ASSIGNMENTON

DATA STRUCTURE

SUBMITTED TO- MR. SANJAY SOOD

SUBMITTED BY-SURENDRA D3804A1510806601

Part-A 1. for a binary tree T, the Pre-Order and In-Order traversal sequences are as Follows:-

Pre-Order: A B L M K N P QIn-Order: L B M A N K Q P

2. for a binary tree T, the Pre-Order and In-Order traversal sequences are as

Follows:-

Pre-Order: A B E H Q R C D K L MIn-Order: B Q R H E A D L K M C

(a) What is the height of the tree?(b)What are the internal nodes?(c) What is its Post-Order traversal sequence?

(a) The tree height is 5.(b)

(c) Post-Order traversal sequence:- R Q H E B L M K D C A

3. Suppose a binary tree is in memory:-

ROOT14

INFO LEFT RIGHT1 H 4 112 R 0 03 174 P 0 0

5 B 18 76 37 E 1 08 69 C 0 1010 F 15 1611 Q 0 1212 S 0 013 014 A 5 915 K 2 016 L 0 017 1318 D 0 0

Ans …

4. Cons3ider the algebraic expression E= (2x + y) (5a – b)3

(a)Draw the tree T which corresponds to the expression E.(b)Find the Pre-Order of T.

(A)..

(B)..ANS. * + * 2 x y ^ - 5 a b 3

Part-B

5. Illustrate the process of deletion in binary Search tree by considering suitable example.Ans..;

Case a (info,left,right,root,loc,par)a. If left[loc]=null and right[loc]=null, then:

Set child:=nullElse if left[loc]!= left then

Set child=left[loc]ElseSet child=right[loc]

[end of structure]b. If par!=null then

If loc=left[par] thenSet left[par]=child

ElseSet right[par]=child

[End of structure]ElseSet root=child

c. Return

Case_b(info,left,right,root,loc,par)a. Find suc and parsuc

Set ptr=right[loc] and save=loc Repeat while left[ptr]!=null

o Set save=ptr and ptr=left[ptr]o End of loop

Set Suc=ptr and parsuc=saveb. [delete inorder successor using procedure]

Call case_a(info,left,right,root,suc,parsuc)c. [replace node N by its inorder successor]

If par!=null then:o If loc=left[par] theno Set left[par]=sucElseo Set right[par]=sucEnd of if structureElseSet root=suc

d. Set left[suc]=left[loc] andRight[suc]=right[loc]

e. Return

Del(info,left,pirht,root,avail,item)a. Call find(info,left,right,root,item,loc,par)b. If loc=null then write ITEM not in tree; and exitc. If right[loc]!=null and left[loc]!=null

Call case_ b Else

Case_ a

d. Set left[loc]=avail and avail=loce. Exit.

6. Create a heap for following series:

11 9 7 15 14 8 10 13

Ans.

7. Illustrate the process of Insertion in binary Search tree by considering suitable example.Ans. EXAMPLE: - Suppose we have a binary search tree and suppose ITEM=20 is given. Then for insertion we follow the following process:-

1. Compare ITEM=20 with the root 34, of the tree T. Since 20<34, proceed to the left child of 36, which is 16.

2. Compare ITEM=20 with 16, since 20>16, proceed to the right child of 16, which is 28.

3. Compare ITEM =20 with 28, since 20< 28 proceed to the left of 28 which is 18.

4. Compare ITEM=20 with 17, since 20>17, and does not have a right child, insert 19 as the right child of 17.