The Question

Given

1. An alphabetical array of dictionary entries and
2. A word to search for

find and return that word's definition (if it exists).

This array of dictionary entries will be formatted like so:

Example

insert 'a'

[ 'a' ]

Entries are alphabetically sorted!

Naive Approach

(aka Brute Force)

insert 'a'

[ 'a' ]

• What is the bigO time complexity?
• Space complexity?

Naive Approach

(aka Brute Force)

insert 'a'

[ 'a' ]

• O(n * m) time, where n = dict.length and m = word.length
• O(1) space

Optimized approach

insert 'a'

[ 'a' ]

What have we not taken full advantage of yet? 

Optimized approach

Binary search

insert 'a'

[ 'a' ]

What next?

Optimized approach

Binary search

insert 'a'

[ 'a' ]

Optimized approach

Binary search

insert 'a'

[ 'a' ]

Strings compared by using > and <

O(m * log n) time

n = dict.length

m = word.length

O(1) space

Optimizing for repeated use

insert 'a'

[ 'a' ]

We usually use dictionaries more than once-

can we optimize for this use case?

Further Optimized approach

insert 'a'

[ 'a' ]

First run: O(n) time to build dictionary object

Subsequent runs: O(1) lookup time!

O(n) space to store our dictionary object

Interviewer Tips

insert 'a'

[ 'a' ]

1. If an interviewee doesn't think of the BS, point to information they are not using e.g. alphabetical order
2. If that doesn't lead them to BS, ask how THEY would look for a word in a dictionary.
3. If your interviewee goes down a rabbit-hole trying to implement a compareByAlphabeticalOrder function, just let them know they can use '<'  and '>' to compare strings.
4. If they complete BS, ask how they can optimize for repeated use- you can hint that there is a way to achieve constant lookup time.

Takeaways?

insert 'a'

[ 'a' ]

What else did you learn from this problem?

What questions do you have?

n = dict.length, m = word.length

*** Might also be considered O(e), entry.length