1. Advanced Data Structure using C++

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LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110) The most natural result of a depth first search of a graph (if it is considered as a function rather than a procedure) is a spanning tree of the vertices reached during the search. Based on this spanning tree, the edges of the original graph can be divided into three classes: forward edges, which point from a node of the tree to one of its descendants, back edges, which point from a node to one of its ancestors, and cross edges, which do neither. Sometimes tree edges, edges which belong to the spanning tree itself, are classified separately from forward edges. It can be shown that if the graph is undirected then all of its edges are tree edges or back edges. Algorithm Of DFS:‐ Start with an arbitrary vertex v. Visit a neighbor w of v. Continue visiting vertices that have not been visited yet. If w has no unvisited neighbors return to the vertex from which you reached w (backtrack). Repeat until all vertices have been visited. Note that each edge will be tested at most twice. The traversed edges will never contain a cycle. <strong>1.</strong> Enqueue the root node. 2. Pop a node from the stack and examine it. If the element sought is found in this node, quit the search and return a result. Otherwise enqueue any successors (the direct child nodes) that have not yet been discovered. Prepared By : Er. Harvinder Singh Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 86 ‐
LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110) 3. If the stack is empty, every node on the graph has been examined – quit the search and return "not found". 4. Repeat from Step 2. 5. Exit Applications of DFS:‐ Algorithms where DFS is used: • Finding connected components. • Topological sorting. • Finding 2‐(edge or vertex)‐connected components. • Finding strongly connected components. • Solving puzzles with only one solution, such as mazes. (DFS can be adapted to find all solutions to a maze by only including nodes on the current path in the visited set.) Prepared By : Er. Harvinder Singh Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 87 ‐
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ADVANCED DATA STRUCTURE NOTES (MT
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