Add palindromic tree for distinct palindrome counting

strings/palindromic_tree.py

@@ -0,0 +1,70 @@
+"""Count distinct palindromic substrings with a palindromic tree (Eertree).
+
+https://codeforces.com/blog/entry/13959
+"""
+
+
+def count_distinct_palindromic_substrings(text: str) -> int:
+    """Return the number of different nonempty palindromic substrings.
+
+    Each new tree node represents one distinct palindrome. The two initial
+    nodes have lengths -1 and 0 and do not count as substrings. Dictionary
+    transitions give expected O(n) time and O(n) space.
+
+    >>> count_distinct_palindromic_substrings("banana")
+    6
+    >>> count_distinct_palindromic_substrings("ababa")
+    5
+    >>> count_distinct_palindromic_substrings("aaaa")
+    4
+    >>> count_distinct_palindromic_substrings("abc")
+    3
+    >>> count_distinct_palindromic_substrings("あいあ")
+    3
+    >>> count_distinct_palindromic_substrings("")
+    0
+    >>> count_distinct_palindromic_substrings(123)
+    Traceback (most recent call last):
+    ...
+    TypeError: text must be a string
+    """
+    if not isinstance(text, str):
+        raise TypeError("text must be a string")
+
+    # The -1 root always extends; the 0 root is the empty palindrome.
+    lengths = [-1, 0]
+    suffix_links = [0, 0]
+    transitions: list[dict[str, int]] = [{}, {}]
+    longest_suffix = 1
+
+    for position, character in enumerate(text):
+        current = longest_suffix
+        while (
+            position - 1 - lengths[current] < 0
+            or text[position - 1 - lengths[current]] != character
+        ):
+            current = suffix_links[current]
+
+        if character in transitions[current]:
+            longest_suffix = transitions[current][character]
+            continue
+
+        new_node = len(lengths)
+        new_length = lengths[current] + 2
+        lengths.append(new_length)
+        suffix_links.append(1)
+        transitions.append({})
+        transitions[current][character] = new_node
+
+        if new_length > 1:
+            candidate = suffix_links[current]
+            while (
+                position - 1 - lengths[candidate] < 0
+                or text[position - 1 - lengths[candidate]] != character
+            ):
+                candidate = suffix_links[candidate]
+            suffix_links[new_node] = transitions[candidate][character]
+
+        longest_suffix = new_node
+
+    return len(lengths) - 2