This notebook was prepared by Donne Martin. Source and license info is on GitHub.

Challenge Notebook

Problem: Find the magic index in an array, where array[i] = i.

Constraints

  • Is the array sorted?
    • Yes
  • Are the elements in the array distinct?
    • No
  • Does a magic index always exist?
    • No
  • If there is no magic index, do we just return -1?
    • Yes
  • Are negative values allowed in the array?
    • Yes
  • If there are multiple magic values, what do we return?
    • Return the left-most one
  • Can we assume this fits memory?
    • Yes

Test Cases

  • None input -> -1
  • Empty array -> -1
a[i]  -4 -2  2  6  6  6  6 10
  i    0  1  2  3  4  5  6  7

Result: 2

a[i]  -4 -2  1  6  6  6  6 10
  i    0  1  2  3  4  5  6  7

Result: 6

a[i]  -4 -2  1  6  6  6  7 10
  i    0  1  2  3  4  5  6  7

Result: -1

Algorithm

Refer to the Solution Notebook. If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start.

Code

In [ ]:
class MagicIndex(object):

    def find_magic_index(self, array):
        # TODO: Implement me
        pass

Unit Test

The following unit test is expected to fail until you solve the challenge.

In [ ]:
# %load test_find_magic_index.py
import unittest


class TestFindMagicIndex(unittest.TestCase):

    def test_find_magic_index(self):
        magic_index = MagicIndex()
        self.assertEqual(magic_index.find_magic_index(None), -1)
        self.assertEqual(magic_index.find_magic_index([]), -1)
        array = [-4, -2, 2, 6, 6, 6, 6, 10]
        self.assertEqual(magic_index.find_magic_index(array), 2)
        array = [-4, -2, 1, 6, 6, 6, 6, 10]
        self.assertEqual(magic_index.find_magic_index(array), 6)
        array = [-4, -2, 1, 6, 6, 6, 7, 10]
        self.assertEqual(magic_index.find_magic_index(array), -1)
        print('Success: test_find_magic')


def main():
    test = TestFindMagicIndex()
    test.test_find_magic_index()


if __name__ == '__main__':
    main()

Solution Notebook

Review the Solution Notebook for a discussion on algorithms and code solutions.