Refer to Chapter 7 of algorithm diagram for details. The original book was written in python, and I wrote it again in PHP, which was slightly improved

Test these three exercises in the book

I found another "difficult" question on the Internet

Upper Code:

class ShortPath{ protected $graph=[];//A graph can be represented only by storing the neighbors corresponding to each node protected $parents=[];//Save the parent relationship, and finally backtrack the shortest path through this array protected $costs;//Cost from start to each node protected $infinity=999999;//Use a large number to represent a positive infinity protected $processed=[];//key of processed node public function __construct($graph) { $this->graph=$graph; //Initialize the parent array, that is, only the neighbors of start are known, that is, the parent of start foreach ($this->graph['start'] as $k=>$v) { $this->parents[$k]='start'; } //Initialize the cost array, that is, only the cost of the neighbor node of start is known, and all other nodes are positive infinite foreach ($this->graph as $k=>$v) { if($k=='start'){ $this->costs=$this->graph['start']; }elseif(empty($this->costs[$k])){ $this->costs[$k]=$this->infinity; } } $this->costs['finish']=$this->infinity; } public function find(){ $nodeKey=$this->findLowestCostNode($this->costs); while ($nodeKey){//As long as there are unprocessed nodes $cost=$this->costs[$nodeKey]; $neighbors=$this->graph[$nodeKey] ?? [];//Take neighbors //Traversing neighbors foreach ($neighbors as $k=> $v) { $newCost=$cost+$v; if($this->costs[$k] > $newCost){ $this->costs[$k]=$newCost;//Update lower overhead $this->parents[$k]=$nodeKey; } } //Debug output echo 'Current node:' .$nodeKey . PHP_EOL; echo 'Neighbours:' . PHP_EOL; print_r($neighbors); echo 'Expenses:' . PHP_EOL; print_r($this->costs); //Now that all neighbors of the node have been processed, mark the node as processed $this->processed[]=$nodeKey; //Find the next node to be processed $nodeKey=$this->findLowestCostNode(); } $this->showResult(); } //Find the shortest one among the unprocessed nodes protected function findLowestCostNode(){ $lowestCost=$this->infinity;//Set positive infinity here so that when you first enter the loop, it must be larger than the first element $lowestCostKey=false;//The key of the shortest path node to return foreach ($this->costs as $k=>$v) { if($v<$lowestCost && !in_array($k,$this->processed)){ $lowestCost=$v; $lowestCostKey=$k; } } return $lowestCostKey; } //Beautify display processing results protected function showResult(){ $path=[]; $key='finish'; //From the end, find the parent and trace back the shortest route while (isset($this->parents[$key])){ array_unshift($path,$key); $key=$this->parents[$key]; } echo 'The shortest path length is:' . $this->costs['finish'] . PHP_EOL; echo 'The route is:start->' . implode('->',$path) . PHP_EOL; } } //Corresponding exercise A $graph1=[ "start"=>[ "a"=>2, "b"=>5, ], "a"=>[ "b"=>8, "d"=>7, ], "b"=>[ "c"=>4, "d"=>2, ], "c"=>[ "finish"=>3, "d"=>6 ], "d"=>[ "finish"=>1 ] ]; //Corresponding Exercise B $graph2=[ "start"=>[ "a"=>10, ], "a"=>[ "c"=>20, ], "b"=>[ "a"=>1, ], "c"=>[ "b"=>1, "finish"=>30, ], ]; //Corresponding exercise C. It can be seen that the algorithm is not suitable for the case with negative weight edges $graph3=[ "start"=>[ "a"=>2, "b"=>2, ], "a"=>[ "c"=>2, "finish"=>2 ], "b"=>[ "a"=>2, ], "c"=>[ "b"=>-100, "finish"=>2, ], ]; //Corresponding to the last question, change v0 in the figure to start and v8 to finish $graph4=[ "start"=>[ "v1"=>1, "v2"=>5, ], "v1"=>[ "start"=>1, "v2"=>3, "v3"=>7, "v4"=>5, ], "v2"=>[ "start"=>5, "v1"=>3, "v4"=>1, ], "v3"=>[ "v1"=>7, "v2"=>2, "v6"=>3, ], "v4"=>[ "v1"=>5, "v2"=>1, "v3"=>2, "v5"=>3, "v6"=>6, "v7"=>9, ], "v5"=>[ "v2"=>6, "v4"=>3, "v7"=>5, ], "v6"=>[ "v3"=>3, "v4"=>6, "v7"=>2, "finish"=>7 ], "v7"=>[ "v4"=>9, "v5"=>5, "v6"=>2, "finish"=>4 ], ]; $obj=new ShortPath($graph4); $obj->find();

Output of the last question

Finally, the pdf version of the book "algorithm diagram" is attached

Link: https://pan.baidu.com/s/1nditk7wayn7c9fz3ldngw password: ij0r