Which approach guarantees an optimal solution with O(n log n) time complexity and O(1) extra space besides the input?
easy🔍 Pattern Recognition Q11 of Q15
Intervals - Remove Covered Intervals
You are given a list of intervals and need to remove all intervals that are covered by another interval. Which approach guarantees an optimal solution with O(n log n) time complexity and O(1) extra space besides the input?
AUse a brute force nested loop to check coverage between every pair of intervals.
BSort intervals by start ascending and end descending, then scan once to count uncovered intervals.
CUse dynamic programming to find the maximum set of non-covered intervals.
DSort intervals by end ascending and greedily pick intervals that do not overlap.
Step-by-Step Solution
Step 1: Understand sorting criteria
Sorting intervals by start ascending and end descending ensures intervals with the same start are ordered from longest to shortest, so coverage can be detected in one pass.
Step 2: Single pass coverage check
By scanning intervals in sorted order and tracking the maximum end seen, we can count intervals that are not covered by any previous interval.
Final Answer:
Option B -> Option B
Quick Check:
Sorting by start ascending and end descending enables O(n log n) sorting plus O(n) scanning [OK]
Quick Trick:Sort by start asc, end desc, then scan once [OK]
Common Mistakes:
MISTAKES
Sorting only by start ascending misses coverage when starts equal
Using nested loops causes TLE on large inputs
Trap Explanation:
PITFALL
Sorting only by start ascending looks simpler but fails to detect coverage when intervals share the same start point.
Interviewer Note:
CONTEXT
Tests if candidate recognizes the pattern and optimal sorting criteria for coverage detection.
Master "Remove Covered Intervals" in Intervals
3 interactive learning modes - each teaches the same concept differently
