Imagine an array of n items from which you can choose. You will place the items you choose into a knapsack of size k. Each item has a size and a value. Of course, you cannot take more items than you have space for in the knapsack. Your goal is to maximize the total value of the items you take.
a. Design a recursive algorithm maxKnapsack to solve this knapsack problem. The parameters to the algorithm are the knapsack, the array of items, and the position within the array of the next item to consider. The algorithm chooses the items for the knapsack and returns a knapsack containing the chosen items. A knapsack can report its size, its contents, the value of its contents, and the size of its contents. Hint: If any items in the array have not yet been considered, retrieve the next item in the array. You can either ignore the item or, if it fits, put it in the knapsack. To decide, make a recursive call for each of these two cases. Compare the knapsacks returned by these calls to see which one has the most valuable contents. Then return that knapsack.
b. Write the classes Knapsack and KnapsackItem. Then write a program that defines the method maxKnapsack. The program should read the size of the knapsack and then the size, value, and name of each available item. Here is some sample input data for a knapsack of size 10:
Size | Value | Name |
1 | 50000 | rare coin |
2 | 7000 | small gold coin |
4 | 10000 | packet of stamps |
4 | 11000 | pearl necklace |
5 | 12000 | silver bar |
10 | 60000 | painting |
After displaying the items, call maxKnapsack. Then display the chosen items, their values, and their total value.
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