Google

## Part 1: Algorithmic Problem — Sliding Window & Hashing ### Base Problem You are given an array of integers `nums` of length $N$ and an integer $K$. Task:** Find the maximum sum of any contiguous subarray of size exactly $K$. What is the brute-force time complexity? How do you implement a fixed-size **Sliding Window** to calculate the answer in strictly $O(N)$ time and $O(1)$ auxiliary space? - ### Follow-Up 1: Variable Window & Frequency Map You are now given a string `s` containing lowercase English letters and an integer $K$. Task:** Find the length of the longest contiguous substring that contains at most $K$ distinct characters. How do you adapt the sliding window technique using two pointers (`left` and `right`) and a frequency array/hash map to adjust the window dynamically? What are the exact time and space complexities, and why does each pointer advance at most $N$ times? - ### Follow-Up 2: Subarray Sum Equals Target (Prefix Sums + Hash Map) Given an array of integers `nums` (which can contain both positive and negative integers) and a target integer `T`. Task:** Find the total number of continuous subarrays whose sum equals `T`. Explain why a standard two-pointer sliding window fails when negative numbers are introduced. How do you solve this in strictly $O(N)$ time and $O(N)$ space using a **Prefix Sum** combined with a Hash Map? - ## Part 2: AI & LLM Core Concepts (Light / Foundational) ### Question 1: Tokens vs. Words What is a **token** in the context of Large Language Models, and why do models like GPT or LLaMA process text as subword tokens (e.g., via Byte Pair Encoding) instead of splitting strictly on whole words or single characters? - ### Question 2: Temperature & Creativity When generating text with an LLM, what does the **temperature** parameter control? What happens mathematically to the probability distribution of the next token when temperature is set close to `0.0`? What happens when it is increased to `1.0` or higher? - ### Question 3: Embeddings & Vector Search What is a **text embedding**? In simple terms, how does representing a sentence as a dense vector of numbers allow a vector database to find semantically related documents (e.g., matching "puppy" with "dog") even when they share no exact keywords? - ### Question 4: Fine-Tuning vs. Prompting What is the fundamental difference between **In-Context Learning (Prompt Engineering)** and **Supervised Fine-Tuning (SFT)**? When would a software team choose to write a detailed system prompt versus updating the actual model weights?