From 41f4b370bdf975dc2203b3c7e4163ad1a8cc596a Mon Sep 17 00:00:00 2001
From: beam <beam@agents.invalid>
Date: Tue, 27 Oct 2026 21:38:46 +0000
Subject: [PATCH] beam: add majority_element (Boyer-Moore) with verified tests

---
 wizard-work/beam/majority_element.py      | 22 ++++++++++++++++++++++
 wizard-work/beam/test_majority_element.py | 14 ++++++++++++++
 2 files changed, 36 insertions(+)
 create mode 100644 wizard-work/beam/majority_element.py
 create mode 100644 wizard-work/beam/test_majority_element.py

diff --git a/wizard-work/beam/majority_element.py b/wizard-work/beam/majority_element.py
new file mode 100644
index 0000000..3d14f06
--- /dev/null
+++ b/wizard-work/beam/majority_element.py
@@ -0,0 +1,22 @@
+"""Boyer-Moore majority vote: element appearing > n/2 times, or None."""
+from __future__ import annotations
+from typing import Any, Iterable, Optional
+
+
+def majority(nums: Iterable[Any]) -> Optional[Any]:
+    arr = list(nums)
+    cand = None
+    count = 0
+    for x in arr:
+        if count == 0:
+            cand = x
+            count = 1
+        elif x == cand:
+            count += 1
+        else:
+            count -= 1
+    if not arr:
+        return None
+    if arr.count(cand) > len(arr) // 2:
+        return cand
+    return None
diff --git a/wizard-work/beam/test_majority_element.py b/wizard-work/beam/test_majority_element.py
new file mode 100644
index 0000000..04b70a6
--- /dev/null
+++ b/wizard-work/beam/test_majority_element.py
@@ -0,0 +1,14 @@
+import unittest
+from majority_element import majority
+
+class TestMajority(unittest.TestCase):
+    def test_basic(self):
+        self.assertEqual(majority([1,1,2]), 1)
+        self.assertEqual(majority([2,2,1,1,1]), 1)
+        self.assertIsNone(majority([1,2,3]))
+        self.assertIsNone(majority([]))
+        self.assertEqual(majority([5]), 5)
+        self.assertEqual(majority([1,1,1,2,2,2,2]), 2)
+
+if __name__ == "__main__":
+    unittest.main()