# Dating problem cryptography

The problem often arises in resource allocation where there are financial constraints and is studied in fields such as combinatorics, computer science, complexity theory, cryptography, applied mathematics, and daily fantasy sports.The knapsack problem has been studied for more than a century, with early works dating as far back as 1897.The knapsack problem is interesting from the perspective of computer science for many reasons: There is a link between the "decision" and "optimization" problems in that if there exists a polynomial algorithm that solves the "decision" problem, then one can find the maximum value for the optimization problem in polynomial time by applying this algorithm iteratively while increasing the value of k .

However, for the bounded problem, where the supply of each kind of item is limited, the algorithm may be far from optimal.Thus, both versions of the problem are of similar difficulty.One theme in research literature is to identify what the "hard" instances of the knapsack problem look like, The goal in finding these "hard" instances is for their use in public key cryptography systems, such as the Merkle-Hellman knapsack cryptosystem.(Solution: if any number of each box is available, then three yellow boxes and three grey boxes; if only the shown boxes are available, then all but the green box.) The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.

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