Unique Substrings With Equal Digit Frequency

Unique Substrings With Equal Digit Frequency

What is this problem about?

In the Unique Substrings With Equal Digit Frequency interview question, you are given a string consisting only of digits. You need to find the number of unique substrings where every digit that appears in the substring appears with the same frequency. For example, in "1212", "12" is valid (1 and 2 both appear once), and "1212" is valid (1 and 2 both appear twice).

Why is this asked in interviews?

This Unique Substrings With Equal Digit Frequency coding problem tests your ability to combine string processing with Rolling Hash or Hash Functions to efficiently identify unique substrings. It requires a solid understanding of frequency counting and sliding window or nested loop logic, along with techniques to avoid the $O(n^3)$ cost of string extraction and storage.

Algorithmic pattern used

The best Hash Table, Counting, Hash Function, Rolling Hash, String interview pattern for this problem is to use nested loops to examine all possible substrings while maintaining a frequency map of digits. For each starting position, expand the substring one digit at a time. Update the count of the new digit and check if all digits in the map have the same frequency. To count unique substrings efficiently, use a Rolling Hash to represent the substring as a number and store these hashes in a Set.

Example explanation

Consider the string "1221".

1. Substring "1": 1 appears once. Valid.
2. Substring "12": 1 and 2 appear once. Valid.
3. Substring "122": 1 appears once, 2 appears twice. Invalid.
4. Substring "1221": 1 and 2 appear twice. Valid.
5. Move to next start: "2", "22" (Valid, 2 appears twice), "221" (Invalid). Total unique valid substrings: "1", "2", "12", "1221", "22", "21". (Wait, "21" is also valid).

Common mistakes candidates make

A common error is using substring() and a Set of Strings, which is slow and memory-intensive for large inputs. Another mistake is not checking the "equal frequency" condition efficiently; you can track the maximum frequency and the number of distinct digits to verify this in $O(1)$ or $O(10)$ time during expansion.

Interview preparation tip

Practice using Rolling Hash (like Rabin-Karp) for problems that require identifying unique substrings. It is a powerful technique that turns string comparisons into integer comparisons, which is a significant optimization in competitive programming and high-performance interviews.