Minimum Sideway Jumps
Time O(n) · Space O(1) · Official statement on LeetCode
Solutions
// Time: O(n)
// Space: O(1)
// greedy solution
class Solution {
public:
int minSideJumps(vector<int>& obstacles) {
int result = 0;
unordered_set<int> lanes = {2};
for (int i = 0; i + 1 < size(obstacles); ++i) {
lanes.erase(obstacles[i + 1]);
if (!empty(lanes)) {
continue;
}
++result;
for (int j = 1; j <= 3; ++j) {
if (j != obstacles[i] && j != obstacles[i + 1]) {
lanes.emplace(j);
}
}
}
return result;
}
};
// Time: O(n)
// Space: O(1)
// dp solution
class Solution2 {
public:
int minSideJumps(vector<int>& obstacles) {
static const int MAX_N = 5 * 1e5;
static const int INF = (MAX_N - 1) + 1;
array<int, 3> dp{1, 0, 1};
for (const auto& i : obstacles) {
if (i) {
dp[i - 1] = INF;
}
for (int j = 0; j < 3; ++j) {
if (j + 1 != i) {
dp[j] = min({dp[0] + (j != 0), dp[1] + (j != 1), dp[2] + (j != 2)});
}
}
}
return *min_element(cbegin(dp), cend(dp));
}
};
Beginner Explanation
What is Minimum Sideway Jumps?
Minimum Sideway Jumps (LeetCode #1824) is a Medium problem that primarily trains greedy.
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 greedy and dynamic programming.
- 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: Greedy, DP.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Minimum Sideway Jumps
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 greedy and dynamic programming.
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(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(n) time and O(1) space.
Pattern focus: greedy and dynamic programming
Use the pattern as a checklist:
- greedy — confirm the invariant holds after each step
- dynamic programming — 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(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 Minimum Sideway Jumps
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for greedy and dynamic programming — 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 greedy and dynamic programming:
- 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: greedy.
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 Minimum Sideway Jumps in a second language (cpp, python).
- Drill 3–5 more problems tagged greedy.
- 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 greedy and dynamic programming 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
Minimum Sideway Jumps (#1824) — Medium. Pattern: greedy and dynamic programming. Complexity: O(n) time / O(1) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Minimum Sideway Jumps?+
The reference solutions aim for O(n) time and O(1) space. Always re-derive complexity from the code you write in the interview.
What pattern does Minimum Sideway Jumps use?+
It primarily maps to greedy and dynamic programming, within the broader topic of greedy.
Is Minimum Sideway Jumps 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/minimum-sideway-jumps/