shortest-path | 易学教程

How to optimize Dijkstra algorithm for a single shortest path between 2 nodes?

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问题 I was trying to understand this implementation in C of the Dijkstra algorithm and at the same time modify it so that only the shortest path between 2 specific nodes (source and destination) is found. However, I don't know exactly what do to. The way I see it, there's nothing much to do, I can't seem to change d[] or prev[] cause those arrays aggregate some important data for the shortest path calculation. The only thing I can think of is stopping the algorithm when the path is found, that is,

Eppstein's algorithm and Yen's algorithm for k shortest paths

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问题 I'm trying to understand exactly how these algorithms work, but I have been unable to find a simple explanation. I would greatly appreciate it if someone could provide or point me to a description of these algorithms that is easier to understand than the description in the original papers. Thanks. 回答1: First of all let me provide you with the links to the papers you were talking about. Eppstein's paper: D. Eppstein, “Finding the k shortest paths,” SIAM J. Comput., vol. 28, no. 2, pp.652–673,

Knight's Shortest Path on Chessboard

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I've been practicing for an upcoming programming competition and I have stumbled across a question that I am just completely bewildered at. However, I feel as though it's a concept I should learn now rather than cross my fingers that it never comes up. Basically, it deals with a knight piece on a chess board. You are given two inputs: starting location and ending location. The goal is to then calculate and print the shortest path that the knight can take to get to the target location. I've never dealt with shortest-path-esque things, and I don't even know where to start. What logic do I employ

graph - How to find Minimum Directed Cycle (minimum total weight)?

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问题 Here is an excise: Let G be a weighted directed graph with n vertices and m edges, where all edges have positive weight. A directed cycle is a directed path that starts and ends at the same vertex and contains at least one edge. Give an O(n^3) algorithm to find a directed cycle in G of minimum total weight. Partial credit will be given for an O((n^2)*m) algorithm. Here is my algorithm. I do a DFS . Each time when I find a back edge , I know I've got a directed cycle. Then I will temporarily

The best shortest path algorithm

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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 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. Weights must be non-negative, so if necessary you have to normalise the values in the graph first. Floyd-Warshall

Dijkstra vs. Floyd-Warshall: Finding optimal route on all node pairs

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问题 I am reading up on Dijkstra's algorithm and the Floyd-Warshall algorithm. I understand that Dijkstra's finds the optimal route from one node to all other nodes and Floyd-Warshall finds the optimal route for all node pairings. My question is would Dijkstra's algorithm be more efficient than Floyd's if I run it on every single node in order to find the optimal route between all pairings. Dijkstra's runtime is O(E + VlogV) where Floyd's is O(V 3 ). If Dijkstra's fails, what would its runtime be

Complexity Of Dijkstra's algorithm

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问题 I read from many sources that Dijkstra's Shortest Path also will run in O(V^2) complexity if using a naive way to get the min element (linear search). However, it can be optimised to O(VLogV) if priority queue is used as this data structure will return min element in O(1) time but takes O(LogV) time to restore the heap property after deleting the min element. I have implemented Dijkstra's algo in the following code for the UVA problem at this link: https://uva.onlinejudge.org/index.php?option

Shortest path to transform one word into another

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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 and/or challenging is preferred. I asked one of my friends (he's a junior) and he said that there is no

How does a Breadth-First Search work when looking for Shortest Path?

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I've done some research, and I seem to be missing one small part of this algorithm. I understand how a Breadth-First Search works, but I don't understand how exactly it will get me to a specific path, as opposed to just telling me where each individual node can go. I guess the easiest way to explain my confusion is to provide an example: So for instance, let's say I have a graph like this: And my goal is to get from A to E (all edges are unweighted). I start at A, because that's my origin. I queue A, followed by immediately dequeueing A and exploring it. This yields B and D, because A is

What is the difference between Dijkstra and Prim's algorithm?

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问题 Can any one tell me the difference between Dijkstra's and Prim's algorithms? I know what each of the algorithms do. But they look the same to me. Dijkstra's algorithm stores a summation of minimum cost edges whereas Prim's algorithm stores at most one minimum cost edge. Isn't this the same? 回答1: Dijsktra's algorithm finds the minimum distance from node i to all nodes (you specify i). So in return you get the minimum distance tree from node i. Prims algorithm gets you the minimum spaning tree