Rope and Tries
Fast String Manipulation
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Table of Contents
 Rope
 Prefix Tree (Trie)
 Suffix Tree
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18
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2
3
Exa
mple_
of
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_a_rope_
struc
ture
Rope
Definition and Operations
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Rope
 Rope == balanced tree for indexed items with fast insert / delete
 Allows fast string edit operations on very long strings
 Rope is a binary tree having leaf nodes
 Each node holds a short string
 Each node has a weight value
equal to length of its string
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Ropes in Practice: When to Use Rope?
 Ropes are efficient for very large strings
 E.g. length > 10 000 000
 For small strings ropes are slower!
 List<T> and StringBuilder performs better for 100 000 chars
 Ropes provide:
 Faster insert / delete operations at random position – O(log(n))
 Slower access by index position – O(log(n))

Arrays provide O(1) access by index
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Create
 String: "Example of a rope."
 Example split:
 Exa
_ are spaces
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 mple_
 of
Left subtree
height
 _a_rope.
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Exa
8
2
3
5
mple_
2
of
String length
8
_a_rope.
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Concat
 First string: "Example of a rope"
 Second string: " concatenation"
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17
8
9
2
3
Exa
mple_
of
4
_a_rope
_con
caten
ation
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Indexing
 Index 12
17
12
12
7
14
5
3
Exa
4
mple
_of_
1
a_r
ope
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Split
 Splitting at index 12
17
14
7
3
Exa
4
mple
_of_
a_r
ope
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Split (2)
13
4
7
3
Exa
4
mple
_of_
1
a_
r
ope
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Insert
 Insert "insert in a " at index 12
17
14
7
3
Exa
4
mple
_of_
a_r
ope
12
Insert (2)
13
8
7
3
Exa
4
mple
_of_
4
a_
inse
1
rt_i
n_a_
r
ope
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Insert (3)
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25
13
8
7
3
Exa
4
mple
_of_
4
a_
inse
1
rt_i
n_a_
r
ope
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Delete
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 Index 13
25
 Length 12
13
8
7
3
Exa
4
mple
_of_
4
a_
inse
1
rt_i
n_a_
r
ope
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Delete (2)
13
8
7
3
Exa
4
mple
_of_
4
a_
inse
1
rt_i
n_a_
r
ope
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Delete (3)
17
13
7
3
Exa
4
mple
_of_
1
a_
r
ope
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Rope (Wintellect BigList<T>)
Live Demo
t
r
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e
Trie
Definition and Operations
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What is Trie?
 Trie (prefix tree) is an ordered tree data structure
 Special tree structure used for fast multi-pattern matching
 Used to store a dynamic set where the keys are usually strings
 Applications:
 Dictionaries
 Text searching
 Compression
Trie - Example
Empty root
 The
 There
 These
r
t
 Trie
o
h
 Tree
p
e
 Rope
e
r
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r
s
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 Their
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Search
 These
r
t
o
h
p
e
e
r
i
r
s
r
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Trie - Dictionary
 Each terminal node can have a value
 Value can be of type T
g
i
 Example of a name-age pairs
o
v
 Each set of keys constructs an
unique trie
s
a
h
n
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 Dictionary<string,
T>
o
24
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Construction
 Lucas - 30
l
u
c
a
s
30
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Construction (2)
 Lucia - 18
l
u
c
a
i
s
30
a
18
25
Construction (3)
 Luigi - 23
l
u
i
c
g
a
i
i
23
s
30
a
18
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Construction (4)
 Loren - 48
l
u
o
i
c
r
g
a
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e
i
23
s
30
a
18
n
48
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Construction (5)
 Logan - 23
l
u
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c
g
a
i
23
s
30
o
g
r
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a
18
n
23
n
48
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Construction (6)
 Colin - 5
c
l
o
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l
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c
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g
a
n
5
i
23
s
30
o
g
r
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n
23
n
48
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Construction (7)
 Coley - 15
c
l
o
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l
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c
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g
a
y
15
n
5
i
23
s
30
o
g
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n
23
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Construction (8)
 Cole - 32
c
l
o
u
l
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c
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32
i
g
a
y
15
n
5
i
23
s
30
o
g
r
i
a
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a
18
n
23
n
48
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Trie - Performance
 Fast search by prefix
 High memory footprint
 Can be improved by remove the one-way chaining - creates radix
trie
 Other fast operations
 Add
 Contains
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Trie - Performance (2)
 Slow implementation using array of 256 elements
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Trie - Performance (3)
 Fast implementation using Dictionary
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Live Demo
Trie
Lab Exercise
Trie - Add
Resources
 http://ahmadsoft.org/source/xref/ropes1.2.5/src/org/ahmadsoft/ropes/
 http://www.geeksforgeeks.org/trie-insert-and-search/
 http://www.sanfoundry.com/java-program-implement-rope/
 https://www.cs.bu.edu/teaching/c/tree/trie/
 http://algs4.cs.princeton.edu/home/
Summary
 Ropes are very fast for large number of
elements and provide fast insertion and
deletion
 Tries are string search trees, which reduce
the time to find a given pattern
 Different implementations
- Radix Trie,
Suffix Tree, Suffix Trie, etc.
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Rope and Tries
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License
 This course (slides, examples, labs, videos, homework, etc.)
is licensed under the "Creative Commons AttributionNonCommercial-ShareAlike 4.0 International" license
 Attribution: this work may contain portions from

"Fundamentals of Computer Programming with C#" book by Svetlin Nakov & Co. under CC-BY-SA license

"Data Structures and Algorithms" course by Telerik Academy under CC-BY-NC-SA license
40
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