BBM 201 DATA S - web.cs.hacettepe.edu.trbbm201/Fall2018/BBM201-Ders12.pdf · BBM 201 –DATA...
35
BBM 201 – DATA STRUCTURES TRIES DEPT. OF COMPUTER ENGINEERING Acknowledgement: The course slides are adapted from the slides prepared by R. Sedgewick and K. Wayne of Princeton University.
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Transcript of BBM 201 DATA S - web.cs.hacettepe.edu.trbbm201/Fall2018/BBM201-Ders12.pdf · BBM 201 –DATA...
BBM 201 – DATA STRUCTURES
TRIES
DEPT. OF COMPUTER ENGINEERING
Acknowledgement: The course slides are adapted from the slides prepared by R. Sedgewick and K. Wayne of Princeton University.
TODAY
‣ Tries
‣ R-way tries
‣ R-way tries
TRIES
Tries. [from retrieval, but pronounced "try"]
• Store characters in nodes (not keys).
• Each node has R children, one for each possible character.
• Store values in nodes corresponding to last characters in keys.
4
Tries
e
r
e
a l
l
s
b
y
o
h
e
t
7
50
3
1
6
4
s
l
l
e
h
s
root
link to trie for all keys
that start with slink to trie for all keys
that start with she
value for she in node
corresponding to last
key character
key value
by 4
sea 6
sells 1
she 0
shells 3
shore 7
the 5
for now, we do not
draw null links
Follow links corresponding to each character in the key.
• Search hit: node where search ends has a non-null value.
• Search miss: reach a null link or node where search ends has null value.
5
Search in a trie
e
r
get("shells")
e
a l
l
s
b
y
o
h
e
t
7
50
3
1
6
4
ss
ll
ll
ee
hh
ss
return value associated
with last key character
(return 3)
3
Follow links corresponding to each character in the key.
• Search hit: node where search ends has a non-null value.
• Search miss: reach a null link or node where search ends has null value.
6
Search in a trie
e
r
get("she")
e
a l
l
s
b
y
o
h
e
t
7
50
3
1
6
4
s
l
l
ee
hh
ss
search may terminated
at an intermediate node
(return 0)
0
Follow links corresponding to each character in the key.
• Search hit: node where search ends has a non-null value.
• Search miss: reach a null link or node where search ends has null value.
7
Search in a trie
e
r
get("shell")
e
a l
l
s
b
y
o
h
e
t
7
50
3
1
6
4
s
ll
ll
ee
hh
ss
no value associated
with last key character
(return null)
Follow links corresponding to each character in the key.
• Search hit: node where search ends has a non-null value.
• Search miss: reach a null link or node where search ends has null value.
8
Search in a trie
e
r
get("shelter")
e
a l
l
s
b
y
o
h
e
t
7
50
3
1
6
4
s
l
ll
ee
hh
ss
no link to 't'
(return null)
Follow links corresponding to each character in the key.
• Encounter a null link: create new node.
• Encounter the last character of the key: set value in that node.
9
Insertion into a trie
e
r
put("shore", 7)
e
a l
l
s
e
l
s
b
y
l
o
h
e
t
hh
ss
7
50
3
1
6
4
Trie construction demo
10
trie
e
Trie construction demo
11
put("she", 0)
h
s
0
value is in node
corresponding to
last character
key is sequence
of characters from
root to value
e
Trie construction demo
12
she
trie
h
s
0
h
e
Trie construction demo
13
she
trie
s
0
h
e
Trie construction demo
14
she
put("sells", 1)
s
l
l
e
ss
1
0
h
e
Trie construction demo
15
she
sells
trie
l
l
s
s
e
1
0
h
e
Trie construction demo
16
she
sells
trie
l
l
s
s
e
0
1
h
ea
Trie construction demo
17
she
sells
put("sea", 2)
l
l
s
ee
ss
2
1
0
h
ea
Trie construction demo
18
she
sells
sea
trie
l
l
s
s
e
1
2 0
a
Trie construction demo
19
she
sells
sea
put("shells", 3)
l
l
s
e
s
l
l
ee
hh
ss
3
1
2 0
a
Trie construction demo
20
she
sells
sea
trie
l
l
s
l
s
s
l
he
e
3
1
2 0
y
b
a
Trie construction demo
21
she
sells
sea
put("by", 4)
l
l
s
l
s
s
l
he
e
4
3
1
2 0
b
y
a
Trie construction demo
22
she
sells
sea
by
trie
l
l
s
l
s
s
l
he
e
3
1
2
4
0
b
y
a
Trie construction demo
23
she
sells
sea
by
put("the", 5)
l
l
s
l
s
s
l
he
e e
h
t
5
3
1
2
4
0
a
Trie construction demo
24
she
sells
sea
by
the
trie
e
l
l
s
l
s
b
y
s
l
h h
t
e e 5
3
1
2
4
0
2a
Trie construction demo
25
put("sea", 6)
l
l
s
e
l
s
b
y
l
h h
e
t
a
ee
ss
6
overwrite
old value with
new value
5
3
1
4
0
Trie construction demo
26
trie
e
a l
l
s
e
l
s
b
y
s
l
h h
e
t
5
3
1
6
4
0
Trie construction demo
27
trie
e
a l
l
s
e
l
s
b
y
s
l
h h
e
t
3
1
6
4
0 5
e
r
Trie construction demo
28
she
sells
sea
by
the
put("shore", 7)
e
a l
l
s
e
l
s
b
y
l
o
h
e
t
hh
ss
7
5
3
1
6
4
0
Trie construction demo
29
she
sells
sea
by
the
shore
trie
e
a l
l
s
e
l
s
b
y
s
l
o
r
e
h
t
h
e 5
7
3
1
6
4
0
30
Trie representation: implementation
Node. A value, plus references to R nodes.
struct Node
{
int value;
Node * next[R];
}
A child node for each character in Alphabet.
No need to search for character, but a
pointer reserved for each character in
memory
#define R 256
Node * root;
put(&root, key, val, 0);
void put(Node ** x, char *key, int val, int d)
{
if (*x == null) *x = getNode();
if (d ==strlen(key)) { *x->value = val; return;}
char c = key[d];
put(&(x->next[c]), key, val, d+1);
}
⋮
31
R-way trie: implementation
extended ASCII
Node * getNode(){
Node * pNode = NULL;
pNode = (Node *)malloc(sizeof(Node));
if (pNode){
for (int i = 0; i < R; i++)
pNode->next[i] = NULL;
}
return pNode;
}
32
R-way trie: implementation (continued)
int get(Node * x, char * key, int d)
{
if (x == null) return -1; //-1 refers no match
if (d == strlen(key)) return x->value;
char c = key[d];
return get(x->next[c], key, d+1);
}
}
33
R-way trie: implementation (continued)
Trie performance
Search hit. Need to examine all L characters for equality.
Search miss.
• Could have mismatch on first character.
• Typical case: examine only a few characters (sublinear).
Space. R null links at each leaf.
(but sublinear space possible if many short strings share common
prefixes)
Bottom line. Fast search hit and even faster search miss, but
wastes space.
34
35
String symbol table implementations cost summary
N = number of entries, L= key length,
R= alphabet size, w= average key length
R-way trie.
• Method of choice for small R.
• Too much memory for large R.
Challenge. Use less memory, e.g., 65,536-way trie for Unicode!
character accesses (typical case)
implementation searchhit Search miss insert
space
(references)
hashing
(separate chaining)
N N 1 N
R-way trie L log R N L RNw
