Lesson 21: Introduction to Algorithms by Mohammad Hajiaghayi: Memoization & Approximation Algorithms
In this session, we continue our discussion with more examples on backtracking, greedy, and dynamic programming, and also introduce approximation algorithms. Backtracking explores all possibilities, while greedy algorithms make local choices and dynamic programming solves overlapping subproblems. Backtracking has exponential complexity, while greedy and dynamic programming have polynomial complexities suited for optimization and problems with optimal substructure, respectively. Notably, memoized dynamic programming reduces backtracking's time complexity from exponential to polynomial by reusing computed subproblem results. We conclude the session by exploring approximation algorithms, which provide polynomial-time solutions that are close to the optimal solution.
#algorithms, #design, #complexity, #induction, #backtracking, #greedy, #dynamicprogramming, #memoization, #approximation, #approximationalgorithm, #optimization, #localstructure, #independentset, #binpacking, #longestcommonsubsequence, #lcs, #editdistance, #exponentialtime, #polynomialtime, #Python, #graphalgorithm, #geeksforgeeks, #hackerrank, #leetcode, #cs, #computerscience
All handwritten and typed notes for this course are available through the website of the instructor
at http://www.cs.umd.edu/~hajiagha/ (Just click on the "Introduction to Algorithms" course from the website).
