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