Design Authentication Manager
Time ctor: O(1) generate: O(1), amortized renew: O(1), amortized count: O(1), amortized · Space O(n) · Official statement on LeetCode
Solutions
// Time: ctor: O(1)
// generate: O(1), amortized
// renew: O(1), amortized
// count: O(1), amortized
// Space: O(n)
class AuthenticationManager {
public:
AuthenticationManager(int timeToLive)
: time_(timeToLive) {
}
void generate(string tokenId, int currentTime) {
evict(currentTime);
lookup_[tokenId] = time_ + currentTime;
}
void renew(string tokenId, int currentTime) {
evict(currentTime);
if (!lookup_.count(tokenId)) {
return;
}
lookup_.remove(tokenId);
lookup_[tokenId] = time_ + currentTime;
}
int countUnexpiredTokens(int currentTime) {
evict(currentTime);
return size(lookup_);
}
private:
void evict(int currentTime) {
while (!empty(lookup_) && lookup_.front().second <= currentTime) {
lookup_.remove(lookup_.front().first);
}
}
template<typename K, typename V>
class OrderedDict {
public:
bool count(const K& key) const {
return map_.count(key);
}
V& operator[](const K& key) {
if (!map_.count(key)) {
list_.emplace_front();
list_.begin()->first = key;
map_[key] = list_.begin();
}
return map_[key]->second;
}
void popitem() {
auto del = list_.front(); list_.pop_front();
map_.erase(del.first);
}
void remove(const K& key) {
list_.erase(map_[key]);
map_.erase(key);
}
pair<K, V> front() const {
return *list_.crbegin();
}
int size() const {
return std::size(list_);
}
int empty() const {
return std::empty(list_);
}
private:
list<pair<K, V>> list_;
unordered_map<K, typename list<pair<K, V>>::iterator> map_;
};
int time_;
OrderedDict<string, int> lookup_;
};
Beginner Explanation
What is Design Authentication Manager?
Design Authentication Manager (LeetCode #1797) is a Medium problem that primarily trains design.
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 general problem-solving.
- 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: OrderedDict.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Design Authentication Manager
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 general problem-solving.
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 (ctor: O(1) generate: O(1), amortized renew: O(1), amortized count: O(1), amortized) 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 ctor: O(1) generate: O(1), amortized renew: O(1), amortized count: O(1), amortized time and O(n) space.
Pattern focus: general problem-solving
Use the pattern as a checklist:
- Identify the dominant pattern and stick to one clear invariant
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 | ctor: O(1) generate: O(1), amortized renew: O(1), amortized count: O(1), amortized |
| 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 Design Authentication Manager
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for general problem-solving — 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 general problem-solving:
- 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: design.
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 Design Authentication Manager in a second language (cpp, python).
- Drill 3–5 more problems tagged design.
- 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 general problem-solving 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
Design Authentication Manager (#1797) — Medium. Pattern: general problem-solving. Complexity: ctor: O(1) generate: O(1), amortized renew: O(1), amortized count: O(1), amortized time / O(n) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Design Authentication Manager?+
The reference solutions aim for ctor: O(1) generate: O(1), amortized renew: O(1), amortized count: O(1), amortized time and O(n) space. Always re-derive complexity from the code you write in the interview.
What pattern does Design Authentication Manager use?+
It primarily maps to general problem-solving, within the broader topic of design.
Is Design Authentication Manager 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/design-authentication-manager/