You are given a list of intervals where each interval has a start and end time. Your goal is to select the maximum number of intervals such that none of the selected intervals overlap. Which algorithmic approach guarantees an optimal solution for this problem?
ADynamic programming that tries all subsets of intervals to find the maximum non-overlapping set.
BSort intervals by their start time and always pick the earliest starting interval first.
CSort intervals by their end time and greedily select intervals that start after the last selected interval ends.
DUse a graph coloring algorithm to assign intervals to different colors ensuring no overlaps.
Step-by-Step Solution
Step 1: Understand the problem goal
The problem requires selecting the maximum number of intervals with no overlaps.
Step 2: Identify the optimal greedy strategy
Sorting intervals by their end time and greedily picking intervals that start after the last selected interval ends ensures the maximum number of intervals are chosen.
Final Answer:
Option C -> Option C
Quick Check:
Greedy by earliest end time is a classic optimal approach [OK]
Quick Trick:Sort by end time for max non-overlapping intervals [OK]
Common Mistakes:
MISTAKES
Sorting by start time and picking earliest start first
Trying brute force DP without pruning
Using graph coloring which is unrelated here
Trap Explanation:
PITFALL
Sorting by start time looks intuitive but can miss optimal solutions because it doesn't consider interval length or end time.
Interviewer Note:
CONTEXT
Tests if candidate knows the classic greedy pattern for interval scheduling.
Master "Non-overlapping Intervals (Max Non-Overlap)" in Intervals
3 interactive learning modes - each teaches the same concept differently
