digital search tree in data structure.

1. presentation
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2. MAHMUDUL HASAN
S.M SAIFUL ISLAM
ARAFAT HOSSAIN
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3. Slide: 3

4. COURSE CODE: CSE 207
 COURSE TITLE: DATA STRUCTURES
 Course instructor: Md. Shamsuj joha
Senior Lecturer
 DEPT. OF COMPUTER SCIENCE AND
ENGINEERING
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5. Definition.
Structure.
Application
Insertion
Search.
Deletion
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6. Definition
Digital search tree is one
kind of binary tree which
contains only binary data.
If the bit of DST starts with
0 then it is in left subtree
and if the bit starts with 1
then it is in right subtree
and this process works
recursively.
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7.  All keys in the left subtree of a
node at level I. Whose have bit i
equal to zero whereas those in the
right subtree of nodes at this level
have bit i = 1.
 New elements require more bits
then previous item. Slide: 7

8.  Digital Search Tree
Root contains one dictionary pair (any pair)
All remaining pairs whose key begins with
a 0 are in the left subtree.
All remaining pairs whose key begins with
a 1 are in the right subtree.
Left and right subtrees are digital subtrees
on remaining bits.
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9. ****
0***
00**
001*
1***
10**
100*
11**
110*
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10.  A 00001
 S 10011
 E 00101
 R 10010
 C 00011
 H 01000
 I 01001
 N 01110
 G 00111
 X 11000
 M 01101
 P 10000
A
E S
R XC H
G I N
M
P
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11. Application – IP routing, packet
classification, firewalls.
IPv4 – 32 bit IP address.
IPv6 – 128 bit IP address.
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12. o IPv4 is the fourth generation of internet protocol version and the most
used version.
o IPv6 is the Internet's next-generation protocol and the current version of
internet protocol which replace the IPv4.
o A firewall is a network security system, either hardware or software based,
that controls incoming and outgoing network traffic based on a set of rules.
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13. Slide:13

14.  To insert an element in DST.
There will be four(4) possible cases.
Tree Empty
 If found ‘0’, then go left
 If found ‘1’ then go right
 If found same key, then
insert with prefix equal
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15.  Insert a key whose value is 1001
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16.  Insert a key whose value is 1001
1001
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A

17.  1001,
 Now insert 0110
1001
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A

18.  1001,0110
1001
0110
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A
B

19.  1001,0110
 Now insert 1111
A
1001
0110
B
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20.  1001,0110,1111
A
1001
0110
B
1111
C
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21.  Now, insert a pair whose key is 0000
A
1001
0110
B
1111
C
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22.  1001,0110,1111,0000
A
1001
0110
B
1111
C
0000
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23.  Now, insert a pair whose key is 0100
A
1001
0110
B
1111
C
0000
D
0100
E
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24.  Now, insert a pair whose key is 0101
A
1001
0110
B
1111
C
0000 0100
0101
D E
G
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25.  Now, insert a pair whose key is 1100
A
1001
0110
B
1111
C
0000 0100
0101
D E
G
1100
F
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26.  Now, insert a pair whose key is 1110
A
1001
0110
B
1111
C
0000 0100
0101
D E
G
1100
F
1110
I
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27. Slide: 27

28. DST search for key K
For each node T in the tree we have 4
possible results.
 T is empty.
 K matches T .
 Current bit of K is a 0 and go to left child.
 Current bit of K is a 1 and go to right child.
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29. Example:
Search
0001
1001
1111
1100
0110
0000 0100
0101 1110
A
B C
D
E
F
G
I
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30. Example:
Search
0001
First bit 0
1001
1111
1100
0110
0000 0100
0101 1110
A
B C
D
E
F
G
I
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31. Example:
Search
0001
First bit 0
Second bit 0
1001
1111
1100
0110
0000 0100
0101 1110
A
B C
D
E
F
G
I
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32. Example:
Search
0001
Not found
1001
1111
1100
0110
0000 0100
0101 1110
A
B C
D
E
F
G
I
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33. Search
1110
Now
1110=I
1001
1111
1100
0110
0000 0100
0101 1110
A
B C
D
E
F
G
I
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34. Search
1110
Now
1110=I
first bit 1
1001
1111
1100
0110
0000 0100
0101 1110
A
B C
D
E
F
G
I
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35. Search
1110
Now
1110=I
second
bit 1
1001
1111
1100
0110
0000 0100
0101 1110
A
B C
D
E
F
G
I
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36. Search
1110
Now
1110=I
Third bit 1
So K
found
1001
1111
1100
0110
0000 0100
0101 1110
A
B C
D
E
F
G
I
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37. Search 0100
Now 0100=E
1001
1111
1100
0110
0000 0100
0101
1110
A
B C
D E F
G
I
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38. Search 0100
Now 0100=E
first Bit 0
1001
1111
1100
0110
0000 0100
0101
1110
A
B C
D E F
G
I
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39. Search 0100
Now 0100=E
second Bit 1
1001
1111
1100
0110
0000 0100
0101
1110
A
B C
D E F
G
I
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40. Search 0100
Now 0100=E
second Bit 1
So K found
1001
1111
1100
0110
0000 0100
0101
1110
A
B C
D E F
G
I
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41. Struct node{
int key,info;
struct node *l,*r ;
}
static struct node *head,*z;
unsigned bits(unsigned x, int k, int j)
return (x>>k) & ~(~0<<j);
Int digital_search(int v)
{
struct node *x=head;
int b=maxb; // maxb is the number of bits in the key to besorted
z->key=v;
while(v!=x->key)
x=(bits(v,b--,1) ? x->r : x->l;
return x->info;
}
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42. Slide:42
DELETION

43.  For each node in the tree we have 3
possible cases.
 No child.
 One child.
 Two children.
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44. Delete in Digital Search Tree
1001
1111
1100
0110
0000 0100
0101 1110
A
B C
D
E F
G
I
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45. Delete in Digital Search Tree
1001
1111
1100
0110
0000 0100
0101 1110
A
B C
D
E F
G
I
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46. Delete in Digital Search Tree
1001
1111
1100
0110
0000 0100
1110
A
B C
D
E F
I
0000
G
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47. Delete in Digital Search Tree
1001
11110110
0000 0100 1110
A
B C
D
E I
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48. Delete in Digital Search Tree
1001
11110110
0000 0100 1100
A
B C
D
E
I
1110
F
0000
G
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49. Delete in Digital Search Tree
1001
1111
0000
0100
11
A
C
D
E
I
1110
F
0101
G
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50. 1.Search key
2. if(key==Node)
free(Node);
if(Node->left==NULL && Node->right==NULL
Do Nothing;
else if(Node->left!=NULL)
Replace Node with next left Node
else if(Node->right!=NULL)
Replace Node with next right Node
else if(Node->right!=NULL && Node->left!=NULL )
Replace Node with next any Node
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51.  Insertion, search and deletion in DST are
easier than the Binary search tree and
AVL tree.
 This tree does not required additional
information to maintain the balance of
the tree because the depth of the tree is
limited by the length of the key element.
 DST requires less memory than Binary
search tree and AVL tree.
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52.  Bitwise operations are not always easy.
 Handling duplicates is problematic.
 Similar problem with keys of different lengths.
 Data is not sorted.
 If a key is long search and comparisons are
costly, this can be problem.
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53.  The digital search trees can be
recommended for use whenever the keys
stored are integers
 Character strings of fixed width.
 DSTs are also suitable in many cases when
the keys are strings of variable length.
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55. Slide: 55

56.  https://www.google.com/search?q=referrance&ie=u
tf-8&oe=utf-8
 http://myweb.utaipei.edu.tw/~lai/af-teach/af-
algorithm-
DS/DSinjava/Digital%20Search%20Tree.ppt
 http://programming.im.ncnu.edu.tw/HorowitzC2e/
lec49.ppt
 https://www.google.com/
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