TAILIEUCHUNG - Thuật toán Algorithms (Phần 40)

Tham khảo tài liệu 'thuật toán algorithms (phần 40)', khoa học tự nhiên, toán học phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | ELEMENTARY GRAPH ALGORITHMS 383 actually visited in the order A FE G D C BH I J K L M. Each connected component leads to a tree called the depth-first search tree. It is important to note that this forest of depth-first search trees is simply another way of drawing the graph all vertices and edges of the graph are examined by the algorithm. Solid lines in the diagram indicate that the lower vertex was found by the algorithm to be on the edge list of the upper vertex and had not been visited at that time so that a recursive call was made. Dotted lines correspond to edges to vertices which had already been visited so the if test in visit failed and the edge was not followed with a recursive call. These comments apply to the time each edge is encountered the if test in visit also guards against following the edge the second time that it is encountered. For example once we ve gone from A to F on encountering F in A s adjacency list we don t want to go back from F to A on encountering A in F s adjacency list . Similarly dotted links are actually checked twice even though we checked that A was already visited while at G on encountering A in G s adjacency list we ll check that G was already visited later on when we re back at A on encountering G in A s adjacency list . A crucial property of these depth-first search trees for undirected graphs is that the dotted links always go from a node to some ancestor in the tree another node in the same tree that is higher up on the path to the root . At any point during the execution of the algorithm the vertices divide into three classes those for which visit has finished those for which visit has only partially finished and those which haven t been seen at all. By definition of visit we won t encounter an edge pointing to any vertex in the first class and if we encounter an edge to a vertex in the third class a recursive call will be made so the edge will be solid in the depth-first search tree . The only vertices remaining are .

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