add Dijkstra algorithm

README.md

@@ -77,12 +77,11 @@
    - [广度优先遍历](dataStructure/Graph/Graph.php)
    - [拓扑排序](dataStructure/Graph/Graph.php)
    - [最短路径之Floyd算法](dataStructure/Graph/Graph.php)
+   - [单源最短路径Dijkstra算法](dataStructure/Graph/Graph.php)
 
 
 #### 《剑指Offer》
 
-> 先用PHP解答一遍，稍后Javascript版本的奉上
-
 - 链表
   - [从头到尾打印链表](offer/LinkedList/1.php)
   - [链表中倒数第k个节点](offer/LinkedList/2.php)

dataStructure/Graph/Graph.php

@@ -1,6 +1,9 @@
 <?php
 namespace DataStructure\Graph;
 
+use DataStructure\Spl\SplPriorityQueue;
+
+
 class Graph
 {
     public static function BFS(&$graph, int $start, array $visited) : \SplQueue
@@ -152,7 +155,7 @@ protected static function topologicalSortV2(array $matrix): \SplQueue
         return $sorted;
     }
 
-    public static function FW(array $graph): array
+    public static function floydWarshall(array $graph): array
     {
         $dist = [];
         $dist = $graph;
@@ -168,5 +171,53 @@ public static function FW(array $graph): array
 
         return $dist;
     }
+
+    public static function Dijkstra(array $graph, string $source, string $target)
+    {
+        $dist = [];
+        $prev = [];
+
+        $queue = new \SplPriorityQueue();
+
+        foreach ($graph as $vertex => $weight) {
+            $dist[$vertex] = PHP_INT_MAX;
+            $prev[$vertex] = null;
+            $queue->insert($vertex, min($weight));
+        }
+
+        $dist[$source] = 0;
+
+        while (!$queue->isEmpty()) {
+            $current = $queue->extract();
+
+            if (!empty($graph[$current])) {
+                foreach($graph[$current] as $vertex => $weight) {
+                    //如果源点到$vertx的距离大于到源点到$current的距离再加上从$current到$vertex的距离
+                    if ($dist[$current] + $weight < $dist[$vertex]) {
+                        //修正源点到$vertex的最短距离
+                        $dist[$vertex] = $dist[$current] + $weight;
+                        //设置最短距离中的上一个节点
+                        $prev[$vertex] = $current;
+                    }
+                }
+            }
+        }
+
+        $stack = new \SplStack();
+        $distance = 0;
+
+        while(isset($prev[$target]) && $prev[$target]) {
+            $stack->push($target);
+            $distance += $graph[$target][$prev[$target]];
+            $target = $prev[$target];
+        }
+
+        if ($stack->isEmpty()) {
+            return ["distance" => 0, "path" => $stack];
+        } else {
+            $stack->push($source);
+            return ["distance" => $distance, "path" => $stack];
+        }
+    }
 }
 

tests/DataStructure/GraphTest.php

@@ -90,7 +90,7 @@ public function testTopologicalSort()
 
     }
 
-    public function testFW()
+    public function testFloydWarshall()
     {
         $totalVertices = 5;
         $graph = [];
@@ -107,9 +107,36 @@ public function testFW()
         $graph[4][1] = $graph[1][4] = 10;
         $graph[3][4] = $graph[4][3] = 20;
 
-        $distance = Graph::FW($graph);
+        $distance = Graph::floydWarshall($graph);
 
         $this->assertEquals(20, $distance[0][4]);
         $this->assertEquals(10, $distance[3][2]);
     }
+
+    public function testDijkstra()
+    {
+        $graph = [
+            'A' => ['B' => 3, 'C' => 5, 'D' => 9],
+            'B' => ['A' => 3, 'C' => 3, 'D' => 4, 'E' => 7],
+            'C' => ['A' => 5, 'B' => 3, 'D' => 2, 'E' => 6, 'F' => 3],
+            'D' => ['A' => 9, 'B' => 4, 'C' => 2, 'E' => 2, 'F' => 2],
+            'E' => ['B' => 7, 'C' => 6, 'D' => 2, 'F' => 5],
+            'F' => ['C' => 3, 'D' => 2, 'E' => 5],
+        ];
+
+        $source = "A";
+        $target = "F";
+
+        $result = Graph::Dijkstra($graph, $source, $target);
+        extract($result);
+
+        $this->assertEquals($distance, 8);
+
+        $way = [];
+        while (!$path->isEmpty()) {
+            $way[] = $path->pop();
+        }
+
+        $this->assertEquals(['A', 'C', 'F'], $way);
+    }
 }