Maximum Trailing Zeros in a Cornered Path
Time O(m * n) · Space O(m * n) · Official statement on LeetCode
Solutions
// Time: O(m * n)
// Space: O(m * n)
// prefix sum
class Solution {
public:
int maxTrailingZeros(vector<vector<int>>& grid) {
const auto& factor = [](int x) {
static const array<int, 2> primes = {2, 5};
array<int, 2> cnt = {0, 0};
for (int i = 0; i < size(primes); ++i) {
while (x && x % primes[i] == 0) {
x /= primes[i];
++cnt[i];
}
}
return cnt;
};
const auto& add = [](const auto& a, const auto& b) {
return array<int, 2>{a[0] + b[0], a[1] + b[1]};
};
const auto& sub = [](const auto& a, const auto& b) {
return array<int, 2>{a[0] - b[0], a[1] - b[1]};
};
const auto& count = [](const auto& a) {
return min(a[0], a[1]);
};
vector<vector<array<int, 2>>> left(size(grid), vector<array<int, 2>>(size(grid[0])));
for (int i = 0; i < size(grid); ++i) {
left[i][0] = factor(grid[i][0]);
for (int j = 1; j < size(grid[0]); ++j) {
left[i][j] = add(left[i][j - 1], factor(grid[i][j]));
}
}
int result = 0;
for (int j = 0; j < size(grid[0]); ++j) {
array<int, 2> total = {0, 0};
for (int i = 0; i < size(grid); ++i) {
total = add(total, factor(grid[i][j]));
}
array<int, 2> up = {0, 0};
for (int i = 0; i < size(grid); ++i) {
const auto& right = j ? sub(left[i].back(), left[i][j - 1]) : left[i].back();
result = max({result, count(add(left[i][j], up)), count(add(right, up))});
up = add(up, factor(grid[i][j]));
const auto& down = sub(total, up);
result = max({result, count(add(left[i][j], down)), count(add(right, down))});
}
}
return result;
}
};
Beginner Explanation
What is Maximum Trailing Zeros in a Cornered Path?
Maximum Trailing Zeros in a Cornered Path (LeetCode #2245) 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 prefix sum.
- 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: Prefix Sum.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Maximum Trailing Zeros in a Cornered Path
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 prefix sum.
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: prefix sum
Use the pattern as a checklist:
- prefix sum — 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 Maximum Trailing Zeros in a Cornered Path
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for prefix sum — 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 prefix sum:
- 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 Maximum Trailing Zeros in a Cornered Path 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 prefix sum 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
Maximum Trailing Zeros in a Cornered Path (#2245) — Medium. Pattern: prefix sum. Complexity: O(m * n) time / O(m * n) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Maximum Trailing Zeros in a Cornered Path?+
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 Maximum Trailing Zeros in a Cornered Path use?+
It primarily maps to prefix sum, within the broader topic of array.
Is Maximum Trailing Zeros in a Cornered Path 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/maximum-trailing-zeros-in-a-cornered-path/