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.