Analysis of Algorithms Chapter - 05 Binary Search Tree

1. Analysis of Algorithms Chapter - 05 Binary Search Tree

2. Binary Search Trees (Chapter 13[12])

3. Preorder, Inorder, Postorder Walks (Chapter 13[12].1)

4. Querying a Binary Search Tree (Section 13[12].2)

5. Min, Max, Successor in a Binary Search Tree (Section 13[12].2)

6. Insertion in a Binary Search Tree (Section 13[12].3) Insert`Note: Tree-Insert begins at the root of the tree and traces a path downward. The pointer x traces the path, and the pointer y is maintained as the parent of x. after initialization, the while loop in line 3-7 causes these two pointer to move down the tree, going left or right depending on the comparison of key[z] with key[x], until x is set to NIL. This NIL occupies the position where we wish to place the input item z. lines 8-13 set the pointers that cause z to be inserted. It runs in O(h) time on a tree of height h.

7. Deletion in a Binary Search Tree (Section 13[12].3) Deleting a node z from a binary search tree. In each case, the node actually removed is lightly shaded. (a) If z has no children, we just remove it.

8. Deletion in a Binary Search Tree (Section 13[12].3) Deleting a node z from a binary search tree. In each case, the node actually removed is lightly shaded. (b) If z has only one child, we splice out z.

9. Deletion in a Binary Search Tree (Section 13[12].3) Deleting a node z from a binary search tree. In each case, the node actually removed is lightly shaded. (c) If z has two children, we splice out its successor y, which has at most one child, and then replace the contents of z with the contents of y.

10. Tree-Delete(T,z) • If left[z] =nil[T] or right[z]=nil[T] • then yz • else yTree-Successor(z) • If left[y]nil[T] • then xleft[y] • else xright[y] • P[x]p[y] • If p[y]=nil[T] • then root[T]x • else if y=left[p[y]] • then left[p[y]]x • else right[p[y]] x • If y z • then key[z] key[y] • {{if y has other fields, copy them, too. • Return y

11. Tree Traversal

15. Trees - Searching

16. Trees - Searching

17. Trees - Searching

18. Trees - Searching

19. Trees - Searching

20. Left-, Right-Rotate: Implementation