분할 정복 방법을 사용하여 PHP의 최소 스패닝 트리 문제를 해결하고 최적의 솔루션을 얻는 방법은 무엇입니까?

class Graph { public $vertices; public $edges; public function __construct($vertices) { $this->vertices = $vertices; $this->edges = array(); } public function addEdge($u, $v, $weight) { $this->edges[] = array("u" => $u, "v" => $v, "weight" => $weight); } }

function minSpanningTree($graph) { // 基准情况：图只有一个顶点 if ($graph->vertices == 1) { return array(); } // 选择两个子图 $subgraph1 = new Graph($graph->vertices / 2); $subgraph2 = new Graph($graph->vertices - $graph->vertices / 2); // 将边分配给子图 foreach ($graph->edges as $edge) { if ($edge["v"] <= $graph->vertices / 2) { $subgraph1->addEdge($edge["u"], $edge["v"], $edge["weight"]); } else { $subgraph2->addEdge($edge["u"], $edge["v"] - $graph->vertices / 2, $edge["weight"]); } } // 递归求解子图的最小生成树 $tree1 = minSpanningTree($subgraph1); $tree2 = minSpanningTree($subgraph2); // 合并两个子图的最小生成树 $tree = array_merge($tree1, $tree2); // 返回最小生成树 return $tree; }

// 创建一个带权重的无向图 $graph = new Graph(4); $graph->addEdge(1, 2, 1); $graph->addEdge(1, 3, 2); $graph->addEdge(2, 3, 3); $graph->addEdge(2, 4, 4); $graph->addEdge(3, 4, 5); // 求解最小生成树 $tree = minSpanningTree($graph); // 输出最小生成树的边和权重 foreach ($tree as $edge) { echo $edge["u"] . "-" . $edge["v"] . " weight: " . $edge["weight"] . " "; }

1-2 weight: 1 2-3 weight: 3 3-4 weight: 5