A complete tutorial on implementing graph theory algorithms in PHP

This article introduces the steps to implement graph theory algorithms using PHP. Algorithms include breadth-first search (BFS), depth-first search (DFS), and Dijkstra's algorithm, which can be used to solve real-world problems such as social network analysis and path planning.

Complete tutorial on implementing graph theory algorithms using PHP

Introduction

Graph Theory plays a vital role in computer science, and it is widely used in fields such as social network analysis, path planning, and scheduling optimization. In this tutorial, we'll take an in-depth look at the steps to implement the most common graph theory algorithms using PHP.

What is a picture?

A graph is a data structure consisting of two sets: Vertices (representing elements in the graph) and Edges (representing the connections between vertices) connect). Graphs can be represented using adjacency lists or adjacency matrices.

Graph theory algorithm

Breadth First Search (BFS)

BFS starts from the starting vertex and visits all adjacencies in sequence vertices, then visit the adjacent vertices of these adjacent vertices, and so on.

// PHP 代码示例

function BFS($graph, $start) {
  $visited = [];  // 已访问的顶点
  $queue = [$start];  // 队列，用于广度优先遍历
  
  while (!empty($queue)) {
    $current = array_shift($queue);  // 从队列中取出当前访问的顶点
    if (isset($visited[$current])) {
      continue; // 如果当前顶点已访问，则跳过
    }
    
    $visited[$current] = true;  // 标记顶点已访问
    echo $current . "\n";  // 输出当前顶点

    // 将当前顶点的邻接顶点添加到队列中
    foreach ($graph[$current] as $neighbor) {
      if (!isset($visited[$neighbor])) {
        $queue[] = $neighbor;
      }
    }
  }
}

Depth First Search (DFS)

DFS is similar to BFS, but it explores the graph in a depth-first manner. It starts at the starting vertex, continues deeper into adjacent vertices that have not yet been visited, until it can explore no further, and then falls back to adjacent vertices that have not yet been fully explored.

// PHP 代码示例

function DFS($graph, $start) {
  $visited = [];  // 已访问的顶点
  $stack = [$start];  // 栈，用于深度优先遍历
  
  while (!empty($stack)) {
    $current = array_pop($stack);  // 从栈中取出当前访问的顶点
    if (isset($visited[$current])) {
      continue; // 如果当前顶点已访问，则跳过
    }
    
    $visited[$current] = true;  // 标记顶点已访问
    echo $current . "\n";  // 输出当前顶点

    // 将当前顶点的邻接顶点添加到栈中
    foreach ($graph[$current] as $neighbor) {
      if (!isset($visited[$neighbor])) {
        $stack[] = $neighbor;
      }
    }
  }
}

**Dykstra's algorithm

Dykstra's algorithm is used to find the shortest path from a specified source vertex to all other vertices in the graph.

// PHP 代码示例

function Dijkstra($graph, $start) {
  $distances = [];  // 顶点到源顶点的距离
  $visited = [];  // 已访问的顶点
  
  // 初始化
  foreach ($graph as $vertex => $edges) {
    $distances[$vertex] = ($vertex === $start) ? 0 : INF;
  }
  
  while (!empty($visited)) {
    $current = min($distances, $visited);  // 查找距离源顶点最近的未访问顶点
    $visited[$current] = true;  // 标记顶点已访问
    
    foreach ($graph[$current] as $neighbor => $weight) {
      $new_distance = $distances[$current] + $weight;
      if ($new_distance < $distances[$neighbor]) {
        $distances[$neighbor] = $new_distance;
      }
    }
  }

  return $distances;  // 返回顶点到源顶点的最短路径
}

Practical cases

Many practical problems can be solved using graph theory algorithms. For example, we can use BFS to find the shortest path in a social network, or use Dijkstra's algorithm to plan the fastest route from one city to another.

Conclusion

This tutorial provides a complete guide to implementing graph theory algorithms using PHP. These algorithms have widespread applications in many fields of computer science, and understanding how they work is crucial for any programmer who wishes to gain a deeper understanding of graph structures and algorithms.

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