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Lec19_GreedyAlgorithms

Lec19_GreedyAlgorithms - Greedy Algorithms The Greedy...

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Greedy Algorithms
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The Greedy Technique(Method) The greedy technique Problems explored The coin changing problem Activity selection
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Optimization problems An optimization problem: Given a problem instance, a set of constraints and an objective function . Find a feasible solution for the given instance for which the objective function has an optimal value either maximum or minimum depending on the problem being solved. A feasible solution satisfies the problem’s constraints The constraints specify the limitations on the required solutions. For example in the knapsack problem we require that the items in the knapsack will not exceed a given weight
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The Greedy Technique(Method) Greedy algorithms make good local choices in the hope that they result in an optimal solution. They result in feasible solutions. Not necessarily an optimal solution. A proof is needed to show that the algorithm finds an optimal solution. A counter example shows that the greedy algorithm does not provide an optimal solution.
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Pseudo-code for Greedy Algorithm set Greedy (Set Candidate){ solution= new Set( ); while (Candidate.isNotEmpty()) { next = Candidate.select(); //use selection criteria, //remove from Candidate and return value if (solution.isFeasible( next)) //constraints satisfied solution.union( next); if (solution.solves()) return solution} //No more candidates and no solution return null }
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Pseudo code for greedy cont.
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