How do you find the diameter of a graph using BFS?

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How do you find the diameter of a graph using BFS?

Algo to find diameter of graph is as follows:

  1. Run BFS on any arbirtray vertex and remember the last node visited (say t)
  2. Run BFS from t and rememver the last node visited (say t’)
  3. shortest distance between t and t’ will be the diameter of the graph.

Why does BFS find the shortest path?

BFS will find the shortest distance simply because of its radial-search pattern which considers nodes in order of their distance from the starting point.

How do you find the diameter of a tree in a linear time?

Quick Explanation –

  1. Take any arbitary node as the root node .
  2. Run dfs from that node and find the farthest node.
  3. let this node be x .
  4. Now run dfs from this node to the farthest away node , let this node be y.
  5. now the count of all the nodes that come along the way of x and y ( including them) is the diameter of the tree.
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How do you find the diameter of an n-ary tree?

This article discuss another approach for computing diameter tree of n-ary tree using bfs.

  1. Step 1: Run bfs to find the farthest node from rooted tree let say A.
  2. Step 2: Then run bfs from A to find farthest node from A let B.
  3. Step 3: Distance between node A and B is the diameter of given tree.

How do you find the longest path in a tree?

  1. Run DFS from any node to find the farthest leaf node. Label that node T.
  2. Run another DFS to find the farthest node from T.
  3. The path you found in step 2 is the longest path in the tree.

What is DFS graph?

Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking.

Why BFS fails to find the shortest path in a weighted graph?

The shortest path between two vertices is defined to be the path whose sum of edge weights is the least. BFS will not work on weighted graphs since the path with the fewest edges may not be the shortest if the edges it contains are expensive.

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Will BFS always find the minimal solution Why?

Breadth first search may use more memory but will always find the shortest path first. Breadth first search expands nodes in order of their distance from the root. It is a path finding algorithm that is capable of always finding the solution if one exists. The solution which is found is always the optional solution.

Can BFS find longest path?

BFS runs in worst-case time , where is the number of nodes, and is the number of edges in the graph. As such, it can’t compute longest paths, since it is NP-hard [1].

How do you find the longest path between two nodes in a tree?

A correct algorithm is:

  1. Run DFS from any node to find the farthest leaf node. Label that node T.
  2. Run another DFS to find the farthest node from T.
  3. The path you found in step 2 is the longest path in the tree.

How to calculate diameter tree of n-ary tree using BFS?

Diameter of a tree using DFS. This article discuss another approach for computing diameter tree of n-ary tree using bfs. Step 1: Run bfs to find the farthest node from rooted tree let say A. Step 2: Then run bfs from A to find farthest node from A let B. Step 3: Distance between node A and B is the diameter of given tree.

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How to find the farthest node from rooted tree in BFS?

1 Run bfs to find the farthest node from rooted tree let say A 2 Then run bfs from A to find farthest node from A let B 3 Distance between node A and B is the diameter of given tree

What are the rules for using BFS algorithm?

Here, are important rules for using BFS algorithm: A queue (FIFO-First in First Out) data structure is used by BFS. You mark any node in the graph as root and start traversing the data from it. BFS traverses all the nodes in the graph and keeps dropping them as completed.

How do you find the longest path in BFS?

This can also be proved by contradiction that if longest path is between two nodes and either or both of two nodes is not a leaf node then we can extend the path to get a longer path. So one way is to first check what nodes are leaf nodes, then start BFS from one of the leaf node to get the node farthest from it.