Add Lyndon factorization (Duval's algorithm),

DIRECTORY.md

@@ -1615,6 +1615,7 @@
   * [Levenshtein Distance](strings/levenshtein_distance.py)
   * [Longest Word In Sentence](strings/longest_word_in_sentence.py)
   * [Lower](strings/lower.py)
+  * [Lyndon Factorization](strings/lyndon_factorization.py)
   * [Manacher](strings/manacher.py)
   * [Min Cost String Conversion](strings/min_cost_string_conversion.py)
   * [Min Window Substring](strings/min_window_substring.py)

strings/lyndon_factorization.py

@@ -0,0 +1,66 @@
+"""
+https://en.wikipedia.org/wiki/Lyndon_word
+https://cp-algorithms.com/string/lyndon_factorization.html
+
+Lyndon factorization (Duval's algorithm)
+
+A Lyndon word is a non-empty string that is strictly smaller than all of its
+proper rotations. Every string can be written uniquely as a concatenation of
+Lyndon words w1 >= w2 >= ... >= wk. Duval's algorithm finds this factorization.
+
+Time Complexity: O(n) - where n is the length of the string
+Space Complexity: O(1) extra, apart from the output
+"""
+
+
+def lyndon_factorization(input_str: str) -> list[str]:
+    """
+    Return the Lyndon factorization of the given string.
+
+    >>> lyndon_factorization("abab")
+    ['ab', 'ab']
+    >>> lyndon_factorization("banana")
+    ['b', 'an', 'an', 'a']
+    >>> lyndon_factorization("aaa")
+    ['a', 'a', 'a']
+    >>> lyndon_factorization("abc")
+    ['abc']
+    >>> lyndon_factorization("cba")
+    ['c', 'b', 'a']
+    >>> lyndon_factorization("a")
+    ['a']
+    >>> lyndon_factorization("")
+    []
+    >>> lyndon_factorization(123)
+    Traceback (most recent call last):
+        ...
+    TypeError: object of type 'int' has no len()
+    """
+    length = len(input_str)
+    factors: list[str] = []
+    start = 0
+
+    while start < length:
+        # `compare` scans ahead while the text keeps repeating the current word
+        compare = start + 1
+        candidate = start
+        while compare < length and input_str[candidate] <= input_str[compare]:
+            if input_str[candidate] < input_str[compare]:
+                candidate = start
+            else:
+                candidate += 1
+            compare += 1
+
+        # The repeated Lyndon word has length (compare - candidate)
+        word_length = compare - candidate
+        while start <= candidate:
+            factors.append(input_str[start : start + word_length])
+            start += word_length
+
+    return factors
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()