Maximum Product of Word Lengths

Maximum Product of Word Lengths

1. What is this problem about?

The Maximum Product of Word Lengths interview question is a string optimization problem that requires you to find the maximum value of length(word1) * length(word2) where the two words do not share any common characters. You are given an array of strings, and you must compare pairs of words to satisfy this condition while maximizing the product of their lengths.

The main challenge is efficiently checking if two strings share common characters. A naive comparison for every pair of words would be too slow, especially if the words are long.

2. Why is this asked in interviews?

This Maximum Product of Word Lengths coding problem is asked by tech giants like Amazon and Google to test a candidate's ability to use Bit Manipulation to optimize character checks. It evaluates if you can transform string data into a more compact and comparable format (like an integer bitmask). It's a great example of how bitwise operations can significantly speed up algorithms that would otherwise be computationally expensive.

3. Algorithmic pattern used

The Array, String, Bit Manipulation interview pattern is the standard solution.

1. Represent each word as a bitmask of 26 bits. If the word contains 'a', set the 0th bit; if it contains 'b', set the 1st bit, and so on.
2. Store these masks in an array alongside the corresponding word lengths.
3. Use a nested loop to compare every pair of masks.
4. Two words share no common characters if (mask1 & mask2) == 0.
5. For every such pair, calculate the product of their lengths and track the maximum.

4. Example explanation

Words: ["abcw", "baz", "foo", "bar", "xtfn", "abcdef"]

• "abcw" mask: 10000000000000000000000111 (bits for a, b, c, w)
• "xtfn" mask: Bits for x, t, f, n set.
• mask("abcw") & mask("xtfn") is 0. Product = 4 * 4 = 16.
• "abcdef" and "foo" share no characters? No, "f" is in both. mask & mask != 0.

The maximum product for this set might be 16 (from "abcw" and "xtfn").

5. Common mistakes candidates make

A common error in the Maximum Product of Word Lengths coding problem is using a hash set or a boolean array for every pair comparison, which leads to a much higher time complexity. Another mistake is not handling the bitmasking correctly (e.g., using the wrong shift amount). Candidates also sometimes forget that multiple words might have the same bitmask but different lengths; you only need to keep the maximum length for each unique bitmask to optimize the pairwise comparison.

6. Interview preparation tip

Bitmasking is an essential tool for string problems involving character sets. Whenever you need to check for the presence or absence of characters from a small set (like the 26 lowercase English letters), an integer bitmask is usually the most efficient representation. Practice converting strings to masks and using bitwise AND to check for intersections.