## Thursday, March 13, 2014

### fastest string searching algorithm.

The Boyer Moore algorithm is the fastest string searching algorithm.

The Boyer Moore algorithm is the fastest string searching algorithm.
It compares the pattern with the actual string from right to left. Most other algorithms
compare from left to right. If the character that is compared with the rightmost pattern
symbol does not occur in the pattern at all, then the pattern can be shifted by m positions
behind this text symbol.
The following example illustrates this situation.
Example:
0 1 2 3 4 5 6 7 8 9 ...
a b b a d a b a c b a
| |
b a b a c |
<------ |
|
b a b a c
The comparison of "d" with "c" at position 4 does not match. "d" does not occur in the
pattern. Therefore, the pattern cannot match at any of the positions 0,1,2,3,4, since all
corresponding windows contain a "d". The pattern can be shifted to position 5. The best
case for the Boyer-Moore algorithm happens if, at each search attempt the first compared
character does not occur in the pattern. Then the algorithm requires only O(n/m)
comparisons .
This method is called bad character heuristics. It can also be applied if the bad character
(the character that causes a mismatch), occurs somewhere else in the pattern. Then the
pattern can be shifted so that it is aligned to this text symbol. The next example illustrates
this situation.
Example:
0 1 2 3 4 5 6 7 8 9 ...
a b b a b a b a c b a
|
b a b a c
<----
|b a b a c
Comparison between "b" and "c" causes a mismatch. The character "b" occurs in the
pattern at positions 0 and 2. The pattern can be shifted so that the rightmost "b" in the
pattern is aligned to "b".