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Fixed wrong step in max_length proof

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Snaipe 2015-05-03 16:19:23 +02:00
parent 1dcba90eb3
commit e8443cd071
1 changed files with 15 additions and 10 deletions
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25
src/extmatch.c
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@ -218,21 +218,26 @@ static int transform(const char *pattern, char *result, const char **errmsg) {
* We must now find the maximal length L such as ∀s, L >= length(T(s))
*
* It is immediately apparent that the largest string will depend on the number
* of occurrences of '!()'. Hence, let s be a string that is a repeating
* sequence of '!()',
* of occurrences of '!()'. Hence, let u be a string that is a repeating
* sequence of '!()' padded by '.' to a multiple of 3,
*
* let N = floor(length(s) / 3),
* let Q = length(s) mod 3,
* ∀s, num('!()') = N (1)
* let N = floor(length(u) / 3),
* let Q = length(u) mod 3,
* hence num('!()') = N.
*
* ∀s, length(T(s)) <= length(s) + 4 * N
* <= 3 * N + Q + 4 * N
* <= 7 * N + 2
* <= 7 * floor(length(s) / 3) + 2
* ∀s | lenght(s) = length(u),
* length(T(s)) <= length(T(u))
* <= length(u) | the original length
* + 4 * N | the expansion of all '!()'
* + Q * diff('.') | the expansion of Q '.'
* <= 3 * N + Q + 4 * N + Q
* <= 7 * N + 4
* <= 7 * floor(length(u) / 3) + 4
* <= 7 * floor(length(s) / 3) + 4
*
*/
static inline size_t max_length(size_t len) {
return 7 * len / 3 + 2;
return 7 * len / 3 + 4;
}
int extmatch(const char *pattern, const char *string, const char **errmsg) {