diff --git a/wizard-work/beam/manacher.py b/wizard-work/beam/manacher.py
new file mode 100644
index 0000000..664064a
--- /dev/null
+++ b/wizard-work/beam/manacher.py
@@ -0,0 +1,49 @@
+"""Manacher's algorithm: longest palindromic substring in O(n)."""
+from __future__ import annotations
+
+
+def longest_palindrome(s: str) -> str:
+    if s == "":
+        return ""
+    # Transform: insert sentinels so every palindrome has odd length.
+    t = "^#" + "#".join(s) + "#$"
+    n = len(t)
+    p = [0] * n
+    c = r = 0
+    for i in range(1, n - 1):
+        mirror = 2 * c - i
+        if i < r:
+            p[i] = min(r - i, p[mirror])
+        # expand
+        while t[i + p[i] + 1] == t[i - p[i] - 1]:
+            p[i] += 1
+        if i + p[i] > r:
+            c = i
+            r = i + p[i]
+    # find center with max radius
+    center = 1
+    for i in range(1, n - 1):
+        if p[i] > p[center]:
+            center = i
+    start = (center - p[center]) // 2
+    return s[start:start + p[center]]
+
+
+def all_palindromic_substrings(s: str) -> list[str]:
+    """Return all distinct palindromic substrings (may be large)."""
+    res = set()
+    n = len(s)
+    for i in range(n):
+        # odd
+        l = r = i
+        while l >= 0 and r < n and s[l] == s[r]:
+            res.add(s[l:r + 1])
+            l -= 1
+            r += 1
+        # even
+        l, r = i, i + 1
+        while l >= 0 and r < n and s[l] == s[r]:
+            res.add(s[l:r + 1])
+            l -= 1
+            r += 1
+    return sorted(res)
diff --git a/wizard-work/beam/test_manacher.py b/wizard-work/beam/test_manacher.py
new file mode 100644
index 0000000..aac2f92
--- /dev/null
+++ b/wizard-work/beam/test_manacher.py
@@ -0,0 +1,46 @@
+import manacher
+
+
+def test_empty():
+    assert manacher.longest_palindrome("") == ""
+
+
+def test_single():
+    assert manacher.longest_palindrome("a") == "a"
+
+
+def test_known():
+    cases = {
+        "babad": "bab",
+        "cbbd": "bb",
+        "a": "a",
+        "ac": "a",
+        "racecar": "racecar",
+        "abacdfgdcaba": "aba",
+        "aaaa": "aaaa",
+        "abacaba": "abacaba",
+    }
+    for s, exp in cases.items():
+        got = manacher.longest_palindrome(s)
+        # accept any maximal-length palindrome
+        assert len(got) == len(exp), (s, got, exp)
+        assert got == got[::-1]
+
+
+def test_all_same():
+    s = "x" * 1000
+    assert manacher.longest_palindrome(s) == s
+
+
+def test_no_palindrome_longer_than_one():
+    s = "abcdef"
+    assert len(manacher.longest_palindrome(s)) == 1
+
+
+def test_even_center():
+    assert manacher.longest_palindrome("abba") == "abba"
+
+
+def test_distinct_substrings_smoke():
+    out = manacher.all_palindromic_substrings("aaa")
+    assert set(out) == {"a", "aa", "aaa"}