Technically, Breadth-first search (BFS) by itself does not let you find the shortest path, simply because BFS is not looking for a shortest path: BFS describes a strategy for searching a graph, but it does not say that you must search for anything in particular. Dijkstra’s algorithm adapts BFS to let you find single-source shortest … Read more
This is laborous case work: A < B and 0 and N-1 are joined by A -> trivial. B < A and 0 and N-1 are joined by B -> trivial. B < A and 0 and N-1 are joined by A -> Do BFS on graph with only K edges. A < B and … Read more
Storing all the visited nodes in a single list is not helpful for finding the shortest path because in the end you have no way of knowing which nodes were the ones that led to the target node, and which ones were dead ends. What you need to do is for every node to store … Read more
Here are some ideas on this. There can only be multiple shortest paths from v->w through node x, either if there are multiple paths into x through the same vertice or if x is encountered multiple time at the same DFS level. Proof: If there are multiple paths entering x through the same vertex there … Read more
Your confusion is stemming from the fact that you apparently assume that DFS algorithm can be obtained from BFS algorithm by replacing the FIFO queue with a LIFO stack. This is a popular misconception – it is simply not true. The classic DFS algorithm cannot be obtained by replacing the BFS queue with a stack. … Read more
Depth first search is more memory efficient than breadth first search as you can backtrack sooner. It is also easier to implement if you use the call stack but this relies on the longest path not overflowing the stack. Also if your graph is directed then you have to not just remember if you have … Read more
Dijkstra allows assigning distances other than 1 for each step. For example, in routing the distances (or weights) could be assigned by speed, cost, preference, etc. The algorithm then gives you the shortest path from your source to every node in the traversed graph. Meanwhile BFS basically just expands the search by one “step” (link, … Read more
Your sum v1 + (incident edges) + v2 + (incident edges) + …. + vn + (incident edges) can be rewritten as (v1 + v2 + … + vn) + [(incident_edges v1) + (incident_edges v2) + … + (incident_edges vn)] and the first group is O(N) while the other is O(E).
Breadth first search Queue<TreeNode> queue = new LinkedList<BinaryTree.TreeNode>() ; public void breadth(TreeNode root) { if (root == null) return; queue.clear(); queue.add(root); while(!queue.isEmpty()){ TreeNode node = queue.remove(); System.out.print(node.element + ” “); if(node.left != null) queue.add(node.left); if(node.right != null) queue.add(node.right); } }
That heavily depends on the structure of the search tree and the number and location of solutions (aka searched-for items). If you know a solution is not far from the root of the tree, a breadth first search (BFS) might be better. If the tree is very deep and solutions are rare, depth first search … Read more