Count Pairs Of Similar Strings

Count Pairs Of Similar Strings

What is this problem about?

The "Count Pairs Of Similar Strings interview question" defines "similar" as having the exact same set of unique characters. For example, "aba" and "ba" are similar because both consist only of the characters 'a' and 'b'. You are given an array of strings and need to count how many pairs $(i, j)$ consist of similar strings.

Why is this asked in interviews?

Companies like TikTok and Adobe ask the "Count Pairs Of Similar Strings coding problem" to test basic string processing and "Bit Manipulation interview pattern" skills. It evaluates if a candidate can find an efficient way to represent a "character set" so that two sets can be compared in $O(1)$ time. It’s a great introductory problem for normalization techniques.

Algorithmic pattern used

This problem follows the String Normalization and Frequency Counting pattern.

1. Bitmasking: Represent each string's character set as an integer. For each character 'c' in the string, set the $(char - 'a')^{th}$ bit in the integer (e.g., if 'a' and 'c' are present, mask is $2^0 + 2^2 = 5$).
2. Frequency Map: Use a hash map to count how many strings produce the same bitmask.
3. Counting Pairs: For a mask that appears $n$ times, the number of pairs is $\binom{n}{2} = \frac{n imes (n - 1)}{2}$.

Example explanation

Words: ["aba", "aabb", "abcd", "bac", "aabc"]

• "aba" -> set {a, b} -> mask 3.
• "aabb" -> set {a, b} -> mask 3.
• "abcd" -> set {a, b, c, d} -> mask 15.
• "bac" -> set {a, b, c} -> mask 7.
• "aabc" -> set {a, b, c} -> mask 7. Mask Frequencies: {3: 2, 7: 2, 15: 1}. Pairs: $\binom{2}{2} + \binom{2}{2} = 1 + 1 = 2$.

Common mistakes candidates make

• Sorting Strings: Sorting every string to find unique characters ($O(N \cdot L \log L)$) is slower than bitmasking ($O(N \cdot L)$).
• Ignoring Counts: Forgetting that if three strings are similar, they form 3 pairs, not 2.
• Nested Loops: Using $O(N^2 \cdot L)$ to compare all pairs of strings.

Interview preparation tip

Bitmasking is the most efficient way to represent a set of items from a small universe (like 26 letters). Practice converting sets to masks, as it is a common "Bit Manipulation interview pattern" for string and array problems.