Engineering Circuits

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C++ :: Topological Sort Algorithm (using DFS)

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A topological sort of a dag G = (V,E) is a linear ordering of all its vertices such that if G contains an edge (u,v), then u appears before v in the ordering. (If the graph contains a cycle, then no linear ordering is possible.) PSEUDOCODE TOPOLOGICAL-SORT(G) call DFS(G) to compute finishing times v.f for each vertex v as each vertex is finished, insert it onto the front of a linked list return the linked list of vertices
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C++ :: Depth-First Search Algorithm (DFS)

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.:: PSEUDOCODE ::. DFS(G) for each vertex u ∈ G.V u.color = WHITE u.π = NIL time = 0 for each vertex u ∈ G.V if u.color == WHITE DFS-VISIT(G,u) DFS-VISIT(G,u) time = time + 1 u.d = time u.color = GRAY for each v ∈ G.Adj[u] if v.color == WHITE v.π = u DFS-VISIT(G,v) u.color = BLACK time = time + 1 u.f = time
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C++ :: Strongly Connected Components Algorithm (SCC)

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Many algorithms that work with directed graphs begin with such a decomposition. After decomposing the graph into strongly connected components, such algorithms run separately on each one and then combine the solutions according to the structure of connections among components. ALGORITHM STRONGLY-CONNECTED-COMPONENTS(G) call DFS(G) to compute finishing times u.f for each vertex u compute GT call DFS(GT), but in the main loop of DFS, consider the verteces in order of decreasing u.f (as computed in line 2) output the vertices of each tree in the depth-first forest formed in line 4 as a separate strongly connected component
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