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

# Solution Notebook¶

## Constraints¶

• Can we assume the inputs are valid?
• No
• Can we assume the strings are ASCII?
• Yes
• Is this case sensitive?
• Yes
• Is a substring a contiguous block of chars?
• Yes
• Do we expect an int as a result?
• Yes
• Can we assume this fits memory?
• Yes

## Test Cases¶

• None -> TypeError
• '', k = 3 -> 0
• 'abcabcdefgghiij', k=3 -> 6
• 'abcabcdefgghighij', k=3 -> 7

## Algorithm¶

We'll use a chars_to_index_map dictionary: char (key) to index (val) map to maintain a sliding window.

The index (val) will keep track of the character index in the input string.

For each character in the string:

• Add the char (key) and index (value) to the map
• If the length of our map is greater than k, then we'll need to eliminate one item
• Scan the map to find the lowest index and remove it
• The new lowest index will therefore be incremented by 1
• The max length will be the current index minus the lower index + 1

Complexity:

• Time: O(n * k), where n is the number of chars, k is the length of the map due to the min() call
• Space: O(n)

## Code¶

In [1]:
class Solution(object):

def longest_substr(self, string, k):
if string is None:
raise TypeError('string cannot be None')
if k is None:
raise TypeError('k cannot be None')
low_index = 0
max_length = 0
chars_to_index_map = {}
for index, char in enumerate(string):
chars_to_index_map[char] = index
if len(chars_to_index_map) > k:
low_index = min(chars_to_index_map.values())
del chars_to_index_map[string[low_index]]
low_index += 1
max_length = max(max_length, index - low_index + 1)
return max_length


## Unit Test¶

In [2]:
%%writefile test_longest_substr.py
import unittest

class TestSolution(unittest.TestCase):

def test_longest_substr(self):
solution = Solution()
self.assertRaises(TypeError, solution.longest_substr, None)
self.assertEqual(solution.longest_substr('', k=3), 0)
self.assertEqual(solution.longest_substr('abcabcdefgghiij', k=3), 6)
self.assertEqual(solution.longest_substr('abcabcdefgghighij', k=3), 7)
print('Success: test_longest_substr')

def main():
test = TestSolution()
test.test_longest_substr()

if __name__ == '__main__':
main()

Overwriting test_longest_substr.py

In [3]:
%run -i test_longest_substr.py

Success: test_longest_substr