![]() ![]() How this problem can be solved by using the Dynamic programming approach? In dynamic programming approach, the complicated problem is divided into sub-problems, then we find the solution of a sub-problem and the solution of the sub-problem will be used to find the solution of a complex problem. Once all the combinations are made, we have to select the combination that provides the maximum profit.Īnother approach to solve the problem is dynamic programming approach. There are 16 possible combinations that can be made by using the above problem. Since there are 4 items so possible combinations will be:Ģ 4 = 16 So. 1 denotes that the item is completely picked and 0 means that no item is picked. The above problem can be solved by using the following method: Example of 0/1 knapsack problem.Ĭonsider the problem having weights and profits are: The fractional knapsack problem is solved by the Greedy approach. For example, we have an item of 3 kg then we can pick the item of 2 kg and leave the item of 1 kg. The fractional knapsack problem means that we can divide the item. The 0/1 knapsack problem is solved by the dynamic programming. This is a 0/1 knapsack problem in which either we pick the item completely or we will pick that item. If we pick the 2kg item then we cannot pick 1kg item from the 2kg item (item is not divisible) we have to pick the 2kg item completely. For example, we have two items having weights 2kg and 3kg, respectively. ![]() The 0/1 knapsack problem means that the items are either completely or no items are filled in a knapsack. First, we will learn about the 0/1 knapsack problem. We will discuss both the problems one by one. ![]() There are two types of knapsack problems: We have to select the items in such a way that the sum of the weight of items should be either smaller than or equal to the weight of the container, and the profit should be maximum. We have to put some items in the knapsack in such a way total value produces a maximum profit.įor example, the weight of the container is 20 kg. Suppose we have given some items which have some weights or profits. Here knapsack is like a container or a bag. ![]()
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