Added doctests , type hints for other/nested_brackets.py (#10872)

* Added doctests , type hints

* Update nested_brackets.py

---------

Co-authored-by: Christian Clauss <cclauss@me.com>

other/nested_brackets.py

@@ -14,31 +14,60 @@ brackets and returns true if S is nested and false otherwise.
 """
 
 
-def is_balanced(s):
-    stack = []
-    open_brackets = set({"(", "[", "{"})
-    closed_brackets = set({")", "]", "}"})
+def is_balanced(s: str) -> bool:
+    """
+    >>> is_balanced("")
+    True
+    >>> is_balanced("()")
+    True
+    >>> is_balanced("[]")
+    True
+    >>> is_balanced("{}")
+    True
+    >>> is_balanced("()[]{}")
+    True
+    >>> is_balanced("(())")
+    True
+    >>> is_balanced("[[")
+    False
+    >>> is_balanced("([{}])")
+    True
+    >>> is_balanced("(()[)]")
+    False
+    >>> is_balanced("([)]")
+    False
+    >>> is_balanced("[[()]]")
+    True
+    >>> is_balanced("(()(()))")
+    True
+    >>> is_balanced("]")
+    False
+    >>> is_balanced("Life is a bowl of cherries.")
+    True
+    >>> is_balanced("Life is a bowl of che{}ies.")
+    True
+    >>> is_balanced("Life is a bowl of che}{ies.")
+    False
+    """
     open_to_closed = {"{": "}", "[": "]", "(": ")"}
-
-    for i in range(len(s)):
-        if s[i] in open_brackets:
-            stack.append(s[i])
-
-        elif s[i] in closed_brackets and (
-            len(stack) == 0 or (len(stack) > 0 and open_to_closed[stack.pop()] != s[i])
+    stack = []
+    for symbol in s:
+        if symbol in open_to_closed:
+            stack.append(symbol)
+        elif symbol in open_to_closed.values() and (
+            not stack or open_to_closed[stack.pop()] != symbol
         ):
             return False
-
-    return len(stack) == 0
+    return not stack  # stack should be empty
 
 
 def main():
     s = input("Enter sequence of brackets: ")
-    if is_balanced(s):
-        print(s, "is balanced")
-    else:
-        print(s, "is not balanced")
+    print(f"'{s}' is {'' if is_balanced(s) else 'not '}balanced.")
 
 
 if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
     main()