Assignment3 - D.P Flashcards
Weighted activities problem with initial cost
Describe the problem
Note: description of a problem contains:
- An instance
- A legal solution
- An optimal solution(what we shall find)
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Weighted activities problem with initial cost
describe:
- A typical sub problem
- The corresponding set of solutions
- Define corresponding OPT value
NOTE:
we should first think of the subsets which construct the set of solutions. Then define a subproblem. “which solutions for sub problems can help you find the solution for opt quite immidietly?”
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Weighted activities problem with initial cost
divide the set of solutions into subsets and construct the formula
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Weighted activities problem with initial cost
what is the proof for the formula construct?
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Weighted activities problem with initial cost
describe the iterative algorithm
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Weighted activities problem with initial cost
what is the run-time of the iterative algorithm?
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Weighted activities problem with initial cost
describe the reconstruction algorithm
Always remember the base case!
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Weighted activities problem with initial cost
- what is the assumption used in the proof of the reconstruction algorithm. Recall, we always proof relying on the assumption.*
- what is the correctness theorem?*
- what is the helping theorem?*
- The assumption:*
- The value contained in M[i] is OPT(i)*
- Correctness theorem:*
Based on the assumption, the algorithm returns an optimal solution for the problem.
- Helping theorem:*
- Based on the assumption, for every k([0,n]) the recover(k) call returns a solution I in Sol(k) with the value M[k].*
Weighted activities problem with initial cost
how is the main theorem and helping theorem proved, in the reconstruction algorithm?
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The thrifty traveler
recall the formal definition
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The thrifty traveler
define Sol and OPT
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The thrifty traveler
describe the subsets of the solution set
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The thrifty traveler
what is the construction formula?
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The thrifty traveler
describe the proof for the construction formula
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The thrifty traveler
describe the algorithm and the construction algorithm
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