/**
* Main program.
*
* @param array $args Command-line arguments.
* @return integer Zero on success; non-zero on failure.
*/
public static function main($args)
{
printf("Application program number 11.\n");
$status = 0;
$g = new GraphAsMatrix(32);
Application11::weightedGraphTest($g);
$g = new GraphAsLists(32);
Application11::weightedGraphTest($g);
$g = new DigraphAsMatrix(32);
Application11::weightedDigraphTest($g);
$g = new DigraphAsLists(32);
Application11::weightedDigraphTest($g);
printf("Critical path analysis.\n");
$g = new DigraphAsMatrix(10);
for ($v = 0; $v < 10; ++$v) {
$g->addVertex($v);
}
$g->addEdge(0, 1, box(3));
$g->addEdge(1, 2, box(1));
$g->addEdge(1, 3, box(4));
$g->addEdge(2, 4, box(0));
$g->addEdge(3, 4, box(0));
$g->addEdge(4, 5, box(1));
$g->addEdge(5, 6, box(9));
$g->addEdge(5, 7, box(5));
$g->addEdge(6, 8, box(0));
$g->addEdge(7, 8, box(0));
$g->addEdge(8, 9, box(2));
printf("%s\n", str($g));
$g2 = Algorithms::criticalPathAnalysis($g);
printf("%s\n", str($g2));
return $status;
}
/**
* Floyd's algorithm to solve the all-pairs, shortest path problem
* for the given edge-weighted, directed graph.
*
* @param object IDigraph $g An edge-weighted, directed graph.
* It is assumed that the edge weights are BoxedIntegers.
* @return object IDigraph An edge-weighted, directed graph.
* There is an edge in the result for each pair of vertices
* if a path that connects those vertices exists.
* The weight on the edge is the length of the shortest path
* between the two vertices it connects.
*/
public static function floydsAlgorithm(IDigraph $g)
{
$n = $g->getNumberOfVertices();
$distance = new DenseMatrix($n, $n);
for ($v = 0; $v < $n; ++$v) {
for ($w = 0; $w < $n; ++$w) {
$distance[array($v, $w)] = Limits::MAXINT;
}
}
foreach ($g->getEdges() as $edge) {
$wt = $edge->getWeight();
$distance[array($edge->getV0()->getNumber(), $edge->getV1()->getNumber())] = unbox($wt);
}
for ($i = 0; $i < $n; ++$i) {
for ($v = 0; $v < $n; ++$v) {
for ($w = 0; $w < $n; ++$w) {
if ($distance[array($v, $i)] != Limits::MAXINT && $distance[array($i, $w)] != Limits::MAXINT) {
$d = $distance[array($v, $i)] + $distance[array($i, $w)];
if ($distance[array($v, $w)] > $d) {
$distance[array($v, $w)] = $d;
}
}
}
}
}
$result = new DigraphAsMatrix($n);
for ($v = 0; $v < $n; ++$v) {
$result->addVertex($v);
}
for ($v = 0; $v < $n; ++$v) {
for ($w = 0; $w < $n; ++$w) {
if ($distance[array($v, $w)] != limits::MAXINT) {
$result->addEdge($v, $w, box($distance[array($v, $w)]));
}
}
}
return $result;
}