Number partitioning | Pseudo-polynomial time algorithms
In computer science, pseudopolynomial time number partitioning is a pseudopolynomial time algorithm for solving the partition problem. The problem can be solved using dynamic programming when the size of the set and the size of the sum of the integers in the set are not too big to render the storage requirements infeasible. Suppose the input to the algorithm is a multiset of cardinality : S = {x1, ..., xN} Let K be the sum of all elements in S. That is: K = x1 + ... + xN. We will build an algorithm that determines whether there is a subset of S that sums to . If there is a subset, then: if K is even, the rest of S also sums to if K is odd, then the rest of S sums to . This is as good a solution as possible. e.g.1 S = {1, 2, 3, 5}, K = sum(S) = 11, K/2 = 5, Find a subset from S that is closest to K/2 -> {2, 3} = 5, 11 - 5 * 2 = 1 e.g.2 S = {1, 3, 7}, K = sum(S) = 11, K/2 = 5, Find a subset from S that is closest to K/2 -> {1, 3} = 4, 11 - 4 * 2 = 3 (Wikipedia).
18. Dynamic Programming, Part 4: Rods, Subset Sum, Pseudopolynomial
MIT 6.006 Introduction to Algorithms, Spring 2020 Instructor: Erik Demaine View the complete course: https://ocw.mit.edu/6-006S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY This is the fourth and final lecture on dynamic programming. This cl
From playlist MIT 6.006 Introduction to Algorithms, Spring 2020
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MIT 6.006 Introduction to Algorithms, Spring 2020 Instructor: Jason Ku View the complete course: https://ocw.mit.edu/6-006S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY This session focuses on preparing for the quiz. High-level concepts are
From playlist MIT 6.006 Introduction to Algorithms, Spring 2020
Lecture 21: Dynamic Programming III: Parenthesization, Edit Distance, Knapsack
MIT 6.006 Introduction to Algorithms, Fall 2011 View the complete course: http://ocw.mit.edu/6-006F11 Instructor: Erik Demaine License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.006 Introduction to Algorithms, Fall 2011
Manfred Madritsch: Normal and Non-Normal Numbers
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From playlist Multiplying and Dividing Mixed Numbers
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This class focuses on hinged dissections. Examples of hinged dissections and several built, reconfigurable applications are offere
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From playlist Number Sense - Decimals, Percents, and Ratios
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From playlist HIM Lectures 2015
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