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KMP
A string to be matched
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| a | b | a | a | c | a | b | a | b | c |
Target string
| 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| a | b | a | b | c |
Prefix Table
string P = “a b a b c”
| Prefix Table |
|---|
| a |
| a b |
| a b a |
| a b a b |
| a b a b c |
Prefix Table Role: in matching strings, met halfway to matching errors requiring backtracking. The matching algorithm to ababx at (x! = C), an error occurs. It is determined to go before the string x abab optimum backtrack point.
Max length of the same Prefix and Suffix
| Prefix Table | Prefix | Suffix | Max length |
|---|---|---|---|
| a | - | - | 0 |
| a b | a | b | 0 |
| a b a | a , a b | a , b a | 1 |
| a b a b | a , a b , a b a | b , a b , b a b | 2 |
Next Array
In the matching process, if there ababc the match has been successful, so you can ignore this situation. And when a problem occurs in matching ababx, looking for the same prefix and suffix abab the maximum , so that a downward movement of the array, the first element value is set to -1
| Index | -1 | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|
| character | - | a | b | a | b | c |
| Next Value | - | -1 | 0 | 0 | 1 | 2 |
index = -1 is the imaginary position, does not exist.
Why jump directly next to it?
Next table can be understood as: the same as before the next index element longest character string preceding the prefix element suffix. So directly out next, has been matched by a suffix, prefix == suffix, prefix it need not match again.
When
abaacababc
ABAB
B to find the wrong maximum aba same prefix and suffix, the length of an index starting from 0, 1 is the next element of the prefix. Ab & because a in the suffix a have been matched by, and prefixes and suffixes are the same, the need to match a prefix again, after the element to align with the point of error prefix.
That is:
A B A acababc
----- A BAB
to sum up
- Calculated next (position error from the matching process, the same suffix given maximum front position of the prefix, the prefix is aligned with a location of the error element, so as to achieve optimization of the back)
- Iterating and back
- Such algorithms difficult to explain in words, draw a diagram easier to understand wailing ~
Code
Liao's too late now, then tomorrow liver.