Improve Duval Algorithm

src/string/duval_algorithm.rs

@@ -1,34 +1,60 @@
-// A string is called simple (or a Lyndon word), if it is strictly smaller than any of its own nontrivial suffixes.
-// Duval (1983) developed an algorithm for finding the standard factorization that runs in linear time and constant space. Source: https://en.wikipedia.org/wiki/Lyndon_word
-fn factorization_with_duval(s: Vec<char>) -> Vec<String> {
-    let n = s.len();
-    let mut i = 0;
-    let mut factorization: Vec<String> = Vec::new();
+//! Implementation of Duval's Algorithm to compute the standard factorization of a string
+//! into Lyndon words. A Lyndon word is defined as a string that is strictly smaller
+//! (lexicographically) than any of its nontrivial suffixes. This implementation operates
+//! in linear time and space.
 
-    while i < n {
-        let mut j = i + 1;
-        let mut k = i;
+/// Performs Duval's algorithm to factorize a given string into its Lyndon words.
+///
+/// # Arguments
+///
+/// * `s` - A slice of characters representing the input string.
+///
+/// # Returns
+///
+/// A vector of strings, where each string is a Lyndon word, representing the factorization
+/// of the input string.
+///
+/// # Time Complexity
+///
+/// The algorithm runs in O(n) time, where `n` is the length of the input string.
+pub fn duval_algorithm(s: &str) -> Vec<String> {
+    factorize_duval(&s.chars().collect::<Vec<char>>())
+}
+
+/// Helper function that takes a string slice, converts it to a vector of characters,
+/// and then applies the Duval factorization algorithm to find the Lyndon words.
+///
+/// # Arguments
+///
+/// * `s` - A string slice representing the input text.
+///
+/// # Returns
+///
+/// A vector of strings, each representing a Lyndon word in the factorization.
+fn factorize_duval(s: &[char]) -> Vec<String> {
+    let mut start = 0;
+    let mut factors: Vec<String> = Vec::new();
 
-        while j < n && s[k] <= s[j] {
-            if s[k] < s[j] {
-                k = i;
+    while start < s.len() {
+        let mut end = start + 1;
+        let mut repeat = start;
+
+        while end < s.len() && s[repeat] <= s[end] {
+            if s[repeat] < s[end] {
+                repeat = start;
             } else {
-                k += 1;
+                repeat += 1;
             }
-            j += 1;
+            end += 1;
         }
 
-        while i <= k {
-            factorization.push(s[i..i + j - k].iter().collect::<String>());
-            i += j - k;
+        while start <= repeat {
+            factors.push(s[start..start + end - repeat].iter().collect::<String>());
+            start += end - repeat;
         }
     }
 
-    factorization
-}
-
-pub fn duval_algorithm(s: &str) -> Vec<String> {
-    return factorization_with_duval(s.chars().collect::<Vec<char>>());
+    factors
 }
 
 #[cfg(test)]
@@ -37,29 +63,35 @@ mod test {
 
     macro_rules! test_duval_algorithm {
         ($($name:ident: $inputs:expr,)*) => {
-        $(
-            #[test]
-            fn $name() {
-                let (text, expected) = $inputs;
-                assert_eq!(duval_algorithm(text), expected);
-            }
-        )*
+            $(
+                #[test]
+                fn $name() {
+                    let (text, expected) = $inputs;
+                    assert_eq!(duval_algorithm(text), expected);
+                }
+            )*
         }
     }
 
     test_duval_algorithm! {
-        multiple: ("abcdabcdababc", ["abcd", "abcd", "ababc"]),
-        all: ("aaa", ["a", "a", "a"]),
+        repeating_with_suffix: ("abcdabcdababc", ["abcd", "abcd", "ababc"]),
+        single_repeating_char: ("aaa", ["a", "a", "a"]),
         single: ("ababb", ["ababb"]),
         unicode: ("അഅഅ", ["അ", "അ", "അ"]),
-    }
-
-    #[test]
-    fn test_factorization_with_duval_multiple() {
-        let text = "abcdabcdababc";
-        assert_eq!(
-            factorization_with_duval(text.chars().collect::<Vec<char>>()),
-            ["abcd", "abcd", "ababc"]
-        );
+        empty_string: ("", Vec::<String>::new()),
+        single_char: ("x", ["x"]),
+        palindrome: ("racecar", ["r", "acecar"]),
+        long_repeating: ("aaaaaa", ["a", "a", "a", "a", "a", "a"]),
+        mixed_repeating: ("ababcbabc", ["ababcbabc"]),
+        non_repeating_sorted: ("abcdefg", ["abcdefg"]),
+        alternating_increasing: ("abababab", ["ab", "ab", "ab", "ab"]),
+        long_repeating_lyndon: ("abcabcabcabc", ["abc", "abc", "abc", "abc"]),
+        decreasing_order: ("zyxwvutsrqponm", ["z", "y", "x", "w", "v", "u", "t", "s", "r", "q", "p", "o", "n", "m"]),
+        alphanumeric_mixed: ("a1b2c3a1", ["a", "1b2c3a", "1"]),
+        special_characters: ("a@b#c$d", ["a", "@b", "#c$d"]),
+        unicode_complex: ("αβγδ", ["αβγδ"]),
+        long_string_performance: (&"a".repeat(1_000_000), vec!["a"; 1_000_000]),
+        palindrome_repeating_prefix: ("abccba", ["abccb", "a"]),
+        interrupted_lyndon: ("abcxabc", ["abcx", "abc"]),
     }
 }