How to implement shortest path finding using Floyd-Warshall algorithm in PHP

In the field of computer science, the Floyd-Warshall algorithm (FW algorithm for short) is a dynamic programming algorithm that solves the shortest path problem for all node pairs. It can solve directed or undirected graphs where the weights of all edges are positive or negative, and has both time and space complexity optimization problems.

In PHP, there are many ways to implement the FW algorithm, one of which is to use a two-dimensional array to represent the heart's adjacency matrix. The following are the specific steps:

1. Build the adjacency matrix

The adjacency matrix is ​​a two-dimensional array in which each element represents the distance between two vertices. If there is no connection between two vertices, the value is infinity. In PHP, the adjacency matrix can be initialized in the following way:

// Initialize an empty adjacency matrix
$adjMatrix = [];

// Fill the adjacency matrix with infinite values
for($i=0; $i<$n; $i++) {
  for($j=0; $j<$n; $j++) {
    $adjMatrix[$i][$j] = INF;
  }
}

// Assign values to the adjacency matrix
for($i=0; $i<count($edges); $i++) {
  $source = $edges[$i][0];
  $dest = $edges[$i][1];
  $weight = $edges[$i][2];
  $adjMatrix[$source][$dest] = $weight;
}

Among them, $n represents the number of nodes in the entire graph, $edges represents the number array of edges, including the starting point, end point and weight of each edge.

2. Construct the matrix dp array

The dp array is also a two-dimensional array, in which each element represents the length of the shortest path from the starting point to the point. Use adjacency matrix for initialization:

$dp = $adjMatrix;

3. Use FW algorithm to find the shortest path

for($k=0; $k<$n; $k++) {
  for($i=0; $i<$n; $i++) {
    for($j=0; $j<$n; $j++) {
      if ($dp[$i][$j] > $dp[$i][$k] + $dp[$k][$j]) {
        $dp[$i][$j] = $dp[$i][$k] + $dp[$k][$j];
      }
    }
  }
}

where $k, $i, $j$ respectively represent the rows and columns in the node matrix subscript.

4. Output result

for($i=0; $i<$n; $i++) {
  for($j=0; $j<$n; $j++) {
    if($dp[$i][$j] == INF) {
      echo "INF ";
    } else {
      echo $dp[$i][$j]." ";
    }
  }
  echo "
";
}

The above is the process of using the FW algorithm to find the shortest path in PHP. It is worth noting that in practical applications, algorithm optimization and performance tuning need to be carried out according to specific situations to meet actual needs.

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