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Here is a simple reasoning that shows your greedy algorithm is correct. No mathematical induction is required. Call an image critical if the greedy algorithm places a guard $0.5$ after it. The algorithm ensures that each critical image is more than $1.5$ away from the previous critical image (except the first image, before which there is no image). That ...


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Check e.g. Jeff Erickson's Algorithms (warning, somewhat though going), it has a thorough chapter on greedy algorithms. He also warns that greedy algorithms very rarely give optimal results (The underlying problem has to have a very particular structure for them to work in all cases, see e.g. Jeremy Kun's "When Greedy Algorithms are Perfect". Sure, ...


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Usually, in the context of dynamic programming and optimization methods, we are interested in problems where we have to "find" some value which maximizes \ minimizes a certain function. For example, take the following problem: You are a cashier in a shop, and a customer gave you an $n$-dollar bill (your country has bills of all kinds! very ...


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Greedy algorithms are often used when solving optimization problems, like finding the maximum or the minimum of a certain quantity, under certain conditions. Solutions that satisfy those extrema are called optimal solutions. To answer your question, let's look at a simple example, change-making problem: Given a set of integer values of coins $C = \{c_1, …, ...


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if you are not able to prove and it's getting difficult then just find one test case that contradicts your greedy approach and you are good to go


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