Minimum Deletions to Make String K-Special

Minimum Deletions to Make String K-Special

1. What is this problem about?

A string is called "K-special" if for any two characters that appear in the string, the absolute difference between their frequencies is at most $K$. The Minimum Deletions to Make String K-Special problem asks for the minimum number of characters to delete to make a given string K-special. This involves either bringing the high frequencies down or removing characters with very low frequencies entirely.

2. Why is this asked in interviews?

This "Medium" problem is asked by DE Shaw and Google because it requires a more nuanced frequency analysis than basic uniqueness problems. The Minimum Deletions to Make String K-Special interview question evaluates whether you can iterate through different "target" frequency ranges and find the optimal one. It tests sorting and the ability to handle multiple frequency targets.

3. Algorithmic pattern used

The algorithmic pattern is Counting, Sorting, and Greedy enumeration.

1. Count the frequencies of all characters and store them in a list.
2. Sort the frequencies.
3. For each frequency $f$ in the list, assume $f$ is the minimum frequency we will allow in our K-special string.
4. If $f$ is the minimum, then any character with frequency less than $f$ must be completely deleted. Any character with frequency greater than $f+K$ must be reduced to $f+K$.
5. Calculate the total deletions for this $f$.
6. Repeat for all $f$ in the list and take the minimum. This "Hash Table, Counting, Sorting, Greedy interview pattern" explores all sensible "minimum frequency" baselines.

4. Example explanation

String: "aabbccc", $K=1$. Frequencies: a: 2, b: 2, c: 3. Sorted: [2, 2, 3].

• Target min freq = 2:
  • 'a' (2): OK.
  • 'b' (2): OK.
  • 'c' (3): Max allowed is $2+1=3$. OK.
  • Total deletions = 0. If $K=0$:
• Target min freq = 2:
  • 'a' (2): OK.
  • 'b' (2): OK.
  • 'c' (3): Must reduce to 2. Deletions = 1.
• Target min freq = 3:
  • 'a' (2): Delete all. Deletions = 2.
  • 'b' (2): Delete all. Deletions = 2.
  • 'c' (3): OK.
  • Total = 4. Min deletions = 1.

5. Common mistakes candidates make

In the Minimum Deletions to Make String K-Special coding problem, candidates often forget that they can delete a character entirely. They only focus on reducing the frequency, which might not be optimal if the character is very rare. Another mistake is not sorting the frequencies, which makes it harder to efficiently calculate the "below minimum" and "above maximum" deletions.

6. Interview preparation tip

When a property must hold for "all pairs," try fixing one end of the constraint (like the minimum value) and seeing how everything else must change to accommodate it. This "Baseline-enumeration interview pattern" is a great way to handle range-based constraints in competitive programming.