Gate2018 cs Q45
| Item Number | Weight in (kgs) | Value in Rupees) |
| 1 | 10 | 60 |
| 2 | 7 | 28 |
| 3 | 4 | 20 |
| 4 | 2 | 24 |
The task is to pick a subset of these items such that their total weight is not more than 11 kgs and their total value is maximized. Moreover, no item may be split. The total value of items picked by an optimal algorithm is denoted by A greedy algorithm sorts the items by their value-to-weight ratios in descending order and packs them greedily, starting from the first item in the ordered list. The total value of items picked by the greedy algorithm is denoted by Vgreedy.
The value of Vopt − Vgreedy is ______ .
Note – Numerical Type question
- Option : C
- Explanation :
After SortingItem No. Weight Value Value/Weight 1 10 60 6 2 7 28 4 3 4 20 5 4 2 24 12
First, we have to Pick item_1 (Value weight ratio is highest). After that Second highest is item_1. but cannot be picked because of its weight. Now item_3 shall be picked. item_2 cannot be included because of its weight. Therefore, overall profit by Vgreedy = 20+24 = 44 Hence, Vopt – Vgreedy = 60-44 = 16 So, answer is 16.Item No. Weight Value Value/Weight 1 2 24 12 2 10 60 6 3 4 20 5 4 7 28 4
