Question

The fractional knapsack problem may be solved optimally by a greedy method by taking a fraction of no more than this number of items.
A. 1 B. 2 C. 3 D. 4

Answer 1

If there are 'n' items the fractional knapsack problem can be solved optimally by a greedy method by taking a fraction of no more than 'n' number of items.

Fractional Knapsack Problem

Given weights and values of n items, we need to put these items in a knapsack of capacity W to get the maximum total value in the knapsack.

In the 0-1 Knapsack problem, we are not allowed to break items. We either take the whole item or discard it.

In Fractional Knapsack, we can break items for maximizing the total value of knapsack. This problem in which we can break an item is also called the fractional knapsack problem.

The basic idea of the greedy approach to solve knapsack problem is to calculate the ratio value/weight for each item and sort the item on basis of this ratio. Then take the item with the highest ratio and add them until we can’t add the next item as a whole and at the end add the next item as much as we can. Which will always be the optimal solution to this problem.