Coloring A Border
Time O(m * n) · Space O(m + n) · Official statement on LeetCode
Solutions
// Time: O(m * n)
// Space: O(m + n)
class Solution {
public:
template <typename T>
struct PairHash {
size_t operator()(const pair<T, T>& p) const {
size_t seed = 0;
seed ^= std::hash<T>{}(p.first) + 0x9e3779b9 + (seed<<6) + (seed>>2);
seed ^= std::hash<T>{}(p.second) + 0x9e3779b9 + (seed<<6) + (seed>>2);
return seed;
}
};
vector<vector<int>> colorBorder(vector<vector<int>>& grid, int r0, int c0, int color) {
static const vector<pair<int, int>> directions{{0, -1}, {0, 1},
{-1, 0}, {1, 0}};
vector<pair<int, int>> borders;
unordered_set<pair<int, int>, PairHash<int>> lookup{make_pair(r0, c0)};
queue<pair<int, int>> q({make_pair(r0, c0)});
while (!q.empty()) {
int r, c;
tie(r, c) = q.front(); q.pop();
bool is_border = false;
for (const auto& dir : directions) {
const auto nr = r + dir.first, nc = c + dir.second;
if (!((0 <= nr && nr < grid.size()) &&
(0 <= nc && nc < grid[0].size()) &&
grid[nr][nc] == grid[r][c])) {
is_border = true;
continue;
}
if (lookup.count(make_pair(nr, nc))) {
continue;
}
lookup.emplace(nr, nc);
q.emplace(nr, nc);
}
if (is_border) {
borders.emplace_back(r, c);
}
}
for (const auto& border : borders) {
grid[border.first][border.second] = color;
}
return grid;
}
};
Beginner Explanation
What is Coloring A Border?
Coloring A Border (LeetCode #1034) is a Medium problem that primarily trains breadth first 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 queue bfs.
- 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 Coloring A Border
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 queue bfs.
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(m + 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(m * n) time and O(m + n) space.
Pattern focus: queue bfs
Use the pattern as a checklist:
- queue bfs — 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(m * n) |
| Space | O(m + 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 Coloring A Border
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for queue bfs — 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 queue bfs:
- 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: breadth first 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 Coloring A Border in a second language (cpp, python).
- Drill 3–5 more problems tagged breadth first 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 queue bfs 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
Coloring A Border (#1034) — Medium. Pattern: queue bfs. Complexity: O(m * n) time / O(m + n) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Coloring A Border?+
The reference solutions aim for O(m * n) time and O(m + n) space. Always re-derive complexity from the code you write in the interview.
What pattern does Coloring A Border use?+
It primarily maps to queue bfs, within the broader topic of breadth first search.
Is Coloring A Border 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/coloring-a-border/