Accounts Merge
Time O(nlogn) · Space O(n) · Official statement on LeetCode
Solutions
// Time: O(nlogn), n is the number of total emails, and the max length of email is 320, p.s. {64}@{255}
// Space: O(n)
class Solution {
public:
vector<vector<string>> accountsMerge(vector<vector<string>>& accounts) {
UnionFind union_find;
unordered_map<string, string> email_to_name;
unordered_map<string, int> email_to_id;
for (const auto& account : accounts) {
const auto& name = account[0];
for (int i = 1; i < account.size(); ++i) {
if (!email_to_id.count(account[i])) {
email_to_name[account[i]] = name;
email_to_id[account[i]] = union_find.get_id();
}
union_find.union_set(email_to_id[account[1]], email_to_id[account[i]]);
}
}
unordered_map<int, set<string>> lookup;
for (const auto& kvp : email_to_name) {
const auto& email = kvp.first;
lookup[union_find.find_set(email_to_id[email])].emplace(email);
}
vector<vector<string>> result;
for (const auto& kvp : lookup) {
const auto& emails = kvp.second;
vector<string> tmp{email_to_name[*emails.begin()]};
for (const auto& email : emails) {
tmp.emplace_back(email);
}
result.emplace_back(move(tmp));
}
return result;
}
private:
class UnionFind {
public:
int get_id() {
set_.emplace_back(set_.size());
return set_.size() - 1;
}
int find_set(const int x) {
if (set_[x] != x) {
set_[x] = find_set(set_[x]); // Path compression.
}
return set_[x];
}
void union_set(const int x, const int y) {
int x_root = find_set(x), y_root = find_set(y);
if (x_root != y_root) {
set_[min(x_root, y_root)] = max(x_root, y_root);
}
}
private:
vector<int> set_;
};
};
Beginner Explanation
What is Accounts Merge?
Accounts Merge (LeetCode #721) is a Medium problem that primarily trains hash table.
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 union find.
- Only then translate the idea into code.
Why this problem matters
It sits in the sweet spot of interview difficulty: multiple valid approaches, clear trade-offs. Official solution notes mention: Union Find.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Accounts Merge
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 union find.
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(nlogn)) and space (O(n)) 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(nlogn) time and O(n) space.
Pattern focus: union find
Use the pattern as a checklist:
- union find — 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(nlogn) |
| Space | O(n) |
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 Accounts Merge
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for union find — 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 union find:
- 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: hash table.
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 Accounts Merge in a second language (cpp, python).
- Drill 3–5 more problems tagged hash table.
- 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 union find 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
Accounts Merge (#721) — Medium. Pattern: union find. Complexity: O(nlogn) time / O(n) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Accounts Merge?+
The reference solutions aim for O(nlogn) time and O(n) space. Always re-derive complexity from the code you write in the interview.
What pattern does Accounts Merge use?+
It primarily maps to union find, within the broader topic of hash table.
Is Accounts Merge good for interviews?+
Yes — as a Medium 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/accounts-merge/