Gate2018 cs Q45

45Consider the weights and values of items listed below. Note that there is only one unit of each item.

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 V_greedy.

The value of V_opt − V_greedy is ______ .

Note – Numerical Type question

Option : C
Explanation :
Item No. Weight Value Value/Weight
1 10 60 6
2 7 28 4
3 4 20 5
4 2 24 12
After Sorting
Item No. Weight Value Value/Weight
1 2 24 12
2 10 60 6
3 4 20 5
4 7 28 4
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 V_greedy = 20+24 = 44
Hence, V_opt – V_greedy = 60-44 = 16
So, answer is 16.

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