The Knapsack Problem is a specific type of resource optimization problem. It asks, "What's the best way to pack your knapsack with items so that you can take as many items as possible without exceeding the weight limit?" Computer scientists and mathematicians have studied this question since it was first proposed in 1943.
Dynamic programming is an algorithm design technique that solves problems by breaking them down into subproblems and storing their solutions for later use instead of recomputing them each time they are needed. A recursive solution would require exponential time because every subproblem must be solved from scratch even if its solution had already been computed earlier on in the process.
Dynamic programming saves time by checking whether previously-computed results are available before recomputing them or discarding them if they have become obsolete due to changes in data values or structure during processing.
It’s also known as the rucksack or backpack problem because it can be used to find out how much you can carry in your bag. You have a set of items, and each item has a weight and value. Your goal is to put together an assortment of items to maximize your profit while staying under some maximum weight limit.
These types of questions often come up when you are trying to optimize something like what products should go on sale at different stores to maximize revenue without going over budget for storage space or shipping costs.
Knapsack dynamic programming uses table-driven methods to solve this kind of optimization problem. Several subproblems may occur multiple times with different values (or weights). If we use the memoization technique then we need only one array containing all solutions instead of using many arrays for every subproblem instance.
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