@@ -49,8 +49,8 @@ impl<C: std::hash::Hash + Eq> Trie<C> {
4949pub struct Matcher < ' a , C : Eq > {
5050 /// The string pattern to search for.
5151 pub pattern : & ' a [ C ] ,
52- /// KMP match failure automaton. fail[i] is the length of the longest
53- /// proper prefix- suffix of pattern[0..=i].
52+ /// KMP match failure automaton: fail[i] is the length of the longest
53+ /// string that's both a proper prefix and a proper suffix of pattern[0..=i].
5454 pub fail : Vec < usize > ,
5555}
5656
@@ -316,18 +316,18 @@ pub fn palindromes(text: &[impl Eq]) -> Vec<usize> {
316316 pal
317317}
318318
319- /// Z algorithm for computing an array Z[..], where Z[i] is the length of the
320- /// longest text substring starting from index i that is **also a prefix** of
321- /// the text.
319+ /// Z algorithm: computes the array Z[..], where Z[i] is the length of the
320+ /// longest text prefix of text[i..] that is **also a prefix** of text.
322321///
323- /// This runs in O(n) time. It can be embedded in a larger algorithm, or used
324- /// for string searching as an alternative to KMP above.
322+ /// It runs in O(n) time, maintaining the invariant that l <= i and
323+ /// text[0..r-l] == text[l..r]. It can be embedded in a larger algorithm,
324+ /// or used for string searching as an alternative to KMP.
325325///
326326/// # Example
327327///
328328/// ```
329329/// use contest_algorithms::string_proc::z_algorithm;
330- /// let z = z_algorithm("ababbababbabababbabababbababbaba".as_bytes() );
330+ /// let z = z_algorithm(b "ababbababbabababbabababbababbaba");
331331/// assert_eq!(
332332/// z,
333333/// vec![
@@ -338,19 +338,18 @@ pub fn palindromes(text: &[impl Eq]) -> Vec<usize> {
338338/// ```
339339pub fn z_algorithm ( text : & [ impl Eq ] ) -> Vec < usize > {
340340 let n = text. len ( ) ;
341- let ( mut l, mut r) = ( 0 , 0 ) ;
342- let mut z = vec ! [ 0 ; n ] ;
343- z[ 0 ] = n ;
341+ let ( mut l, mut r) = ( 1 , 1 ) ;
342+ let mut z = Vec :: with_capacity ( n ) ;
343+ z. push ( n ) ;
344344 for i in 1 ..n {
345- if i < r {
346- z[ i] = min ( r - i, z[ i - l] ) ;
347- }
348- while i + z[ i] < n && text[ i + z[ i] ] == text[ z[ i] ] {
349- z[ i] += 1 ;
350- }
351- if i + z[ i] > r {
345+ if r > i + z[ i - l] {
346+ z. push ( z[ i - l] ) ;
347+ } else {
352348 l = i;
353- r = i + z[ i] ;
349+ while r < i || ( r < n && text[ r - i] == text[ r] ) {
350+ r += 1 ;
351+ }
352+ z. push ( r - i) ;
354353 }
355354 }
356355 z
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