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Held: Friday, May 1, 1998
static boolean pathBetween(GraphNode source, GraphNode destination) { // Base case if (source.equals(destination)) return true; // Recursive case: see if there's a path from // a neighbor to the destination. for(Iterator neighbors = source.getNeighbors()); neighbors.hasMoreElements(); ) { GraphNode neighbor = neighbors.nextElement(); if pathBetween(neighbor,destination) return true; } // If we reach this point, we've effectively tried every // possible way to reach the destination. It must not // be possible. return false; } // reachable
+----+ | ^ v | A -> C -> D -> B
Is there a path from A to B? Is B equal to A? No. Pick some neighbor of A. C is the only one. Is there a path from C to B? Is B equal to C? No. Pick some neighbor of C. Let's pick A. Is there a path from A to B? Is B equal to A? No. Pick some neighbor of A. C is the only one. Is there a path form C to B? ...
static boolean pathBetween(GraphNode source, GraphNode destination) { // Note that we've seen the source. mark(source); // Base case: we're already there. if (source.equals(destination)) return true; // Recursive case: try all the neighbors. for(Iterator neighbors = source.getNeighbors()); neighbors.hasMoreElements(); ) { GraphNode neighbor = (Node) neighbors.nextElement(); if (!marked(neighbor) && pathBetween(neighbor,destination)) return true; } // Tried everything. Give up. return false; } // reachable
/** * Determine if there is a path from source to destination in the * "current" graph. nodes_to_check is used to govern the order * in which nodes are checked. If it is a queue, we do a breadth-first * search. If it is a stack, we do a depth-first search. */ public boolean pathBetween(GraphNode source, GraphNode destination, Linear nodes_to_check) { // Clear the collection of nodes_to_check for safety's sake. nodes_to_check.clear(); // Add the source. mark(source); nodes_to_check.add(source); // Keep going until we reach the destination or run out of // nodes. while (!nodes_to_check.empty()) { GraphNode next_node = nodes_to_check.remove(); // Have we found it? if (next_node.equals(destination) { return true; } // If we haven't found it, note that we should check all // of its neighbors. else { Iterator neighbors = next_node.getNeighbors(); while (neighbors.hasMoreElements()) { nodes_to_check.add(neighbor.nextElement()); } } // else } // while there are nodes left to check // We've checked all the nodes reachable from the source // node. None of them is the destination. Give up. return false; } // pathBetween
On to Dijkstra's Shortest Path Algorithm
Back to Introduction to Graphs
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