#!/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: Given an array of n integers, find an int not in the input.  Use a minimal amount of memory.
# 
# * [Constraints](#Constraints)
# * [Test Cases](#Test-Cases)
# * [Algorithm](#Algorithm)
# * [Code](#Code)
# * [Unit Test](#Unit-Test)

# ## Constraints
# 
# * Are we working with non-negative ints?
#     * Yes
# * What is the range of the integers?
#     * Discuss the approach for 4 billion integers
#     * Implement for 32 integers
# * Can we assume the inputs are valid?
#     * No

# ## Test Cases
# 
# * None -> Exception
# * [] -> Exception
# * General case
#     * There is an int excluded from the input -> int
#     * There isn't an int excluded from the input -> None

# ## Algorithm
# 
# The problem states to use a minimal amount of memory.  We'll use a bit vector to keep track of the inputs.
# 
# Say we are given 4 billion integers, which is 2^32 integers.  The number of non-negative integers would be 2^31.  With a bit vector, we'll need 4 billion bits to map each integer to a bit.  Say we had only 1 GB of memory or 2^32 bytes.  This would leave us with 8 billion bits.
# 
# To simplify this exercise, we'll work with an input of up to 32 ints that we'll map to a bit vector of 32 bits.
# 
# <pre>
# 
# input = [0, 1, 2, 3, 4...28, 29, 31]
# 
# bytes          [         1          ]  [          2         ] [          3          ] [          4          ]
# index       =  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
# bit_vector  =  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1
# 
# result = 30
# 
# * Loop through each item in the input, setting bit_vector[item] = True.
# * Loop through the bit_vector, return the first index where bit_vector[item] == False.
# 
# </pre>
# 
# Complexity:
# * Time: O(b), where b is the number of bits
# * Space: O(b)

# ## Code

# In[1]:


from bitstring import BitArray  # Run pip install bitstring


class Bits(object):

    def new_int(self, array, max_size):
        if not array:
            raise TypeError('array cannot be None or empty')
        bit_vector = BitArray(max_size)
        for item in array:
            bit_vector[item] = True
        for index, item in enumerate(bit_vector):
            if not item:
                return index
        return None


# ## Unit Test

# In[2]:


get_ipython().run_cell_magic('writefile', 'test_new_int.py', "import unittest\n\n\nclass TestBits(unittest.TestCase):\n\n    def test_new_int(self):\n        bits = Bits()\n        max_size = 32\n        self.assertRaises(TypeError, bits.new_int, None, max_size)\n        self.assertRaises(TypeError, bits.new_int, [], max_size)\n        data = [item for item in range(30)]\n        data.append(31)\n        self.assertEqual(bits.new_int(data, max_size), 30)\n        data = [item for item in range(32)]\n        self.assertEqual(bits.new_int(data, max_size), None)\n        print('Success: test_find_int_excluded_from_input')\n\n\ndef main():\n    test = TestBits()\n    test.test_new_int()\n\n\nif __name__ == '__main__':\n    main()\n")


# In[3]:


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