Update my-calendar-i.py

Python/my-calendar-i.py

@@ -1,4 +1,4 @@
-# Time:  O(n^2)
+# Time:  O(nlogn) on average, O(n^2) on worst case
 # Space: O(n)
 
 # Implement a MyCalendar class to store your events.
@@ -28,8 +28,50 @@
 # Note:
 # - The number of calls to MyCalendar.book per test case will be at most 1000.
 # - In calls to MyCalendar.book(start, end), start and end are integers in the range [0, 10^9].
-
+
+class Node:
+    def __init__(self, start, end):
+        self.__start = start
+        self.__end = end
+        self.__left = None
+        self.__right = None
+
+
+    def insert(self, node):
+        if node.__start >= self.__end:
+            if not self.__right:
+                self.__right = node
+                return True
+            return self.__right.insert(node)
+        elif node.__end <= self.__start:
+            if not self.__left:
+                self.__left = node
+                return True
+            return self.__left.insert(node)
+        else:
+            return False
+
+
 class MyCalendar(object):
+    def __init__(self):
+        self.__root = None
+
+
+    def book(self, start, end):
+        """
+        :type start: int
+        :type end: int
+        :rtype: bool
+        """
+        if self.__root is None:
+            self.__root = Node(start, end)
+            return True
+        return self.root.insert(Node(start, end))
+
+
+# Time:  O(n^2)
+# Space: O(n)
+class MyCalendar2(object):
 
     def __init__(self):
         self.__calendar = []