Which algorithmic approach best guarantees efficient insertion and interval merging in this scenario?
easy🔍 Pattern Recognition Q11 of Q15
Intervals - Data Stream as Disjoint Intervals
You are given a stream of integers arriving one by one. After each insertion, you need to maintain a list of disjoint intervals that cover all the numbers seen so far, merging intervals if necessary. Which algorithmic approach best guarantees efficient insertion and interval merging in this scenario?
AUse a brute force approach by storing all numbers and sorting them each time intervals are requested.
BUse dynamic programming to precompute all possible intervals and update them incrementally.
CUse a balanced tree or sorted container to insert intervals and merge them on each insertion efficiently.
DUse a greedy algorithm that merges intervals only when requested, without maintaining sorted order.
Step-by-Step Solution
Solution:
Step 1: Understand the problem constraints
The problem requires maintaining disjoint intervals dynamically as numbers arrive, with efficient insertion and merging.
Step 2: Evaluate approaches
Brute force sorting each time (A) is inefficient. Dynamic programming (B) is not suitable for dynamic interval merging. Greedy merging only on request (D) leads to inefficient queries. Balanced tree or sorted container (C) supports O(log n) insertion and merging, making it optimal.
Final Answer:
Option C -> Option C
Quick Check:
Balanced tree supports efficient insertion and merging [OK]
Quick Trick:Balanced tree supports efficient dynamic interval merging [OK]
Common Mistakes:
MISTAKES
Thinking brute force sorting is efficient enough
Confusing DP with interval merging
Assuming greedy merging on request is optimal
Trap Explanation:
PITFALL
Brute force sorting looks simple but is inefficient for frequent insertions, tempting candidates to pick it.
Interviewer Note:
CONTEXT
Tests if candidate can identify the optimal data structure pattern for dynamic interval merging.
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