Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Dynamic Programming: Memoization and Bottom-Up Approach

In course

CS-250: Algorithms I

The students learn the theory and practice of basic concepts and techniques in algorithms. The course covers mathematical induction, techniques for analyzing algorithms, elementary data structures, major algorithmic paradigms such as dynamic programming, s ...

Description

This lecture covers dynamic programming concepts such as memoization and the bottom-up approach. It explains the process of optimizing recursive algorithms by storing results and solving smaller sub-problems first. The instructor demonstrates how to apply these techniques to problems like rod cutting and the change-making problem, providing insights into time complexity and optimal solution reconstruction.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (3)

Ola Nils Anders Svensson

Alessandro Chiesa

Alessandro Chiesa is a faculty member in computer science. He conducts research in complexity theory, cryptography, and security, with a focus on the theoretical foundations and practical implementations of cryptographic proofs that are short and easy to verify. He is a co-author of several zkSNARK libraries, and is a co-inventor of the Zerocash protocol. He has co-founded Zcash and StarkWare Industries. He is a recipient of a Sloan Research Fellowship (2021), an Okawa Foundation Research Grant (2020), and Google Faculty Research Awards (2018 and 2017). He was included in MIT Technology Review's "35 Innovators Under 35" list in 2018.

Mikhail Kapralov

Official source

Ontological neighbourhood

Theoretical computer science

Theory of computation: Computational complexity theory

Related concepts (18)

Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor.

Complexity class

In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly analyzed resources are time and memory. In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like time or memory. In particular, most complexity classes consist of decision problems that are solvable with a Turing machine, and are differentiated by their time or space (memory) requirements.

P (complexity)

In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class. It contains all decision problems that can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time. Cobham's thesis holds that P is the class of computational problems that are "efficiently solvable" or "tractable". This is inexact: in practice, some problems not known to be in P have practical solutions, and some that are in P do not, but this is a useful rule of thumb.

Computational complexity

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.

NP (complexity)

In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems. NP is the set of decision problems for which the problem instances, where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine. NP is the set of decision problems solvable in polynomial time by a nondeterministic Turing machine.

Related lectures (32)

Dynamic Programming: Solving Sequential Problems Efficiently

Explores dynamic programming for efficient problem-solving, illustrated with binomial coefficients and Pascal's triangle.

Algorithmic Complexity: Travel Time Analysis

Covers algorithmic complexity and travel time analysis, focusing on measuring the time taken by algorithms and evaluating their performance.

Complexity & Induction: Algorithms & Proofs

Covers worst-case complexity, algorithms, and proofs including mathematical induction and recursion.

Algorithmic Challenges: Solutions and Optimization

Explores algorithmic challenges, time complexity, optimization, recursion, and probability calculations.

Complexity of Algorithms