1. Algorithms and Computation
MIT OpenCourseWare
45 min, 39 sec
An overview of the Introduction to Algorithms course, its goals, and fundamental concepts.
Summary
- Jason Ku introduces the course alongside other instructors, Eric Demaine and Justin Solomon.
- The course aims to teach problem-solving, proving algorithm correctness, arguing efficiency, and communication of ideas.
- A computational problem is introduced as a binary relation between sets of inputs and correct outputs.
- An algorithm's correctness and efficiency are discussed, with the use of induction for proving correctness and asymptotic analysis for efficiency.
- The course will cover data structures, graph algorithms, and dynamic programming.
Chapter 1
Chapter 2
The course's primary goals are to solve computational problems and effectively communicate solutions.
- Students will learn to solve computational problems, prove correctness, argue efficiency, and communicate solutions.
- Writing will be a significant part of the course, emphasizing the communication of ideas over coding.
Chapter 3
A computational problem is defined, and the importance of problem specification is discussed.
- A computational problem is a binary relation between a set of inputs and a set of correct outputs.
- Problems are typically defined using predicates to check correctness, rather than enumerating all input-output pairs.
Chapter 4
An algorithm is a function that maps inputs to correct outputs, and its correctness must be proven.
- An algorithm must output a correct result for each input, often verified using induction.
- The example of checking for matching birthdays in a class illustrates an algorithm and the concept of proving its correctness.
Chapter 5
Efficiency is discussed in the context of comparing algorithm performance and using asymptotic analysis.
- Efficiency is not about actual time but the number of fundamental operations performed relative to input size.
- The class uses asymptotic notation such as big O, omega, and theta to describe algorithm efficiency.
Chapter 6
A model of computation is established, and the structure of the course is outlined.
- The word RAM model is used for theoretical analysis of algorithms, with operations such as binary arithmetic and memory read/write in constant time.
- The course will cover data structures, graph algorithms, and dynamic programming across three quizzes.
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