AF
Progress
#3268HardPremium on LC~50 min

Find Overlapping Shifts II

Time O(n^2) · Space O(n^2) · Official statement on LeetCode

sql
mysql

Solutions

# Time:  O(n^2)
# Space: O(n^2)

# line sweep
WITH events_cte AS (
    SELECT employee_id,
           start_time AS event_time,
           +1 as event_type
    FROM EmployeeShifts
    UNION ALL
    SELECT employee_id,
           end_time AS event_time,
           -1 as event_type
    FROM EmployeeShifts
    ORDER BY 1, 2, 3
), line_sweep_cte AS (
    SELECT employee_id,
           @event_count := @event_count + event_type AS event_count
    FROM events_cte, (SELECT @event_count := 0) init
), max_count_cte AS (
    SELECT employee_id,
       MAX(event_count) AS max_overlapping_shifts
    FROM line_sweep_cte
    GROUP BY 1
    ORDER BY NULL
), overlap_cte AS (
    SELECT e1.employee_id,
           TIMESTAMPDIFF(MINUTE, e2.start_time, IF(e1.end_time < e2.end_time, e1.end_time, e2.end_time)) AS overlap_duration
    FROM EmployeeShifts e1
    INNER JOIN EmployeeShifts e2
        ON e1.employee_id = e2.employee_id
    WHERE e1.start_time < e2.start_time
      AND e1.end_time > e2.start_time
), total_duration_cte AS (
    SELECT employee_id,
           SUM(overlap_duration) AS total_overlap_duration
    FROM overlap_cte
    GROUP BY 1
    ORDER BY NULL
)

SELECT c.employee_id,
       max_overlapping_shifts,
       IFNULL(total_overlap_duration, 0) AS total_overlap_duration
FROM max_count_cte c
LEFT JOIN total_duration_cte d
     ON c.employee_id = d.employee_id
ORDER BY 1;


# Time:  O(n^2)
# Space: O(n^2)
# window function, combinatorics
WITH time_cte AS (
    SELECT employee_id, start_time AS time
    FROM EmployeeShifts
    UNION
    SELECT employee_id, end_time AS time
    FROM EmployeeShifts
), segments_cte AS (
    SELECT employee_id,
           time AS start_time,
           LEAD(time) OVER(PARTITION BY employee_id ORDER BY time) AS end_time
    FROM time_cte
), counts_cte AS (
    SELECT s.employee_id,
           s.start_time,
           s.end_time,
           COUNT(*) AS cnt
    FROM segments_cte s
    INNER JOIN EmployeeShifts e 
        ON s.employee_id = e.employee_id
    WHERE s.start_time >= e.start_time
      AND s.end_time <= e.end_time
    GROUP BY 1, 2, 3
    ORDER BY NULL
)

SELECT employee_id,
       MAX(cnt) AS max_overlapping_shifts,
       SUM(cnt * (cnt - 1) / 2 * TIMESTAMPDIFF(MINUTE, start_time, end_time)) AS total_overlap_duration 
FROM counts_cte
GROUP BY 1
ORDER BY 1;

Beginner Explanation

What is Find Overlapping Shifts II?

Find Overlapping Shifts II (LeetCode #3268) is a Hard problem that primarily trains sql.

How to think about it

  1. Restate the goal in your own words before coding.
  2. Work a tiny example by hand so the invariant becomes obvious.
  3. Identify the pattern — this problem aligns with general problem-solving.
  4. Only then translate the idea into code.

Why this problem matters

Hard problems force you to combine patterns and prove complexity carefully — interview gold. Official solution notes mention: Line Sweep, Window Function, Combinatorics.

AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.

Interview Walkthrough

Interview approach for Find Overlapping Shifts II

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

  1. Define the state you track (pointers, DP cell, set membership, stack top, etc.).
  2. Explain the transition when you process the next element.
  3. Call out time (O(n^2)) and space (O(n^2)) before coding.
  4. 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^2) time and O(n^2) space.

Pattern focus: general problem-solving

Use the pattern as a checklist:

  • Identify the dominant pattern and stick to one clear invariant

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(n^2)
Space O(n^2)

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 Find Overlapping Shifts II

  1. Skipping edge cases — empty collections, single-element inputs, max constraints.
  2. Wrong invariant for general problem-solving — updating state too early or too late.
  3. Mutating input unexpectedly when the problem forbids it.
  4. Off-by-one in windows, ranges, or binary search bounds.
  5. Ignoring overflow / precision for integer arithmetic problems.
  6. Overengineering — jumping to an advanced structure when a simpler approach works.

Alternative Approaches

AI expand later

Alternatives

Placeholder for multi-approach comparison. Future AI content generation can expand:

  • Brute force baseline
  • Optimal general problem-solving solution
  • Space-optimized rewrite

Prompt slot: expand alternatives for find-overlapping-shifts-ii.

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: sql.

Follow-up Interview Questions

Follow-ups

  1. How does the solution change if the input is a stream?
  2. Can you solve it in-place?
  3. What if duplicates must be handled differently?
  4. How would you parallelize the approach?
  5. Design tests that would break a buggy implementation.

Practice Recommendations

What to practice next

  1. Re-solve Find Overlapping Shifts II in a second language (mysql).
  2. Drill 3–5 more problems tagged sql.
  3. Teach the solution out loud in under 5 minutes.
  4. Add this problem to your revision calendar in 3 days and 14 days.

Visualization

Conceptual diagram for Find Overlapping Shifts II: show input structure (sql), 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

Find Overlapping Shifts II (#3268) — Hard. Pattern: general problem-solving. Complexity: O(n^2) time / O(n^2) space. Re-derive the invariant before coding.

FAQs

What is the time complexity of Find Overlapping Shifts II?+

The reference solutions aim for O(n^2) time and O(n^2) space. Always re-derive complexity from the code you write in the interview.

What pattern does Find Overlapping Shifts II use?+

It primarily maps to general problem-solving, within the broader topic of sql.

Is Find Overlapping Shifts II good for interviews?+

Yes — as a Hard 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/find-overlapping-shifts-ii/