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| 1 | +<?php |
| 2 | + |
| 3 | +namespace Mouf\Database\SchemaAnalyzer; |
| 4 | + |
| 5 | +use Fhaculty\Graph\Edge; |
| 6 | +use Fhaculty\Graph\Exception\UnexpectedValueException; |
| 7 | +use Fhaculty\Graph\Vertex; |
| 8 | +use SplPriorityQueue; |
| 9 | + |
| 10 | +/** |
| 11 | + * Dijkstra's shortest path algorithm modified to measure all possible shortest paths. |
| 12 | + */ |
| 13 | +class MultiDijkstra |
| 14 | +{ |
| 15 | + /** |
| 16 | + * Get all edges on shortest path for this vertex. |
| 17 | + * |
| 18 | + * @throws UnexpectedValueException when encountering an Edge with negative weight |
| 19 | + * @throws MultiDijkstraNoPathException |
| 20 | + * |
| 21 | + * @return array<string, Vertex[]> where key is the destination vertex name and value is an array of possible origin vertex |
| 22 | + */ |
| 23 | + public static function findShortestPaths(Vertex $startVertex, Vertex $endVertex) |
| 24 | + { |
| 25 | + $totalCostOfCheapestPathTo = []; |
| 26 | + // start node distance |
| 27 | + $totalCostOfCheapestPathTo[$startVertex->getId()] = 0; |
| 28 | + |
| 29 | + $endVertexId = $endVertex->getId(); |
| 30 | + |
| 31 | + // just to get the cheapest vertex in the correct order |
| 32 | + $cheapestVertex = new SplPriorityQueue(); |
| 33 | + $cheapestVertex->setExtractFlags(SplPriorityQueue::EXTR_BOTH); |
| 34 | + $cheapestVertex->insert($startVertex, 0); |
| 35 | + |
| 36 | + // predecessors |
| 37 | + $predecesEdgeOfCheapestPathTo = []; |
| 38 | + |
| 39 | + // mark vertices when their cheapest path has been found |
| 40 | + $usedVertices = [$startVertex->getId() => true]; |
| 41 | + |
| 42 | + $isFirst = true; |
| 43 | + |
| 44 | + // Repeat until all vertices have been marked |
| 45 | + $totalCountOfVertices = count($startVertex->getGraph()->getVertices()); |
| 46 | + for ($i = 0; $i < $totalCountOfVertices; ++$i) { |
| 47 | + $currentVertex = null; |
| 48 | + $currentVertexId = null; |
| 49 | + $isEmpty = false; |
| 50 | + if ($isFirst) { |
| 51 | + $currentVertex = $startVertex; |
| 52 | + $currentCost = 0; |
| 53 | + $currentVertexId = $currentVertex->getId(); |
| 54 | + } else { |
| 55 | + do { |
| 56 | + // if the priority queue is empty there are isolated vertices, but the algorithm visited all other vertices |
| 57 | + if ($cheapestVertex->isEmpty()) { |
| 58 | + $isEmpty = true; |
| 59 | + break; |
| 60 | + } |
| 61 | + // Get cheapest unmarked vertex |
| 62 | + $cheapestResult = $cheapestVertex->extract(); |
| 63 | + $currentVertex = $cheapestResult['data']; |
| 64 | + $currentCost = $cheapestResult['priority']; |
| 65 | + $currentVertexId = $currentVertex->getId(); |
| 66 | + // Vertices can be in the priority queue multiple times, with different path costs (if vertex is already marked, this is an old unvalid entry) |
| 67 | + } while (isset($usedVertices[$currentVertexId])); |
| 68 | + } |
| 69 | + |
| 70 | + // Check premature end condition |
| 71 | + // If the end vertex is marked as done and the next lowest possible weight is bigger than end vertix, |
| 72 | + // we are done processing. |
| 73 | + |
| 74 | + |
| 75 | + // catch "algorithm ends" condition |
| 76 | + if ($isEmpty) { |
| 77 | + break; |
| 78 | + } |
| 79 | + |
| 80 | + if ($isFirst) { |
| 81 | + $isFirst = false; |
| 82 | + } |
| 83 | + |
| 84 | + // mark this vertex |
| 85 | + $usedVertices[$currentVertexId] = true; |
| 86 | + |
| 87 | + if (isset($usedVertices[$endVertexId]) && $totalCostOfCheapestPathTo[$endVertexId] < -$currentCost) { |
| 88 | + break; |
| 89 | + } |
| 90 | + |
| 91 | + // check for all edges of current vertex if there is a cheaper path (or IN OTHER WORDS: Add reachable nodes from currently added node and refresh the current possible distances) |
| 92 | + foreach ($currentVertex->getEdgesOut() as $edge) { |
| 93 | + $weight = $edge->getWeight(); |
| 94 | + if ($weight < 0) { |
| 95 | + throw new UnexpectedValueException('Dijkstra not supported for negative weights - Consider using MooreBellmanFord'); |
| 96 | + } |
| 97 | + |
| 98 | + $targetVertex = $edge->getVertexToFrom($currentVertex); |
| 99 | + $targetVertexId = $targetVertex->getId(); |
| 100 | + |
| 101 | + // if the targetVertex is marked, the cheapest path for this vertex has already been found (no negative edges) { |
| 102 | + if (!isset($usedVertices[$targetVertexId])) { |
| 103 | + // calculate new cost to vertex |
| 104 | + $newCostsToTargetVertex = $totalCostOfCheapestPathTo[$currentVertexId] + $weight; |
| 105 | + |
| 106 | + if ((!isset($predecesEdgeOfCheapestPathTo[$targetVertexId])) |
| 107 | + // is the new path cheaper? |
| 108 | + || $totalCostOfCheapestPathTo[$targetVertexId] > $newCostsToTargetVertex) { |
| 109 | + |
| 110 | + // Not an update, just a new insert with lower cost |
| 111 | + $cheapestVertex->insert($targetVertex, -$newCostsToTargetVertex); |
| 112 | + // so the lowest cost will be extracted first |
| 113 | + // and higher cost will be skipped during extraction |
| 114 | + |
| 115 | + // update/set costs found with the new connection |
| 116 | + $totalCostOfCheapestPathTo[$targetVertexId] = $newCostsToTargetVertex; |
| 117 | + // update/set predecessor vertex from the new connection |
| 118 | + $predecesEdgeOfCheapestPathTo[$targetVertexId] = [$edge]; |
| 119 | + } elseif ($totalCostOfCheapestPathTo[$targetVertexId] == $newCostsToTargetVertex) { |
| 120 | + // Same length paths. We need to add the predecessor to the list of possible predecessors. |
| 121 | + $predecesEdgeOfCheapestPathTo[$targetVertexId][] = $edge; |
| 122 | + } |
| 123 | + } |
| 124 | + } |
| 125 | + } |
| 126 | + |
| 127 | + if (!isset($totalCostOfCheapestPathTo[$endVertexId])) { |
| 128 | + throw new MultiDijkstraNoPathException("No path found between vertex '".$startVertex->getId()."' and vertex '".$endVertex->getId()."'"); |
| 129 | + } |
| 130 | + |
| 131 | + // algorithm is done, return resulting edges |
| 132 | + return $predecesEdgeOfCheapestPathTo; |
| 133 | + } |
| 134 | + |
| 135 | + /** |
| 136 | + * @param array<string, Vertex[]> $predecesEdgesArray key is the destination vertex name and value is an array of possible origin vertex |
| 137 | + * |
| 138 | + * @return Edge\Base[] |
| 139 | + */ |
| 140 | + public static function getCheapestPathFromPredecesArray(Vertex $startVertex, Vertex $endVertex, array $predecesEdgesArray) |
| 141 | + { |
| 142 | + $edges = []; |
| 143 | + $currentVertex = $endVertex; |
| 144 | + while ($currentVertex !== $startVertex) { |
| 145 | + $predecessorEdges = $predecesEdgesArray[$currentVertex->getId()]; |
| 146 | + if (count($predecessorEdges) > 1) { |
| 147 | + throw new MultiDijkstraAmbiguityException("There are many possible shortest paths to link vertex '".$startVertex->getId()."' to '".$endVertex->getId()."'"); |
| 148 | + } |
| 149 | + /* @var $edge \Fhaculty\Graph\Edge\Base */ |
| 150 | + $edge = $predecessorEdges[0]; |
| 151 | + $edges[] = $edge; |
| 152 | + if ($currentVertex === $edge->getVerticesStart()->getVertexFirst()) { |
| 153 | + $currentVertex = $edge->getVerticesTarget()->getVertexFirst(); |
| 154 | + } else { |
| 155 | + $currentVertex = $edge->getVerticesStart()->getVertexFirst(); |
| 156 | + } |
| 157 | + } |
| 158 | + |
| 159 | + return array_reverse($edges); |
| 160 | + } |
| 161 | + |
| 162 | + /** |
| 163 | + * @param Vertex $startVertex |
| 164 | + * @param Vertex $endVertex |
| 165 | + * @param array $predecesEdgesArray |
| 166 | + * |
| 167 | + * @return Edge\Base[][] |
| 168 | + */ |
| 169 | + public static function getAllPossiblePathsFromPredecesArray(Vertex $startVertex, Vertex $endVertex, array $predecesEdgesArray) |
| 170 | + { |
| 171 | + $edgesPaths = []; |
| 172 | + |
| 173 | + if ($startVertex === $endVertex) { |
| 174 | + return []; |
| 175 | + } |
| 176 | + |
| 177 | + $predecessorEdges = $predecesEdgesArray[$endVertex->getId()]; |
| 178 | + |
| 179 | + foreach ($predecessorEdges as $edge) { |
| 180 | + if ($endVertex === $edge->getVerticesStart()->getVertexFirst()) { |
| 181 | + $nextVertex = $edge->getVerticesTarget()->getVertexFirst(); |
| 182 | + } else { |
| 183 | + $nextVertex = $edge->getVerticesStart()->getVertexFirst(); |
| 184 | + } |
| 185 | + |
| 186 | + $edgesPaths2 = self::getAllPossiblePathsFromPredecesArray($startVertex, $nextVertex, $predecesEdgesArray); |
| 187 | + if ($edgesPaths2) { |
| 188 | + foreach ($edgesPaths2 as &$edges2) { |
| 189 | + $edges2[] = $edge; |
| 190 | + } |
| 191 | + } else { |
| 192 | + $edgesPaths2 = [[$edge]]; |
| 193 | + } |
| 194 | + |
| 195 | + $edgesPaths = array_merge($edgesPaths, $edgesPaths2); |
| 196 | + } |
| 197 | + |
| 198 | + return $edgesPaths; |
| 199 | + } |
| 200 | +} |
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