The solution to this problem is based on the idea of finding the articulation points of the graph. An articulation point is a vertex whose removal disconnects the graph into two or more disconnected components.
To find the articulation points, we use a modified version of the depth-first search algorithm. We maintain the depth of each node and the lowest depth reachable from the node using back edges. If a child node has a back edge to one of its ancestors, then the ancestor is not an articulation point. Otherwise, if the lowest depth reachable from the child node is greater than or equal to the depth of the current node, then the current node is an articulation point.
Once we have identified the articulation points, we can find the critical links by removing each link and checking if any of the articulation points is no longer reachable from the other side of the link.
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Use a graph data structure to represent the network of nodes and links. You can use an adjacency list or an adjacency matrix to store the connections between nodes.
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To implement the depth-first search algorithm, you can use a recursive function that visits each node and updates its depth and lowest reachable depth.
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To check if a link is critical, you can remove the link from the graph and check if any of the articulation points is no longer reachable from the other side of the link. To do this, you can use a modified version of the depth-first search algorithm that starts from the other side of the link and checks if any of the articulation points is reachable.
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To optimize the algorithm, you can use memoization to avoid recalculating the depth and lowest reachable depth of each node multiple times. You can also use a set or a hash table to store the list of articulation points and the list of critical links, to avoid duplicates.
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Use good coding practices, such as using meaningful variable names, writing comments to explain the code, and testing the code with different inputs and edge cases.