Which algorithmic approach guarantees an optimal and efficient solution for this problem?
easy🔍 Pattern Recognition Q11 of Q15
Intervals - Merge Intervals
You are given a list of time intervals representing booked meeting rooms. Your task is to combine all overlapping intervals into the minimum number of non-overlapping intervals. Which algorithmic approach guarantees an optimal and efficient solution for this problem?
AUse a greedy approach that always merges the earliest starting interval with the next one without sorting.
BSort intervals by start time and then merge overlapping intervals in a single pass.
CUse dynamic programming to find the maximum number of non-overlapping intervals and then merge accordingly.
DCheck every pair of intervals with nested loops to merge overlaps until no overlaps remain.
Step-by-Step Solution
Step 1: Understand the problem requires merging overlapping intervals efficiently.
Sorting intervals by their start time ensures that overlapping intervals are adjacent, enabling a single pass merge.
Step 2: Evaluate each option's approach.
Use a greedy approach that always merges the earliest starting interval with the next one without sorting. fails because without sorting, intervals may be merged incorrectly or missed. Use dynamic programming to find the maximum number of non-overlapping intervals and then merge accordingly. is unrelated as DP is not needed here. Check every pair of intervals with nested loops to merge overlaps until no overlaps remain. is brute force with O(n²) time, inefficient for large inputs. Sort intervals by start time and then merge overlapping intervals in a single pass. correctly sorts and merges in O(n log n) time.
Final Answer:
Option B -> Option B
Quick Check:
Sorting + one pass merge is the classic optimal pattern for merging intervals. [OK]
Quick Trick:Sort intervals first, then merge in one pass [OK]
Common Mistakes:
MISTAKES
Trying to merge without sorting
Using nested loops leading to O(n²) time
Trap Explanation:
PITFALL
Greedy without sorting looks simpler but misses overlaps; brute force is correct but inefficient.
Interviewer Note:
CONTEXT
Tests if candidate recognizes the canonical pattern beyond just knowing the problem name.
Master "Merge Intervals" in Intervals
3 interactive learning modes - each teaches the same concept differently
