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The DFS tree and observation 1 are the core of Tarjan's bridge-finding algorithm. Typical tutorials about finding bridges only mention the DFS tree in passing and start by defining weird arrays
A directed DFS tree is an explicit representation of a DFS traversal of a directed graph. When a node is visited for the first time, it is added to the tree, either as a root if it was visited in the beginning of a DFS call, or as the child of the node it got visited from.
Codeforces Graph Theory/ Problem Solving/ Algorithm Series:This is the first video of my Codeforces Graph Series. This is an introductory tutorial that discu...
Here is one of the simplest ways: Run a DFS from any node $$$p$$$. Let $$$a$$$ be a node whose distance from node $$$p$$$ is maximized. Run another DFS from node $$$a$$$. Let $$$b$$$ be a node whose distance from node $$$a$$$ is maximized. $$$a \rightarrow b$$$ is a diameter.
Here is one of the simplest ways: Run a DFS from any node p p. Let a a be a node whose distance from node p p is maximized. Run another DFS from node a a. Let b b be a node whose distance from node a a is maximized. a → b a → b is a diameter. Tree = edges of a diameter + forest.
21 mar 2023 · Example: Implement DFS using an adjacency list take a directed graph of size n=10, and randomly select the number of edges in the graph varying from 9 to 45. Identify each edge as the forwarding edge, tree edge, back edge, and cross edge.
The idea of a bridge tree is to shrink the maximal components without a bridge into one node, leaving only the bridges of the original graph as the edges in the bridge tree. In the above image, the bridges of the graph are marked in red.
