找到两个图节点之间的所有路径 [英] Find all paths between two graph nodes

问题描述

我的工作Dijkstras算法的implemtation检索路线在网络上相互连接的节点之间的最短路径。我有implentation工作。它返回所有的最短路径给所有当我通过起始节点到算法中的节点。

I am working on an implemtation of Dijkstras Algorithm to retrieve the shortest path between interconnected nodes on a network of routes. I have the implentation working. It returns all the shortest paths to all the nodes when I pass the start node into the algorithm.

我的提问： 如何去有关检索从节点A的所有可能路径要说节点G或从节点A甚至所有可能的路径，并返回到节点A

My Question: How does one go about retrieving all possible paths from Node A to say Node G or even all possible paths from Node A and back to Node A

推荐答案

查找所有可能的路径是一个很难的问题，因为有简单的路径指数数。即使找到第k最短路径[或最长路径]有 NP难。

Finding all possible paths is a hard problem, since there are exponential number of simple paths. Even finding the kth shortest path [or longest path] are NP-Hard.

一个可能的解决您的所有路径[或所有路径达到一定长度] 取值到 T 是 BFS 的，不保持一个访问设置，或加权版本 - 你可能需要使用统一成本搜索

One possible solution to find all paths [or all paths up to a certain length] from s to t is BFS, without keeping a visited set, or for the weighted version - you might want to use uniform cost search

注意，还具有周期每图形[它不是一个 DAG 的]可能存在的路径无限多在取值到 T 。

Note that also in every graph which has cycles [it is not a DAG] there might be infinite number of paths between s to t.

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