Which modification to the sweep line algorithm ensures correct minimum platform calculation?
hard🎤 Interviewer Follow-up Q15 of Q15
Intervals - Minimum Number of Platforms Required
Suppose trains can arrive and depart multiple times (reusing platforms) and the schedule may include negative time values (e.g., early morning times). Which modification to the sweep line algorithm ensures correct minimum platform calculation?
AUse the same sweep line approach but ensure sorting handles negative times correctly and process events with departure before arrival on tie.
BUse dynamic programming to handle multiple arrivals and departures per train.
CSwitch to nested loops checking overlaps since negative times break sorting assumptions.
DIgnore negative times and treat them as zero to simplify sorting.
Step-by-Step Solution
Solution:
Step 1: Recognize that negative times do not affect event sorting if handled correctly
Sorting supports negative values naturally; no need to ignore or clamp them.
Step 2: Maintain departure-before-arrival ordering on tie to avoid overcounting
This ordering is critical regardless of time values or multiple arrivals/departures.
Step 3: Continue using sweep line approach for efficiency and correctness
Nested loops or DP are inefficient or unnecessary for this variant.
Final Answer:
Option A -> Option A
Quick Check:
Sweep line with correct sorting handles negative and multiple events [OK]
Quick Trick:Sorting handles negative times; keep departure before arrival on tie [OK]
Common Mistakes:
MISTAKES
Ignoring negative times or clamping them
Switching to inefficient nested loops unnecessarily
Misordering events causing overcounting
Trap Explanation:
PITFALL
Negative times seem unusual but sorting supports them; ignoring or clamping breaks correctness.
Interviewer Note:
CONTEXT
Tests candidate's ability to adapt sweep line to edge cases and maintain correctness.
Master "Minimum Number of Platforms Required" in Intervals
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