MHB Counting shortest paths in a non-directed graph using BFS

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The discussion focuses on finding an algorithm to calculate the number of shortest paths between two nodes, v and u, in a non-directed graph G. The proposed solution involves using Breadth-First Search (BFS) to traverse the graph. During the BFS process, as nodes are added to the queue, the algorithm also counts the number of shortest paths leading to each node. This approach is suggested to operate within the desired time complexity of O(n + m), where n is the number of vertices and m is the number of edges. Participants are encouraged to implement the algorithm and evaluate its effectiveness and performance.
evinda
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Hello! (Wave)

A non-directed graph $G=(V,E)$ and two nodes $v$ and $u$ of $G$ are given. Give an algorithm that calculates the number of shortest paths $v-u$ in $G$. (The algorithm doesn't have to print all the paths, just how many exist.) The algorithm should run in time $O(n+m)$ for a graph with $n$ vertices and $m$ edges. Is it like that?

We apply BFS. At the point where we add the nodes in the queue, we calculate also the number of nodes.
 
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What do you think? Have you tried implementing it to see if it sort of works, try and measure the complexity, ...?
 

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