Teams

Group 1 | Thomas, Isaac |

Group 2 | Preston, Kyle |

Group 3 | Flynn, John, Boning |

Given a set of distinct positive integers, find the largest subset such that every pair (Si, Sj) of elements in this subset satisfies: Si % Sj = 0 or Sj % Si = 0.

If there are multiple solutions, return any subset is fine.

nums: [1,2,3] Result: [1,2] (of course, [1,3] will also be ok)

nums: [1,2,4,8] Result: [1,2,4,8]

You are to find a **dynamic programming** solution to this problem, and implement it on Leetcode.

- Can you think of a bottom-up approach? How is the larger problem a made up of sub-problems?
- Review the solution in class of Weighted Interval Scheduling. Consider the methods and data structures of that.
- DP usually depends on the ordering of objects. How might ordering here be useful?
- How is an optimal solution for a given size problem useful in constructing a solution for a larger problem.
- For a given problem size of
*n*, can you first solve all of the problems for 0<*i*<=*n*-1 and keep track of those solutions with some sort of a data structure? - If you have solved (and have available) the solutions for all smaller problems, how can you select and use the smaller solutions to create a solution for n?

Turn in:

- Source code for your solution
- Samples runs showing the operation with input and outputs.
- An explaination of how this problem includes the concept of an optimal substructure.
- A complete runtime asymptotic analysis.

Be prepared to discuss you solutions in class.

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