#1914Medium~35 min
Cyclically Rotating a Grid
Time O(m * n) · Space O(1) · Official statement on LeetCode
Solutions
// Time: O(m * n)
// Space: O(1)
// inplace rotation
class Solution {
public:
vector<vector<int>> rotateGrid(vector<vector<int>>& grid, int k) {
int m = size(grid), n = size(grid[0]);
const int count = min(m, n) / 2;
for (int i = 0; i < count; ++i, m -= 2, n -= 2) {
const int total = 2 * ((m - 1) + (n - 1));
const int nk = k % total;
const int num_cycles = gcd(total, nk);
const int cycle_len = total / num_cycles;
for (int offset = 0; offset < num_cycles; ++offset) {
const auto& [r, c] = getIndex(m, n, offset);
for (int j = 1; j < cycle_len; ++j) {
const auto& [nr, nc] = getIndex(m, n, (offset + j * nk) % total);
swap(grid[i + nr][i + nc], grid[i + r][i + c]);
}
}
}
return grid;
}
private:
pair<int, int> getIndex(int m, int n, int l) {
if (l < m - 1) {
return {l, 0};
}
if (l < (m - 1) + (n - 1)) {
return {m - 1, l - (m - 1)};
}
if (l < (m - 1) + (n - 1) + (m - 1)) {
return {(m - 1) - (l - ((m - 1) + (n - 1))), n - 1};
}
return {0, (n - 1) - (l - ((m - 1) + (n - 1) + (m - 1)))};
}
};
// Time: O(m * n)
// Space: O(1)
// inplace rotation
class Solution2 {
public:
vector<vector<int>> rotateGrid(vector<vector<int>>& grid, int k) {
int m = size(grid), n = size(grid[0]);
const int count = min(m, n) / 2;
for (int i = 0; i < count; ++i, m -= 2, n -= 2) {
const int total = 2 * ((m - 1) + (n - 1));
const int nk = k % total;
reverse(&grid, m, n, i, 0, total - 1);
reverse(&grid, m, n, i, 0, nk - 1);
reverse(&grid, m, n, i, nk, total - 1);
}
return grid;
}
private:
void reverse(vector<vector<int>> *grid,
int m, int n, int i,
int left, int right) {
for (; left < right; ++left, --right) {
auto [lr, lc] = getIndex(m, n, left);
auto [rr, rc] = getIndex(m, n, right);
swap((*grid)[i + lr][i + lc], (*grid)[i + rr][i + rc]);
}
}
pair<int, int> getIndex(int m, int n, int l) {
if (l < m - 1) {
return {l, 0};
}
if (l < (m - 1) + (n - 1)) {
return {m - 1, l - (m - 1)};
}
if (l < (m - 1) + (n - 1) + (m - 1)) {
return {(m - 1) - (l - ((m - 1) + (n - 1))), n - 1};
}
return {0, (n - 1) - (l - ((m - 1) + (n - 1) + (m - 1)))};
}
};
Beginner Explanation
What is Cyclically Rotating a Grid?
Cyclically Rotating a Grid (LeetCode #1914) 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: Inplace.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Cyclically Rotating a 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(m * 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(m * 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(m * 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 Cyclically Rotating a 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 Cyclically Rotating a 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
Conceptual diagram for Cyclically Rotating a Grid: show input structure (array), highlight the moving parts of the general problem-solving approach, and annotate each step with the maintained invariant and complexity.
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
Cyclically Rotating a Grid (#1914) — Medium. Pattern: general problem-solving. Complexity: O(m * n) time / O(1) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Cyclically Rotating a Grid?+
The reference solutions aim for O(m * n) time and O(1) space. Always re-derive complexity from the code you write in the interview.
What pattern does Cyclically Rotating a Grid use?+
It primarily maps to general problem-solving, within the broader topic of array.
Is Cyclically Rotating a 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/cyclically-rotating-a-grid/