-     * @since 1.0.0
-     */
-    public function getMinDepth(Node $node = null) : int
-    {
-        $currentNode = $node ?? $this->root;
-
-        if ($currentNode === null) {
-            return 0;
-        }
-
-        $depth     = [];
-        $neighbors = $this->getNeighbors($currentNode);
-
-        foreach ($neighbors as $neighbor) {
-            $depth[] = $this->getMaxDepth($neighbor);
-        }
-
-        $depth = empty($depth) ? 0 : $depth;
-
-        return \min($depth) + 1;
-    }
-
-    /**
-     * Perform task on tree nodes in level order.
-     *
-     * @param Node     $node     Tree node
-     * @param \Closure $callback Task to perform
-     *
-     * @return void
-     *
-     * @since 1.0.0
-     */
-    public function levelOrder(Node $node, \Closure $callback) : void
-    {
-        $depth = $this->getMaxDepth();
-
-        for ($i = 1; $i < $depth; ++$i) {
-            $nodes = $this->getLevel($i);
-            callback($nodes);
-        }
-    }
-
-    /**
-     * Check if node is leaf.
-     *
-     * @param Node $node Tree node
-     *
-     * @return bool
-     *
-     * @since 1.0.0
-     */
-    public function isLeaf(Node $node) : bool
-    {
-        return \count($this->getEdgesOfNode($node)) === 1;
-    }
-
-    /**
-     * Get all nodes of a specific level.
-     *
-     * @param int  $level Level to retrieve
-     * @param Node $node  Tree node
-     *
-     * @return Node[]
-     *
-     * @since 1.0.0
-     */
-    public function getLevelNodes(int $level, Node $node) : array
-    {
-        --$level;
-        $neighbors = $this->getNeighbors($node);
-        $nodes     = [];
-
-        if ($level === 1) {
-            return $neighbors;
-        }
-
-        foreach ($neighbors as $neighbor) {
-            \array_merge($nodes, $this->getLevelNodes($level, $neighbor));
-        }
-
-        return $nodes;
-    }
-
-    /**
-     * Check if the tree is full.
-     *
-     * @param int $type Child nodes per non-leaf node
-     *
-     * @return bool
-     *
-     * @since 1.0.0
-     */
-    public function isFull(int $type) : bool
-    {
-        if (\count($this->edges) % $type !== 0) {
-            return false;
-        }
-
-        foreach ($this->nodes as $node) {
-            $neighbors = \count($this->getNeighbors($node));
-
-            if ($neighbors !== $type && $neighbors !== 0) {
-                return false;
-            }
-        }
-
-        return true;
-    }
-
-    /**
-     * Perform action on tree in pre-order.
-     *
-     * @param Node     $node     Tree node
-     * @param \Closure $callback Task to perform on node
-     *
-     * @return void
-     *
-     * @since 1.0.0
-     */
-    public function preOrder(Node $node, \Closure $callback) : void
-    {
-        if (\count($this->nodes) === 0) {
-            return;
-        }
-
-        $callback($node);
-        $neighbors = $this->getNeighbors($node);
-
-        foreach ($neighbors as $neighbor) {
-            // todo: get neighbors needs to return in ordered way
-            $this->preOrder($neighbor, $callback);
-        }
-    }
-
-    /**
-     * Perform action on tree in post-order.
-     *
-     * @param Node     $node     Tree node
-     * @param \Closure $callback Task to perform on node
-     *
-     * @return void
-     *
-     * @since 1.0.0
-     */
-    public function postOrder(Node $node, \Closure $callback) : void
-    {
-        if (\count($this->nodes) === 0) {
-            return;
-        }
-
-        $neighbors = $this->getNeighbors($node);
-
-        foreach ($neighbors as $neighbor) {
-            // todo: get neighbors needs to return in ordered way
-            $this->postOrder($neighbor, $callback);
-        }
-
-        $callback($node);
-    }
-}
diff --git a/tests/Stdlib/Graph/GraphTest.php b/tests/Stdlib/Graph/GraphTest.php
index 3f242b9e1..62a58b9f8 100644
--- a/tests/Stdlib/Graph/GraphTest.php
+++ b/tests/Stdlib/Graph/GraphTest.php
@@ -50,7 +50,6 @@ class GraphTest extends \PHPUnit\Framework\TestCase
         self::assertTrue($graph->isCircleFree());
 
         self::assertEquals([], $graph->getBridges());
-        self::assertEquals([], $graph->getCircle());
         self::assertEquals([], $graph->getFloydWarshallShortestPath());
         self::assertEquals([], $graph->getDijkstraShortestPath());
         self::assertEquals([], $graph->depthFirstTraversal());