Empfohlen
Weitere ähnliche Inhalte
Ähnlich wie Data structure and algorithm
Ähnlich wie Data structure and algorithm (20)
Mehr von SabthamiS1
Kürzlich hochgeladen
Kürzlich hochgeladen (20)
Data structure and algorithm
- 1. NADARSARASWATHI COLLEGE OF ARTS AND SCIENCE DATA STRUCTURE ALOGIRTHM TECHNIQUES FOR BINARY TREES TECHNIQUES FOR GRAPHS PRESENTED BY: S.SABTHAMI I.M.Sc(IT)
- 2. Binary Tree Traversal Traversal is the process of visiting every node once visiting a node entails doing some processing at that node, but when describing a traversal strategy
- 3. Binary Tree Traversal Techniques Three recursive techniques for binary tree traversal In each technique, the left subtree is traversed recursively, the right subtree is traversed recursively, and the root is visited What distinguishes the techniques from one another is the order of those 3 tasks
- 4. Preoder, Inorder, Postorder In Preorder, the root is visited before (pre) the subtrees traversals In Inorder, the root is visited in-between left and right subtree traversal In Preorder, the root is visited after (pre) the subtrees traversals Preorder Traversal: 1. Visit the root 2. Traverse left subtree 3. Traverse right subtree Inorder Traversal: 1. Traverse left subtree 2. Visit the root 3. Traverse right subtree Postorder Traversal: 1. Traverse left subtree 2. Traverse right subtree 3. Visit the root
- 5. Illustrations for Traversals Assume: visiting a node is printing its label Preorder: A B F G H C D E I J K Inorder: G F H B A D C E J I K Postorder: G H F B D J K I E C A A B C D E I J K F G H
- 6. Code for the Traversal Techniques The code for visitis up to you to provide, depending on the application A typical example for visit(…) is to print out the data part of its input node
- 7. ALGORITHM FOR PREORDER void preOrder(Tree *tree){ if (tree->isEmpty( )) return; visit(tree->getRoot( )); preOrder(tree->getLeftSubtree()); preOrder(tree->getRightSubtree()); }
- 8. ALGORITHM FOR INORDER void inOrder(Tree *tree){ if (tree->isEmpty( )) return; inOrder(tree->getLeftSubtree( )); visit(tree->getRoot( )); inOrder(tree->getRightSubtree( )); }
- 9. ALGORITHM FOR POSTORDER void PostOrder(struct Treenode*t) { if(t){ PostOrder(t->1child); PostOrder(t->child); Visit(t); } }
- 10. Graph Traversal Depth-First Traversal Breadth-First Traversal
- 11. Depth-First Traversal algorithm dft(x) visit(x) FOR each y such that (x,y) is an edge DO IF <y was not visited yet > THEN dft(y)
- 12. Depth-First Traversal A recursive algorithm implicitly recording a “backtracking” path from the root to the node currently under consideration
- 13. DEPTH-FIRST TRAVERSAL • Depth first search is another way of traversing graphs, which is closely related to preorder traversal of a tree. • the Breath-first search tree is typically "short and bushy", the DFS tree is typically "long and stringy".
- 18. BREADTH-FIRST TRAVERSAL • Each vertex is clearly • marked at most once, • added to the list at most once (since that happens only when it's marked), and • removed from the list at most once. ◦ Since the time to process a vertex is proportional to the length of its adjacency list, the total time for the whole algorithm is O(m). • A tree T constructed by the algorithm is called a breadth first search tree. • The traversal goes a level at a time, left to right within a level (where a level is defined simply in terms of distance from the root of the tree).
- 19. BREADTH-FIRST TRAVERSAL • Every edge of G can be classified into one of three groups. • Some edges are in T themselves. • Some connect two vertices at the same level of T. • The remaining ones connect two vertices on two adjacent levels. It is not possible for an edge to skip a level. • Breadth-first search tree really is a shortest path tree starting from its root.
- 24. Relation between BFS and DFS Both of these search algorithms now keep a list of edges to explore; the only difference between the two is while both algorithms adds items to the end of L, • BFS removes them from the beginning, which results in maintaining the list as a queue • DFS removes them from the end, maintaining the list as a stack.
- 25. BFS and DFS in directed graphs The same search routines work essentially unmodified for directed graphs. ◦ The only difference is that when exploring a vertex v, we only want to look at edges (v,w) going out of v; we ignore the other edges coming into v.
- 26. BFS AND DFS IN DIRECTED GRAPHS For BFS in directed graphs each edge of the graph either • connects two vertices at the same level • goes down exactly one level • goes up any number of levels. For DFS, each edge either connects an ancestor to • a descendant • a descendant to an ancestor • one node to a node in a previously visited subtree.