Algorithm to delete the specific node from binary searchtree, Data Structure & Algorithms

Q. Write down an algorithm to delete the specific node from binary search tree. Trace the algorithm to delete a node (10) from the following given tree.

1882_binary tree.png

Ans.

Algorithm for Delete ting the specific Node From the Binary Search Tree

To delete the specific node following possibilities may arise

1)      Node id a terminal node

2)      Node have only one child

3)      Node having 2 children.

DEL(INFO, LEFT, RIGT, ROOT, AVAIL, ITEM)

A binary search tree T is in the memory, and an ITEM of information is given as follows.
 This algorithm deletes the specific ITEM from the tree.

1. [to Find the locations of ITEM and its parent] Call FIND(INFO, RIGHT, ROOT, ITEM, LOC, PAR).

2. [ITEM in tree?]

if LOC=NULL, then write : ITEM not in tree, and Exit.

3. [Delete node containing ITEM.]

if RIGHT[LOC] != NULL and LEFT[LOC] !=NULL then:

Call CASEB(INFO,LEFT,RIGHT,ROOT,LOC,PAR). Else:

Call CASEA (INFO,LEFT,RIGHT,ROOT,LOC,PAR).

[End of if structure.]

4. [Return deleted node to AVAIL list.] Set LEFT[LOC]:=AVAIL and AVAIL:=LOC.

5. Exit.

CASEB(INFO,LEFT,RIGHT,ROOT,LOC,PAR)

This procedure will delete the node N at LOC location, where N has two children. The pointer PAR gives us the location of the parent of N, or else PAR=NULL indicates that N is a root node. The pointer SUC gives us the location of the inorder successor of N, and PARSUC gives us the location of the parent of the inorder successor.

1. [Find SUC and PARSUC.]

(a) Set PTR: = RIGHT[LOC] and SAVE:=LOC. (b) Repeat while LEFT[PTR] ≠  NULL:

Set SAVE:=PTR and PTR:=LEFT[PTR]. [End of loop.]

(c) Set SUC : = PTR and PARSUC:=SAVE.

2. [Delete inorder successor]

Call CASEA (INFO, LEFT, RIGHT, ROOT, SUC, PARSUC).

3. [Replace node N by its inorder successor.] (a) If PAR≠NULL, then:

If LOC = LEFT[PAR], then: Set LEFT[PAR]:=SUC.

Else:

Set RIGHT[PAR]: = SUC. [End of If structure.]

Else:

Set ROOT: = SUC. [End of If structure.]

(b) Set LEFT[SUC]:= LEFT [LOC] and

RIGHT[SUC]:=RIGHT[LOC]

4. Return.

CASEA(INFO, LEFT, RIGHT, ROOT, LOC, PAR)

This procedure deletes the node N at LOC location, where N does not contain two children. The pointer PAR gives us the location of the parent of N, or else PAR=NULL indicates that N is a root node. The pointer CHILD gives us the location of the only child of the N, or else CHILD = NULL indicates N has no children.

1. [Initializes CHILD.]

If LEFT[LOC] = NULL and RIGHT[LOC] = NULL, then: Set CHILD:=NULL.

Else if LEFT[LOC]≠NULL, then:

Set CHILD: = LEFT[LOC].

Else

Set CHILD:=RIGHT[LOC] [End of If structue.]

2. If PAR ≠  NULL, then:

If LOC = LEFT [PAR], then:

Set LEFT[PAR]:=CHILD.

Else:

Set RIGHT[PAR]:CHILD = CHILD [End of If structure.]

Else:

Set ROOT : = CHILD.

[End of If structure.]

3. Return.

Inorder traversal of the tree is

4 6 10 11 12 14 15 20

To delete 10

PAR = Parent of 10 ie 15

SUC = inorder succ of 10 ie. 11

PARSUC = Parent of inorder succ ie 12

PTR = RIGHT [LOC]

Address of 12    SAVE: = address of 10

SAVE: = address of 12

PTR = address of 11

SUC = ADDRESS OF 11

PAR SUCC:= ADDRESS OF 12

CHILD = NULL

LEFT [PARSUC] = CHILD= NULL LEFT [PAR]= ADDRESS OF 11

LEFT [SUC] = LEFT [LOC] = ADDRESS OF 6

RIGHT [SUC] = RIGHT[LOC] = ADDRESS OF 12

Posted Date: 7/12/2012 8:43:20 AM | Location : United States







Related Discussions:- Algorithm to delete the specific node from binary searchtree, Assignment Help, Ask Question on Algorithm to delete the specific node from binary searchtree, Get Answer, Expert's Help, Algorithm to delete the specific node from binary searchtree Discussions

Write discussion on Algorithm to delete the specific node from binary searchtree
Your posts are moderated
Related Questions
Post order traversal: The children of node are visited before the node itself; the root is visited last. Each node is visited after its descendents are visited. Algorithm fo

/* The program accepts matrix like input & prints the 3-tuple representation of it*/ #include void main() { int a[5][5],rows,columns,i,j; printf("enter the order of

advanatges of dynamic data structure in programming


1. Give both a high-level algorithm and an implementation (\bubble diagram") of a Turing machine for the language in Exercise 3.8 (b) on page 160. Use the ' notation to show the co

Q. Write down the algorithm which does depth first search through an un-weighted connected graph. In an un-weighted graph, would breadth first search or depth first search or neith

Q. Write down an algorithm to insert a node in the beginning of the linked list.                         Ans: /* structure containing a link part and link part

Graph terminologies : Adjacent vertices: Two vertices a & b are said to be adjacent if there is an edge connecting a & b. For instance, in given Figure, vertices 5 & 4 are adj

explain the prims''s algorithm with suitable example?