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This week, we’ll solve one of the most popular Dynamic Programming problems. Are you ready for the challenge?

Today we will cover:

• Longest Increasing Subsequence

• Throttling and Backpressure

Read time: under 4 minutes

CODING CHALLENGE

Longest Increasing Subsequence

Given an integer array nums, return the length of the longest strictly increasing subsequence.

Example 1:

Input: nums = [10,9,2,5,3,7,101,18]
Output: 4
Explanation: The longest increasing subsequence is [2,3,7,101], therefore the length is 4.

Example 2:

Input: nums = [0,1,0,3,2,3]
Output: 4

Solve the problem here before reading the solution.

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SOLUTION

To solve this problem efficiently, we'll use dynamic programming with binary search.

The algorithm works as follows:

1. We start with an empty subsequence array.

2. We iterate the input array from left to right. For each number, we either:

   1. Append it to the subsequence if it's larger than all existing elements

   2. Replace the smallest element that is greater than or equal to it using binary search

3. The length of the subsequence array gives us the length of the longest increasing subsequence.

Binary search allows us to efficiently find and replace elements, giving us the O(n log n) time complexity.

SYSTEM DESIGN

Throttling and Backpressure

When systems get overwhelmed with too many requests, they can crash or become unresponsive. This is a common problem in APIs and distributed systems. Throttling and backpressure are two techniques that help prevent system overload.

Throttling limits how many requests a client can make within a specific time period. For example, an API might allow only 100 requests per minute from each user. When a client exceeds this limit, their requests are rejected until the next time window begins. This protects the server from being overwhelmed and ensures fair resource distribution among all clients.

While throttling works by rejecting excess requests, backpressure takes a different approach. Instead of rejection, it slows down the rate at which requests are accepted. Think of water flowing through a pipe. If you pour too fast, water backs up at the entrance. Similarly, backpressure makes the sender slow down when the receiver can't keep up.

Backpressure is especially important in streaming systems where data flows continuously. For example, if a service processing video streams can't keep up with incoming data, it signals the sender to slow down rather than dropping frames or crashing.

There are several ways to implement throttling:

• Token bucket: Clients get tokens that replenish over time

• Leaky bucket: Requests are processed at a constant rate

• Fixed window: Simple counter reset at fixed intervals

• Sliding window: More accurate but complex to implement

Backpressure can be implemented through:

• Buffer limits: Stop accepting new requests when buffer is full

• Flow control: Use protocols that support speed control

• Queue monitoring: Adjust accept rate based on queue size

Here's a comparison of both approaches:

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NEWS

This Week in the Tech World

OpenAI builds LinkedIn rival: ChatGPT maker develops AI-powered recruitment platform to compete with Microsoft's LinkedIn. Service includes certification programs targeting 10 million Americans by 2030 amid job displacement concerns.

Ex-WhatsApp security chief sues Meta: Former head of security alleges 1,500 engineers had unrestricted access to user data without audit trails. Attaullah Baig claims retaliation after reporting cybersecurity failures to CEO Mark Zuckerberg.

OpenAI expands India presence: Company sees 111 million ChatGPT downloads in India, surpassing US market with 10.2 million August downloads. Plans include local data center, office opening, and education programs despite legal challenges.

Microsoft signs $19B Nebius deal: AI infrastructure firm Nebius secures massive multi-year Microsoft contract for GPU computing power. The Amsterdam-based company, spun out from Russian Yandex, sees stock surge 51% on the cloud services agreement.

Anthropic pays $1.5B copyright settlement: AI company agrees to pay authors $3,000 per pirated work covering 500,000 titles used for training. "First of its kind" settlement requires destruction of all illegally copied books.

UAE launches K2 Think AI model: Abu Dhabi's MBZUAI releases 32 billion parameter reasoning model challenging OpenAI and DeepSeek. Built on Alibaba's Qwen 2.5, the compact system matches larger rivals' performance using advanced reasoning techniques.

ASML invests $1.3B in Mistral: Dutch chip equipment giant takes 11% stake in French AI startup at $13.8 billion valuation. The partnership aims to reduce Silicon Valley dependence as Europe builds independent AI capabilities amid US trade tensions.

Google faces $3.45B EU fine: European Commission hits Google with antitrust penalty for favoring its own advertising technology services. Regulators demand end to self-preferencing practices that harm publishers, advertisers, and competitors.

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