Fill a Special Grid
Time O(4^n) · Space O(1) · Official statement on LeetCode
Solutions
// Time: O(4^n)
// Space: O(1)
// array
class Solution {
public:
vector<vector<int>> specialGrid(int n) {
const int total = 1 << n;
vector<vector<int>> result(total, vector<int>(total));
const auto& copy = [&](int l, int r1, int c1, int r2, int c2) {
for (int i = 0; i < l; ++i) {
for (int j = 0; j < l; ++j) {
result[r2 + i][c2 + j] = result[r1 + i][c1 + j] + l * l;
}
}
};
for (int i = 0, l = 1; i < n; ++i, l <<= 1) {
int r = 0, c = total - l;
for (const auto& [dr, dc] : vector<pair<int, int>>{{l, 0}, {0, -l}, {-l, 0}}) {
const int nr = r + dr, nc = c + dc;
copy(l, r, c, nr, nc);
tie(r, c) = pair(nr, nc);
}
}
return result;
}
};
// Time: O(4^n)
// Space: O(n)
// divide and conquer
class Solution2 {
public:
vector<vector<int>> specialGrid(int n) {
const int total = 1 << n;
vector<vector<int>> result(total, vector<int>(total));
int idx = 0;
const function<void (int, int, int)> divide_and_conquer = [&](int l, int r, int c) {
if (l == 1) {
result[r][c] = idx++;
return;
}
l >>= 1;
for (const auto& [dr, dc] : vector<pair<int, int>>{{0, l}, {l, 0}, {0, -l}, {-l, 0}}) {
r += dr;
c += dc;
divide_and_conquer(l, r, c);
}
};
divide_and_conquer(total, 0, 0);
return result;
}
};
Beginner Explanation
What is Fill a Special Grid?
Fill a Special Grid (LeetCode #3537) is a Medium problem that primarily trains array.
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: Divide and Conquer, Array.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Fill a Special Grid
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 (O(4^n)) 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(4^n) time and O(1) 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 | O(4^n) |
| 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 Fill a Special Grid
- 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: array.
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 Fill a Special Grid in a second language (cpp, python).
- Drill 3–5 more problems tagged array.
- 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
Fill a Special Grid (#3537) — Medium. Pattern: general problem-solving. Complexity: O(4^n) time / O(1) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Fill a Special Grid?+
The reference solutions aim for O(4^n) time and O(1) space. Always re-derive complexity from the code you write in the interview.
What pattern does Fill a Special Grid use?+
It primarily maps to general problem-solving, within the broader topic of array.
Is Fill a Special Grid 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/fill-a-special-grid/