shortest-path | 易学教程

Using BFS for Weighted Graphs

阅读更多关于 Using BFS for Weighted Graphs

问题 I was revising single source shortest path algorithms and in the video, the teacher mentions that BFS/DFS can't be used directly for finding shortest paths in a weighted graph (I guess everyone knows this already) and said to work out the reason on your own. I was wondering the exact reason/explanation as to why it can't be used for weighted graphs. Is it due to the weights of the edges or anything else ? Can someone explain me as I feel a little confused. PS: I went through this question and

Shortest path (fewest nodes) for unweighted graph

阅读更多关于 Shortest path (fewest nodes) for unweighted graph

问题 I'm trying build a method which returns the shortest path from one node to another in an unweighted graph. I considered the use of Dijkstra's but this seems a bit overkill since I only want one pair. Instead I have implemented a breadth-first search, but the trouble is that my returning list contains some of the nodes that I don't want - how can I modify my code to achieve my goal? public List<Node> getDirections(Node start, Node finish){ List<Node> directions = new LinkedList<Node>(); Queue

How to calculate the shortest path between two points in a grid

阅读更多关于 How to calculate the shortest path between two points in a grid

问题 I know that many algorithms are available for calculating the shortest path between two points in a graph or a grid, like breadth-first, all-pairs (Floyd's), Dijkstra's. However, as I noticed, all of these algorithms compute all the paths in that graph or grid, not only those between the two points we are interested in. MY QUESTION IS: if I have a grid, i.e. a two dimensional array, and I'm interested in computing the shortest path between two points, say P1 and P2, and if there are

Why doesn't Dijkstra's algorithm work for negative weight edges?

阅读更多关于 Why doesn't Dijkstra's algorithm work for negative weight edges?

Can somebody tell me why Dijkstra's algorithm for single source shortest path assumes that the edges must be non-negative. I am talking about only edges not the negative weight cycles. Recall that in Dijkstra's algorithm, once a vertex is marked as "closed" (and out of the open set) - the algorithm found the shortest path to it , and will never have to develop this node again - it assumes the path developed to this path is the shortest. But with negative weights - it might not be true. For example: A / \ / \ / \ 5 2 / \ B--(-10)-->C V={A,B,C} ; E = {(A,C,2), (A,B,5), (B,C,-10)} Dijkstra from A

The best shortest path algorithm

阅读更多关于 The best shortest path algorithm

问题 What is the difference between the "Floyd-Warshall algorithm" and "Dijkstra's Algorithm" , and which is the best for finding the shortest path in a graph? I need to calculate the shortest path between all the pairs in a net and save the results to an array as follows: **A B C D E** A 0 10 15 5 20 B 10 0 5 5 10 C 15 5 0 10 15 D 5 5 10 0 15 E 20 10 15 15 0 回答1: Dijkstra's algorithm finds the shortest path between a node and every other node in the graph. You'd run it once for every node.

Negative weights using Dijkstra's Algorithm

阅读更多关于 Negative weights using Dijkstra's Algorithm

I am trying to understand why Dijkstra's algorithm will not work with negative weights. Reading an example on Shortest Paths , I am trying to figure out the following scenario: 2 A-------B \ / 3 \ / -2 \ / C From the website: Assuming the edges are all directed from left to right, If we start with A, Dijkstra's algorithm will choose the edge (A,x) minimizing d(A,A)+length(edge), namely (A,B). It then sets d(A,B)=2 and chooses another edge (y,C) minimizing d(A,y)+d(y,C); the only choice is (A,C) and it sets d(A,C)=3. But it never finds the shortest path from A to B, via C, with total length 1.

Shortest path to transform one word into another

阅读更多关于 Shortest path to transform one word into another

问题 For a Data Structures project, I must find the shortest path between two words (like \"cat\" and \"dog\" ), changing only one letter at a time. We are given a Scrabble word list to use in finding our path. For example: cat -> bat -> bet -> bot -> bog -> dog I\'ve solved the problem using a breadth first search, but am seeking something better (I represented the dictionary with a trie). Please give me some ideas for a more efficient method (in terms of speed and memory). Something ridiculous

Finding all the shortest paths between two nodes in unweighted undirected graph

阅读更多关于 Finding all the shortest paths between two nodes in unweighted undirected graph

问题 I need help finding all the shortest paths between two nodes in an unweighted undirected graph . I am able to find one of the shortest paths using BFS, but so far I am lost as to how I could find and print out all of them. Any idea of the algorithm / pseudocode I could use? 回答1: As a caveat, remember that there can be exponentially many shortest paths between two nodes in a graph. Any algorithm for this will potentially take exponential time. That said, there is a relatively straightforward

Negative weights using Dijkstra's Algorithm

阅读更多关于 Negative weights using Dijkstra's Algorithm

问题 I am trying to understand why Dijkstra\'s algorithm will not work with negative weights. Reading an example on Shortest Paths, I am trying to figure out the following scenario: 2 A-------B \\ / 3 \\ / -2 \\ / C From the website: Assuming the edges are all directed from left to right, If we start with A, Dijkstra\'s algorithm will choose the edge (A,x) minimizing d(A,A)+length(edge), namely (A,B). It then sets d(A,B)=2 and chooses another edge (y,C) minimizing d(A,y)+d(y,C); the only choice is