K-Similar Strings
Time O(n * n!/(ca!*...*cz!)) · Space O(n * n!/(ca!*...*cz!)) · Official statement on LeetCode
Solutions
// Time: O(n * n!/(c_a!*...*c_z!), n is the length of A, B,
// c_a...c_z is the count of each alphabet,
// n = sum(c_a...c_z)
// Space: O(n * n!/(c_a!*...*c_z!)
class Solution {
public:
int kSimilarity(string A, string B) {
queue<string> q;
unordered_set<string> lookup;
lookup.emplace(A);
q.emplace(A);
int result = 0;
while (!q.empty()) {
for (int size = q.size() - 1; size >= 0; --size) {
auto s = q.front(); q.pop();
if (s == B) {
return result;
}
int i;
for (i = 0; s[i] == B[i]; ++i);
for (int j = i + 1; j < s.length(); ++j){
if (s[j] == B[j] || s[i] != B[j]) {
continue;
}
swap(s[i], s[j]);
if (!lookup.count(s)) {
lookup.emplace(s);
q.emplace(s);
}
swap(s[i], s[j]);
}
}
++result;
}
return result;
}
};
Beginner Explanation
What is K-Similar Strings?
K-Similar Strings (LeetCode #854) is a Hard problem that primarily trains breadth first search.
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 queue bfs.
- Only then translate the idea into code.
Why this problem matters
Hard problems force you to combine patterns and prove complexity carefully — interview gold.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for K-Similar Strings
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 queue bfs.
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(n * n!/(ca!*...cz!))) and space (O(n * n!/(ca!...*cz!))) 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(n * n!/(ca!...cz!)) time and **O(n * n!/(ca!...cz!)) space.
Pattern focus: queue bfs
Use the pattern as a checklist:
- queue bfs — confirm the invariant holds after each step
Multiple methods appear in the source solutions — compare them and explain when each is preferable.
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(n * n!/(ca!...cz!)) |
| Space | **O(n * n!/(ca!...cz!)) |
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 K-Similar Strings
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for queue bfs — 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
Alternatives
The source file includes more than one method. Compare:
- Primary optimized path — best complexity for typical interviews.
- Secondary approach — often brute force, sorting-based, or space-optimized variant.
Practice articulating when you would pick each (constraints, readability, follow-ups).
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 queue bfs:
- 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: breadth first search.
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 K-Similar Strings in a second language (cpp, python).
- Drill 3–5 more problems tagged breadth first search.
- 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 queue bfs 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
K-Similar Strings (#854) — Hard. Pattern: queue bfs. Complexity: O(n * n!/(ca!*...*cz!)) time / O(n * n!/(ca!*...*cz!)) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of K-Similar Strings?+
The reference solutions aim for O(n * n!/(ca!*...*cz!)) time and O(n * n!/(ca!*...*cz!)) space. Always re-derive complexity from the code you write in the interview.
What pattern does K-Similar Strings use?+
It primarily maps to queue bfs, within the broader topic of breadth first search.
Is K-Similar Strings 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/k-similar-strings/