Minimum Operations to Make Character Frequencies Equal
Time O(26 * n) · Space O(26) · Official statement on LeetCode
Solutions
// Time: O(26 * n)
// Space: O(26)
// freq table, dp
class Solution {
public:
int makeStringGood(string s) {
vector<int> cnt(26);
for (const auto& x : s) {
++cnt[x - 'a'];
}
int mx = 0, mn = size(s);
for (const auto& x : cnt) {
mx = max(mx, x);
mn = min(mn, x);
}
int result = size(s);
for (int f = mn; f <= mx; ++f) {
// dp1: min number of the last one of the operations is insert
// dp2: min number of the last one of the operations is delete
int dp1 = 0, dp2 = 0;
for (int i = 0; i < 26; ++i) {
if (!cnt[i]) {
continue;
}
int new_dp1 = 0, new_dp2 = 0;
if (cnt[i] >= f) {
new_dp1 = size(s);
new_dp2 = min(dp1, dp2) + (cnt[i] - f);
} else {
const int free = i - 1 >= 0 ? (cnt[i - 1] >= f ? cnt[i - 1] - f : cnt[i - 1]) : 0;
new_dp1 = min(min(dp1, dp2) + (f - cnt[i]), dp2 + max((f - cnt[i]) - free, 0));
new_dp2 = min(dp1, dp2) + cnt[i];
}
dp1 = new_dp1;
dp2 = new_dp2;
}
result = min({result, dp1, dp2});
}
return result;
}
};
Beginner Explanation
What is Minimum Operations to Make Character Frequencies Equal?
Minimum Operations to Make Character Frequencies Equal (LeetCode #3389) is a Hard problem that primarily trains dynamic programming.
How to think about it
- Restate the goal in your own words before coding.
- Work a tiny example by hand so the invariant becomes obvious.
- Identify the pattern — this problem aligns with dynamic programming.
- Only then translate the idea into code.
Why this problem matters
Hard problems force you to combine patterns and prove complexity carefully — interview gold. Official solution notes mention: Freq Table, DP.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Minimum Operations to Make Character Frequencies Equal
Opening (30–60 seconds)
- Clarify inputs/outputs and edge cases (empty input, single element, duplicates, overflow).
- State a brute force so the interviewer knows you can solve it naively.
- Propose the optimal direction tied to dynamic programming.
Core solution narrative
- Define the state you track (pointers, DP cell, set membership, stack top, etc.).
- Explain the transition when you process the next element.
- Call out time (O(26 * n)) and space (O(26)) before coding.
- Code cleanly; narrate variable names.
What interviewers listen for
- Correctness on edge cases
- Complexity honesty
- Ability to discuss trade-offs (e.g., hash map space vs. sort + two pointers)
Follow-up questions they may ask
- Can you solve it with less memory?
- What if the input stream is infinite / doesn't fit in RAM?
- How would tests look for adversarial inputs?
Optimized Approach
Optimized solution notes
The reference solutions on AlgoForge target O(26 * n) time and O(26) space.
Pattern focus: dynamic programming
Use the pattern as a checklist:
- dynamic programming — confirm the invariant holds after each step
Start from the primary solution, then rewrite from memory to lock it in.
Implementation tips
- Prefer readable names over micro-optimizations in interviews.
- Extract helpers only when they clarify (e.g., expand-around-center, DFS visit).
- After AC-level logic, re-scan for off-by-one and null checks.
Complexity Analysis
Complexity
| Measure | Bound |
|---|---|
| Time | O(26 * n) |
| Space | O(26) |
How to justify this in an interview
- Time: count loops, map/set operations, and recursive branching; state average vs worst case if relevant.
- Space: include hash maps, recursion stack, and output allocation when the problem asks for it.
If your implementation differs from the reference, re-derive big-O from your code — never memorize a complexity you cannot defend.
Common Mistakes
Common mistakes on Minimum Operations to Make Character Frequencies Equal
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for dynamic programming — updating state too early or too late.
- Mutating input unexpectedly when the problem forbids it.
- Off-by-one in windows, ranges, or binary search bounds.
- Ignoring overflow / precision for integer arithmetic problems.
- Overengineering — jumping to an advanced structure when a simpler approach works.
Alternative Approaches
AI expand laterAlternatives
Placeholder for multi-approach comparison. Future AI content generation can expand:
- Brute force baseline
- Optimal dynamic programming solution
- Space-optimized rewrite
Prompt slot: expand alternatives for minimum-operations-to-make-character-frequencies-equal.
Edge Cases
Edge cases checklist
- Minimum input size
- Maximum input size / time limits
- Duplicates and already-sorted input
- Negative numbers / zeros (if applicable)
- Disconnected structures (graphs/trees)
- Single path vs branching recursion depth
Pattern Recognition
Spotting this pattern
Signal phrases that point to dynamic programming:
- Sorted input or ability to sort without changing the answer class
- Need for contiguous subarray / substring → consider sliding window
- Need for O(1) membership → hash set/map
- Optimal substructure + overlapping subproblems → DP
- Connectivity / components → graph DFS/BFS or Union-Find
Primary topics: dynamic programming.
Follow-up Interview Questions
Follow-ups
- How does the solution change if the input is a stream?
- Can you solve it in-place?
- What if duplicates must be handled differently?
- How would you parallelize the approach?
- Design tests that would break a buggy implementation.
Practice Recommendations
What to practice next
- Re-solve Minimum Operations to Make Character Frequencies Equal in a second language (cpp, python).
- Drill 3–5 more problems tagged dynamic programming.
- Teach the solution out loud in under 5 minutes.
- Add this problem to your revision calendar in 3 days and 14 days.
Visualization
Study checklist
- Read the official problem statement on LeetCode
- Solve on paper / whiteboard first
- Implement the dynamic programming approach
- Verify edge cases from the checklist
- State time and space complexity aloud
- Compare with the AlgoForge reference solution
- Schedule a revision session
Revision notes
Minimum Operations to Make Character Frequencies Equal (#3389) — Hard. Pattern: dynamic programming. Complexity: O(26 * n) time / O(26) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Minimum Operations to Make Character Frequencies Equal?+
The reference solutions aim for O(26 * n) time and O(26) space. Always re-derive complexity from the code you write in the interview.
What pattern does Minimum Operations to Make Character Frequencies Equal use?+
It primarily maps to dynamic programming, within the broader topic of dynamic programming.
Is Minimum Operations to Make Character Frequencies Equal good for interviews?+
Yes — as a Hard problem it is a solid practice target. Pair it with related problems in the same pattern family for spaced repetition.
Where can I read the official statement?+
Open the official LeetCode page for constraints and examples: https://leetcode.com/problems/minimum-operations-to-make-character-frequencies-equal/