#!/usr/bin/env python
# coding: utf-8

# This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges).

# # Solution Notebook

# ## Problem: Check if a binary tree is balanced.
# 
# * [Constraints](#Constraints)
# * [Test Cases](#Test-Cases)
# * [Algorithm](#Algorithm)
# * [Code](#Code)
# * [Unit Test](#Unit-Test)

# ## Constraints
# 
# * Is a balanced tree one where the heights of two sub trees of any node doesn't differ by more than 1?
#     * Yes
# * If this is called on a None input, should we raise an exception?
#     * Yes
# * Can we assume we already have a Node class with an insert method?
#     * Yes
# * Can we assume this fits memory?
#     * Yes

# ## Test Cases
# 
# * None -> No
# * 1 -> Yes
# * 5, 3, 8, 1, 4 -> Yes
# * 5, 3, 8, 9, 10 -> No

# ## Algorithm
# 
# The algorithm will be similar to where we get the height of a tree as seen in [here](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_height/height_solution.ipynb).
# 
# However, we could check whether the tree is balanced while also checking for the heights.
# 
# * Base case: If the root is None, return 0
# * Recursively check whether the left sub tree is balanced, and get its height left_height
# * Recursively check whether the right sub tree is balanced, and get its height right_height
# * Compare left_height and right_height
# * Return 1 + max(left_height, right_height)
#     
# Complexity:
# * Time: O(n)
# * Space: O(h), where h is the height of the tree

# ## Code

# In[1]:


get_ipython().run_line_magic('run', '../bst/bst.py')


# In[2]:


class BstBalance(Bst):

    def _check_balance(self, node):
        if node is None:
            return 0
        left_height = self._check_balance(node.left)
        if left_height == -1:
            return -1
        right_height = self._check_balance(node.right)
        if right_height == -1:
            return -1
        diff = abs(left_height - right_height)
        if diff > 1:
            return -1
        return 1 + max(left_height, right_height)

    def check_balance(self):
        if self.root is None:
            raise TypeError('root cannot be None')
        height = self._check_balance(self.root)
        return height != -1


# ## Unit Test

# In[3]:


get_ipython().run_cell_magic('writefile', 'test_check_balance.py', "import unittest\n\n\nclass TestCheckBalance(unittest.TestCase):\n\n    def test_check_balance_empty(self):\n        bst = BstBalance(None)\n        bst.check_balance()\n\n    def test_check_balance(self):\n        bst = BstBalance(Node(5))\n        self.assertEqual(bst.check_balance(), True)\n\n        bst.insert(3)\n        bst.insert(8)\n        bst.insert(1)\n        bst.insert(4)\n        self.assertEqual(bst.check_balance(), True)\n\n        bst = BstBalance(Node(5))\n        bst.insert(3)\n        bst.insert(8)\n        bst.insert(9)\n        bst.insert(10)\n        self.assertEqual(bst.check_balance(), False)\n\n        bst = BstBalance(Node(3))\n        bst.insert(2)\n        bst.insert(1)\n        bst.insert(5)\n        bst.insert(4)\n        bst.insert(6)\n        bst.insert(7)\n        self.assertEqual(bst.check_balance(), True)\n\n        print('Success: test_check_balance')\n\n\ndef main():\n    test = TestCheckBalance()\n    test.assertRaises(TypeError, test.test_check_balance_empty)\n    test.test_check_balance()\n\n\nif __name__ == '__main__':\n    main()\n")


# In[4]:


get_ipython().run_line_magic('run', '-i test_check_balance.py')