Merge pull request #153 from rzarno/master

Bellman-Ford

Author: darwinz

DIRECTORY.md

@@ -23,6 +23,7 @@
   * [Stack](./DataStructures/Stack.php)
 
 ## Graphs
+  * [Bellmanford](./Graphs/BellmanFord.php)
   * [Breadthfirstsearch](./Graphs/BreadthFirstSearch.php)
   * [Depthfirstsearch](./Graphs/DepthFirstSearch.php)
 

Graphs/BellmanFord.php

@@ -0,0 +1,52 @@
+<?php
+
+class Edge
+{
+    public $start;
+    public $end;
+    public int $weight;
+}
+
+/**
+ * The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the
+ * other vertices in a weighted digraph.
+ * (https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm).
+ *
+ * @author Michał Żarnecki https://github.com/rzarno
+ * @param array $verticies An array of verticies names
+ * @param Edge[] $edges An array of edges
+ * @return string $start The starting vertex
+ */
+function bellmanFord(array $verticesNames, array $edges, string $start, bool $verbose = false)
+{
+    $vertices = array_combine($verticesNames, array_fill(0, count($verticesNames), PHP_INT_MAX));
+
+    $change = true;
+    $round = 1;
+    while ($change) {
+        if ($verbose) {
+            echo "round $round\n";
+        }
+        $change = false;
+        foreach ($vertices as $vertice => $minWeight) {
+            if ($verbose) {
+                echo "checking vertice $vertice\n";
+            }
+            if ($start === $vertice) {
+                $vertices[$vertice] = 0;
+            }
+
+            foreach ($edges[$vertice] as $edge) {
+                if ($vertices[$edge->end] > $vertices[$vertice] + $edge->weight) {
+                    if ($verbose) {
+                        echo "replace $vertice " . $vertices[$edge->end] . " with " . $vertices[$vertice] + $edge->weight . "\n ";
+                    }
+                    $vertices[$edge->end] = $vertices[$vertice] + $edge->weight;
+                    $change = true;
+                }
+            }
+        }
+        $round++;
+    }
+    return $vertices;
+}

tests/Graphs/BellmanFordTest.php

@@ -0,0 +1,48 @@
+<?php
+
+require_once __DIR__ . '/../../vendor/autoload.php';
+require_once __DIR__ . '/../../Graphs/BellmanFord.php';
+
+use PHPUnit\Framework\TestCase;
+
+class BellmanFordTest extends TestCase
+{
+    public function testBellmanFord()
+    {
+        $edgesRaw = [
+            ['S', 8, 'E'],
+            ['E', 1, 'D'],
+            ['D', -1, 'C'],
+            ['S', 10, 'A'],
+            ['D', -4, 'A'],
+            ['A', 2, 'C'],
+            ['C', -2, 'B'],
+            ['B', 1, 'A'],
+        ];
+        $vertices = ['S', 'A', 'B', 'C', 'D', 'E',];
+
+        #prepare array of edges listed by edge start to simplify Bellman-Ford updating weights of other edges
+        $edges = [];
+        foreach ($edgesRaw as $edgeRaw) {
+            $edge = new Edge();
+            $edge->start = $edgeRaw[0];
+            $edge->end = $edgeRaw[2];
+            $edge->weight = $edgeRaw[1];
+            if (!isset($edges[$edgeRaw[0]])) {
+                $edges[$edgeRaw[0]] = [];
+            }
+            $edges[$edgeRaw[0]][] = $edge;
+        }
+
+        $result = bellmanFord($vertices, $edges, 'S');
+
+        $this->assertEquals($result, [
+            'S' => 0,
+            'A' => 5,
+            'B' => 5,
+            'C' => 7,
+            'D' => 9,
+            'E' => 8
+        ]);
+    }
+}