[Solved] Consider two approaches to count intervals containing each point:... When is approach 1 preferable over approach 2? | Intervals

Intervals - Count of Intervals Containing Each Point

Consider two approaches to count intervals containing each point: 1) Sorting intervals and points, then using binary search to count intervals starting before and ending after each point. 2) Using a line sweep algorithm with event sorting. When is approach 1 preferable over approach 2?

AWhen the number of points m is much larger than intervals n

BWhen memory is limited and auxiliary space must be minimized

CWhen intervals are very large and points are few

DWhen intervals and points are both very large and need fastest runtime

Step-by-Step Solution

Solution:

Step 1: Compare space usage
Binary search approach stores only sorted starts and ends arrays, using less auxiliary space than line sweep's event list.
Step 2: Trade-off analysis
Line sweep uses more space for events but can be faster; binary search uses less space but may be slower for large m.
Final Answer:
Option B -> Option B
Quick Check:
Binary search approach is better when memory is constrained [OK]

Quick Trick: Binary search uses less auxiliary space than line sweep [OK]

Common Mistakes:

MISTAKES

Assuming binary search is always faster
Ignoring space complexity differences
Confusing when to use each approach

Trap Explanation:

PITFALL

Candidates often overlook space trade-offs and pick binary search for speed only.

Interviewer Note:

CONTEXT

Tests understanding of trade-offs between time and space in interval counting approaches.

Master "Count of Intervals Containing Each Point" in Intervals

3 interactive learning modes - each teaches the same concept differently

Try It Solution Trace

More Intervals Quizzes

When is approach 1 preferable over approach 2?

Step 1: Compare space usage

Step 2: Trade-off analysis

Final Answer:

Quick Check:

Want More Practice?