18. Eventual Safe States
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The problem can be found at the following link:
A node is terminal if all child nodes are terminal or having no childs. To find the eventual safe states in a directed graph, I use a depth-first search (DFS) approach. With DFS, I check all connected nodes of a current node, and if all nodes are eventually terminals, I mark this node as terminal as well.
We can implement this approach as follows:
I start by iterating through each node and perform a DFS to determine if it's safe.
If I visit a node that has already been determined as safe, I return true.
If I encounter a node that is already in the process of being visited (marked as visited but not yet determined safe), I return false to avoid cycles.
For each edge, I recursively call the DFS function. If all edges of a node lead to safe states, I mark that node as safe.
Time Complexity: O(V + E)
, where V
is the number of nodes (vertices) and E
is the number of edges in the graph.
Auxiliary Space Complexity: O(V)
, where V
is the number of nodes. This space is used for marking nodes as safe or not.
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