LeetCode #3085 — MEDIUM

Minimum Deletions to Make String K-Special

Move from brute-force thinking to an efficient approach using hash map strategy.

Solve on LeetCode
The Problem

Problem Statement

You are given a string word and an integer k.

We consider word to be k-special if |freq(word[i]) - freq(word[j])| <= k for all indices i and j in the string.

Here, freq(x) denotes the frequency of the character x in word, and |y| denotes the absolute value of y.

Return the minimum number of characters you need to delete to make word k-special.

Example 1:

Input: word = "aabcaba", k = 0

Output: 3

Explanation: We can make word 0-special by deleting 2 occurrences of "a" and 1 occurrence of "c". Therefore, word becomes equal to "baba" where freq('a') == freq('b') == 2.

Example 2:

Input: word = "dabdcbdcdcd", k = 2

Output: 2

Explanation: We can make word 2-special by deleting 1 occurrence of "a" and 1 occurrence of "d". Therefore, word becomes equal to "bdcbdcdcd" where freq('b') == 2, freq('c') == 3, and freq('d') == 4.

Example 3:

Input: word = "aaabaaa", k = 2

Output: 1

Explanation: We can make word 2-special by deleting 1 occurrence of "b". Therefore, word becomes equal to "aaaaaa" where each letter's frequency is now uniformly 6.

Constraints:

  • 1 <= word.length <= 105
  • 0 <= k <= 105
  • word consists only of lowercase English letters.
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: You are given a string word and an integer k. We consider word to be k-special if |freq(word[i]) - freq(word[j])| <= k for all indices i and j in the string. Here, freq(x) denotes the frequency of the character x in word, and |y| denotes the absolute value of y. Return the minimum number of characters you need to delete to make word k-special.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Hash Map · Greedy

Example 1

"aabcaba"
0

Example 2

"dabdcbdcdcd"
2

Example 3

"aaabaaa"
2

Related Problems

  • Minimum Deletions to Make Character Frequencies Unique (minimum-deletions-to-make-character-frequencies-unique)
Step 02

Core Insight

What unlocks the optimal approach

  • Count the frequency of each letter.
  • Suppose we select several characters as the final answer, and let <code>x</code> be the character with the smallest frequency in the answer. It can be shown that out of the selected characters, the optimal solution will never delete an occurrence of character <code>x</code> to obtain the answer.
  • We will fix a character <code>c</code> and assume that it will be the character with the smallest frequency in the answer. Suppose its frequency is <code>x</code>.
  • Then, for every other character, we will count the number of occurrences that will be deleted. Suppose that the current character has <code>y</code> occurrences. <ol> <li>If y < x, we need to delete all of them.</li> <li> if y > x + k, we should delete y - x - k of such character.</li> <li> Otherwise we don’t need to delete it.</li></ol>
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #3085: Minimum Deletions to Make String K-Special
class Solution {
    private List<Integer> nums = new ArrayList<>();

    public int minimumDeletions(String word, int k) {
        int[] freq = new int[26];
        int n = word.length();
        for (int i = 0; i < n; ++i) {
            ++freq[word.charAt(i) - 'a'];
        }
        for (int v : freq) {
            if (v > 0) {
                nums.add(v);
            }
        }
        int ans = n;
        for (int i = 0; i <= n; ++i) {
            ans = Math.min(ans, f(i, k));
        }
        return ans;
    }

    private int f(int v, int k) {
        int ans = 0;
        for (int x : nums) {
            if (x < v) {
                ans += x;
            } else if (x > v + k) {
                ans += x - v - k;
            }
        }
        return ans;
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n × |\Sigma|)
Space
O(|\Sigma|)

Approach Breakdown

EXHAUSTIVE
O(2ⁿ) time
O(n) space

Try every possible combination of choices. With n items each having two states (include/exclude), the search space is 2ⁿ. Evaluating each combination takes O(n), giving O(n × 2ⁿ). The recursion stack or subset storage uses O(n) space.

GREEDY
O(n log n) time
O(1) space

Greedy algorithms typically sort the input (O(n log n)) then make a single pass (O(n)). The sort dominates. If the input is already sorted or the greedy choice can be computed without sorting, time drops to O(n). Proving greedy correctness (exchange argument) is harder than the implementation.

Shortcut: Sort + single pass → O(n log n). If no sort needed → O(n). The hard part is proving it works.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Mutating counts without cleanup

Wrong move: Zero-count keys stay in map and break distinct/count constraints.

Usually fails on: Window/map size checks are consistently off by one.

Fix: Delete keys when count reaches zero.

Using greedy without proof

Wrong move: Locally optimal choices may fail globally.

Usually fails on: Counterexamples appear on crafted input orderings.

Fix: Verify with exchange argument or monotonic objective before committing.