Analog and digital C - Greedy, Study notes of Digital & Analog Electronics

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Greedy Algorithms

Optimization problems

• (^) An optimization problem is one in which you want to find, not just a solution, but the best solution
• (^) A “greedy algorithm” sometimes works well for optimization problems
• (^) A greedy algorithm works in phases. At each phase: - (^) You take the best you can get right now, without regard for future consequences - (^) You hope that by choosing a local optimum at each step, you will end up at a global optimum 2

A failure of the greedy

algorithm

• (^) In some (fictional) monetary system, “krons” come in 1 kron, 7 kron, and 10 kron coins
• (^) Using a greedy algorithm to count out 15 krons, you would get - (^) A 10 kron piece - (^) Five 1 kron pieces, for a total of 15 krons - (^) This requires six coins
• (^) A better solution would be to use two 7 kron pieces and one 1 kron piece - (^) This only requires three coins
• (^) The greedy algorithm results in a solution, but not in an optimal solution 4

Greedy Vs. Dynamic Programming Greedy choice property

• (^) We can make whatever choice seems best at the moment and then solve the subproblems that arise later.
• (^) The choice made by a greedy algorithm may depend on choices made so far but not on future choices or all the solutions to the subproblem.
• (^) It iteratively makes one greedy choice after another, reducing each given problem into a smaller one.
• (^) In other words, a greedy algorithm never reconsiders its choices. This is the main difference from dynamic programming, which is exhaustive and is guaranteed to find the solution.
• (^) After every stage, dynamic programming makes decisions based on all the decisions made in the previous stage, and may reconsider the previous stage's algorithmic path to solution. 5

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