From 44c06faae7a19b003f03ed74d7e61c49ae645dce Mon Sep 17 00:00:00 2001
From: xiexian <3468714225@qq.com>
Date: Mon, 28 Sep 2026 13:47:40 +0800
Subject: [PATCH] Add Lyndon factorization with Duval's algorithm

---
 strings/lyndon_factorization.py | 49 +++++++++++++++++++++++++++++++++
 1 file changed, 49 insertions(+)
 create mode 100644 strings/lyndon_factorization.py

diff --git a/strings/lyndon_factorization.py b/strings/lyndon_factorization.py
new file mode 100644
index 000000000000..ea0ec1c829e9
--- /dev/null
+++ b/strings/lyndon_factorization.py
@@ -0,0 +1,49 @@
+"""Factor a string into Lyndon words using Duval's linear-time algorithm.
+
+https://cp-algorithms.com/string/lyndon_factorization.html
+"""
+
+
+def lyndon_factorization(text: str) -> list[str]:
+    """Return the unique non-increasing sequence of Lyndon words in ``text``.
+
+    A Lyndon word is strictly smaller than each of its nontrivial rotations.
+    The empty string has an empty factorization.
+
+    >>> lyndon_factorization("banana")
+    ['b', 'an', 'an', 'a']
+    >>> lyndon_factorization("abab")
+    ['ab', 'ab']
+    >>> lyndon_factorization("aaaa")
+    ['a', 'a', 'a', 'a']
+    >>> lyndon_factorization("")
+    []
+    >>> lyndon_factorization(123)
+    Traceback (most recent call last):
+    ...
+    TypeError: text must be a string
+    """
+    if not isinstance(text, str):
+        raise TypeError("text must be a string")
+
+    factors: list[str] = []
+    start = 0
+    length = len(text)
+
+    while start < length:
+        candidate = start
+        end = start + 1
+
+        while end < length and text[candidate] <= text[end]:
+            if text[candidate] < text[end]:
+                candidate = start
+            else:
+                candidate += 1
+            end += 1
+
+        factor_length = end - candidate
+        while start <= candidate:
+            factors.append(text[start : start + factor_length])
+            start += factor_length
+
+    return factors