In this paper, we introduce a new topic, data proportion detection, which enables the automatic estimation of pre-training data proportions by analyzing the generated outputs of LLMs. We provide rigorous theoretical proofs, practical algorithms, and preliminary experimental results for data proportion detection.

4 days ago · DSA (Data Structures and Algorithms) is the study of organizing data efficiently using data structures like arrays, stacks, and trees, paired with step-by-step procedures (or algorithms) to solve problems effectively.

DSA is about finding efficient ways to store and retrieve data, to perform operations on data, and to solve specific problems. By understanding DSA, you can: Decide which data structure or algorithm is best for a given situation. Make programs that run faster or use less memory.

Jan 3, 2011 · Approach: This book describes many techniques for representing data. These techniques are presented within the context of the following principles: Each data structure and each algorithm has costs and benefits. Practitioners need a thorough understanding of how to assess costs and benefits to be able to adapt to new design challenges.

Dec 2, 2023 · In this section, we’ll explore key guidelines and considerations for selecting, implementing, and optimizing data structures and algorithms in the context of Big Data.

2 days ago · This essential guide covers fundamental data structures (arrays, hash tables, trees), core algorithms (sorting, searching, path-finding), and graph techniques (traversal, shortest paths, cycle detection) with their time/space complexities and Python implementations. Each concept is presented with real-world applications and practical code examples to help you both in technical interviews and ...

Feb 3, 2023 · We summarize the performance characteristics of classic algorithms and data structures for sorting, priority queues, symbol tables, and graph processing. We also summarize some of the mathematics useful in the analysis of algorithms, including commonly encountered functions; useful formulas and approximations; properties of logarithms ...

Prove the “inductive case” i.e. if P(k) is true, then P(k+1) is true. Why we care: To show an algorithm is correct or has a certain running time no matter how big a data structure or input value is (Our “n” will be the data structure or input size.)

Particularly as the volume of available data skyrockets, one of the most important aspects of programming consists of defining data structures to represent that information. Classes. Class definitions make it possible to combine related pieces of information into an integrated unit. Arrays. Arrays make it possible to store ordered lists of data.

Motivating Quotation “Every program depends on algorithms and data structures, but few programs depend on the invention of brand new ones.”