mccrieght’s algorithm for linear- time suffix tree construction example
TRANSCRIPT
McCrieght’s algorithm for linear-time suffix tree construction
Example
Example string: AAAAAAA1 2 3 4 5 6 7 8
A A A A A A A $
rootT0:
Conventions: • Ti corresponds to the tree after i iterations.• Suffix numbering and string indexing starts from 1 and ends at n.• Only for convenience in presentation, edge-labels are shown as strings.
In the implementation, it is assumed that edge-labels are storedas a pair of integers.
T1:
Initial tree:Denotes suffix links
Example string: AAAAAAA1 2 3 4 5 6 7 8
A A A A A A A $
rootT0: root
T1:
1
AA
AA
AA
A$
Tally of cost
Number of character comparisons
0
Number of node hops 0
Iteration: 1
For this iteration:
Example string: AAAAAAA1 2 3 4 5 6 7 8
A A A A A A A $
rootT2:
1
AA
AA
AA
A$
Tally of cost
Number of character comparisons
7
Number of node hops 0
Iteration: 2
rootT1:
1
AA
AA
AA
A$
Case IB
2
$For this iteration:
Example string: AAAAAAA1 2 3 4 5 6 7 8
A A A A A A A $
rootT3:
1
AA
AA
AA
A$
Tally of cost
Number of character comparisons
1
Number of node hops 1
Iteration: 3
Case IIB
2
$
rootT2:
1
AA
AA
AA
A$
2
$
=AAAAAA = A ’
3
$
For this iteration:
Example string: AAAAAAA1 2 3 4 5 6 7 8
A A A A A A A $
rootT4:
1
AA
AA
AA
A$
Tally of cost
Number of character comparisons
1
Number of node hops 1
Iteration: 4
Case IIB
2
$
rootT3:
1
AA
AA
A
AA
$2
$
=AAAAA = A ’
3
$
3
$ 4
$
For this iteration:
Example string: AAAAAAA1 2 3 4 5 6 7 8
A A A A A A A $
rootT5:
1
AA
AA
AA
A$
Tally of cost
Number of character comparisons
1
Number of node hops 1
Iteration: 5
Case IIB
2
$
rootT4:
1
AA
AA
A
AA
$2
$
=AAAA = A ’
3
$
3
$ 4
$4
$5
$
For this iteration:
Example string: AAAAAAA1 2 3 4 5 6 7 8
A A A A A A A $
rootT6:
1
AA
AA
AA
A$
Tally of cost
Number of character comparisons
1
Number of node hops 1
Iteration: 6
Case IIB
2
$
rootT5:
1
AA
AA
A
AA
$2
$
=AAA = A ’
3
$
3
$ 4
$4
$5
$5
$6
$
For this iteration:
Example string: AAAAAAA1 2 3 4 5 6 7 8
A A A A A A A $
rootT7:
1
AA
AA
AA
A$
Tally of cost
Number of character comparisons
1
Number of node hops 1
Iteration: 7
Case IIB
2
$
rootT6:
1
AA
AA
A
AA
$2
$
=AA = A ’
3
$
3
$ 4
$4
$5
$5
$6
$6
$7
$
For this iteration:
Example string: AAAAAAA1 2 3 4 5 6 7 8
A A A A A A A $
rootT8:
1
AA
AA
AA
A$
Tally of cost
Number of character comparisons
0
Number of node hops 0
Iteration: 8
Case IIB
2
$
rootT7:
1
AA
AA
A
AA
$2
$
=A = A ’
3
$
3
$ 4
$4
$5
$5
$6
$6
$7
$7
$8
$ TOTAL Tally of cost over all iterations
Number of character comparisons
12
Number of node hops 5
For this iteration: