Sqrt(x)
Time O(logn) · Space O(1) · Official statement on LeetCode
Solutions
// Time: O(logn)
// Space: O(1)
class Solution {
public:
int mySqrt(int x) {
if (x < 2) {
return x;
}
int left = 1, right = x / 2;
while (left <= right) {
const auto mid = left + (right - left) / 2;
if (mid > x / mid) {
right = mid - 1;
} else {
left = mid + 1;
}
}
return left - 1;
}
};
Beginner Explanation
What is Sqrt(x)?
Sqrt(x) (LeetCode #69) is a Medium problem that primarily trains binary 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 binary search.
- 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.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Sqrt(x)
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 binary search.
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(logn)) and space (O(1)) 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(logn) time and O(1) space.
Pattern focus: binary search
Use the pattern as a checklist:
- binary search — 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(logn) |
| Space | O(1) |
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 Sqrt(x)
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for binary search — 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 binary search solution
- Space-optimized rewrite
Prompt slot: expand alternatives for sqrtx.
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 binary search:
- 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: binary 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 Sqrt(x) in a second language (cpp, python).
- Drill 3–5 more problems tagged binary 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 binary search 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
Sqrt(x) (#69) — Medium. Pattern: binary search. Complexity: O(logn) time / O(1) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Sqrt(x)?+
The reference solutions aim for O(logn) time and O(1) space. Always re-derive complexity from the code you write in the interview.
What pattern does Sqrt(x) use?+
It primarily maps to binary search, within the broader topic of binary search.
Is Sqrt(x) 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/sqrtx/