[Solved] Suppose intervals can be reused multiple times (i.e., you can merge overlapping intervals repeatedly, possibly... Which modification to the merge intervals algorithm correctly handles this scenario? | Intervals

Intervals - Merge Intervals

Suppose intervals can be reused multiple times (i.e., you can merge overlapping intervals repeatedly, possibly reusing intervals). Which modification to the merge intervals algorithm correctly handles this scenario?

AUse the same sorting + one pass merge approach; repeated intervals will be merged naturally.

BSort intervals and repeatedly apply the merge pass until no changes occur, which may take multiple passes.

CUse a brute force nested loop approach to merge intervals until no overlaps remain.

DUse a graph-based approach to find connected components of overlapping intervals and merge each component.

Step-by-Step Solution

Step 1: Understand that reusing intervals means overlaps can form complex connected groups.
Simple one-pass merge assumes intervals appear once and sorted order suffices.
Step 2: Recognize that overlapping intervals form connected components in a graph.
Building a graph where intervals are nodes and edges represent overlaps allows merging all connected intervals correctly.
Step 3: Evaluate options.
Use the same sorting + one pass merge approach; repeated intervals will be merged naturally. fails because one pass merge assumes no reuse. Sort intervals and repeatedly apply the merge pass until no changes occur, which may take multiple passes. is inefficient and may not terminate quickly. Use a brute force nested loop approach to merge intervals until no overlaps remain. is brute force and inefficient. Use a graph-based approach to find connected components of overlapping intervals and merge each component. correctly models the problem and merges all connected intervals.
Final Answer:
Option D -> Option D
Quick Check:
Graph connected components capture all overlapping intervals including reuse. [OK]

Quick Trick: Model reuse as graph connected components [OK]

Common Mistakes:

MISTAKES

Assuming one pass merge works with reuse
Using repeated merges without termination guarantee

Trap Explanation:

PITFALL

Naive repeated merges seem plausible but are inefficient and may fail on complex overlaps.

Interviewer Note:

CONTEXT

Tests candidate's ability to adapt and generalize interval merging beyond standard assumptions.

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Which modification to the merge intervals algorithm correctly handles this scenario?

Step 1: Understand that reusing intervals means overlaps can form complex connected groups.

Step 2: Recognize that overlapping intervals form connected components in a graph.

Step 3: Evaluate options.

Final Answer:

Quick Check:

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