Grid Teleportation Traversal
Time O(m * n) · Space O(m * n) · Official statement on LeetCode
Solutions
// Time: O(m * n)
// Space: O(m * n)
// 0-1 bfs
class Solution {
public:
int minMoves(vector<string>& matrix) {
static const vector<pair<int, int>> DIRECTIONS = {{0, 1}, {0, -1},
{1, 0}, {-1, 0}};
const int m = size(matrix), n = size(matrix[0]);
vector<vector<pair<int, int>>> lookup(26);
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (matrix[i][j] == '.' || matrix[i][j] == '#') {
continue;
}
lookup[matrix[i][j] - 'A'].emplace_back(i, j);
}
}
vector<vector<bool>> lookup2(m, vector<bool>(n));
deque<tuple<int, int, int>> dq = {{0, 0, 0}};
while (!empty(dq)) {
const auto [step, i, j] = dq.front(); dq.pop_front();
if (lookup2[i][j]) {
continue;
}
lookup2[i][j] = true;
if (i == m - 1 && j == n - 1) {
return step;
}
for (const auto& [di, dj] : DIRECTIONS) {
const int ni = i + di, nj = j + dj;
if (!(0 <= ni && ni < m && 0 <= nj && nj < n && matrix[ni][nj] != '#' && !lookup2[ni][nj])) {
continue;
}
dq.emplace_back(step + 1, ni, nj);
}
if (matrix[i][j] == '.') {
continue;
}
for (const auto& [ni, nj] : lookup[matrix[i][j] - 'A']) {
if (lookup2[ni][nj]) {
continue;
}
dq.emplace_front(step, ni, nj);
}
lookup[matrix[i][j] - 'A'].clear();
}
return -1;
}
};
Beginner Explanation
What is Grid Teleportation Traversal?
Grid Teleportation Traversal (LeetCode #3552) 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. Official solution notes mention: 0-1 BFS, Deque.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Grid Teleportation Traversal
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
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(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 Grid Teleportation Traversal
- 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
AI expand laterAlternatives
Placeholder for multi-approach comparison. Future AI content generation can expand:
- Brute force baseline
- Optimal queue bfs solution
- Space-optimized rewrite
Prompt slot: expand alternatives for grid-teleportation-traversal.
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 Grid Teleportation Traversal 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
Grid Teleportation Traversal (#3552) — 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 Grid Teleportation Traversal?+
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 Grid Teleportation Traversal use?+
It primarily maps to queue bfs, within the broader topic of breadth first search.
Is Grid Teleportation Traversal 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/grid-teleportation-traversal/