valid parenthesizations

dotfiles/lib/python/parenthesizations.py

@@ -0,0 +1,22 @@
+from backports.functools_lru_cache import lru_cache
+
+
+def parenthesizations(pairs):
+    parenthesizations = _parenthesizations(pairs * 2, net=0)
+    return call_count, parenthesizations
+
+
+@lru_cache(maxsize=None)
+def _parenthesizations(length, net=0):
+    if net > length or net < 0:
+        raise Exception()
+    if net == length:
+        return [')' * length]
+    res = prepend('(', _parenthesizations(length-1, net=net + 1))
+    if net > 0:
+        res.extend(prepend(')', _parenthesizations(length-1, net=net - 1)))
+    return res
+
+
+def prepend(char, items):
+    return [char + item for item in items]