Data Streams & Interval Problems: Overview

Published: Sun Feb 15 2026 | Modified: Sat Feb 07 2026 , 4 minutes reading.

Typical Business Scenarios

Handling data that changes over time or requires complex range-based queries is a core requirement in high-performance systems:

Financial Trading: “What was the highest stock price between 10:00 AM and 2:00 PM?” (RMQ - Range Minimum/Maximum Query).
Ad-Tech: Calculating the total spend of a campaign across millions of specific time intervals.
Game Development: Real-time leaderboards where player scores change every second (Dynamic Updates).
Monitoring: Finding the median latency of the last 10,000 requests in a sliding window.
Logistics: Determining the total load in a specific geographical segment of a route.

Is the data Static or Dynamic?
- Static (No updates): Use a Sparse Table for $O(1)$ range queries.
- Dynamic (Frequent updates): Use a Segment Tree or Fenwick Tree.
What is the query type?
- Range Sum: Fenwick Tree is the most memory-efficient and easiest to implement.
- Complex Range Ops (Min/Max/Gcd): Segment Tree is the universal solution.
Is it a Continuous Stream?
- Yes: Use Sliding Windows (Monotonic Queues) or Two Heaps for real-time statistics like medians.

6.1 Segment Tree: The Swiss Army Knife. Supports range updates and range queries in $O(\log N)$ .
6.2 Fenwick Tree (BIT): A lightweight structure for prefix sums and point updates.
6.3 Sparse Table: Precalculates results to answer range minimum queries in constant $O(1)$ time.
6.4 Monotonic Queue: Efficiently finding the max/min in a sliding window of size $K$ .
6.5 Two Heaps: The standard pattern for finding the median in a live data stream.

Requirement	Algorithm	Query Time	Update Time	Memory
Static Range Min/Max	Sparse Table	$O(1)$	N/A	$O(N \log N)$
Dynamic Range Sum	Fenwick Tree	$O(\log N)$	$O(\log N)$	$O(N)$
Dynamic Range Min/Max	Segment Tree	$O(\log N)$	$O(\log N)$	$O(4N)$
Window Max/Min	Monotonic Queue	$O(1)$	$O(1)$ amortized	$O(K)$
Stream Median	Two Heaps	$O(1)$	$O(\log N)$	$O(N)$

“Interval structures trade a bit of preprocessing and memory to turn slow linear scans into lightning-fast logarithmic or constant lookups.”