Let's say we've got an input:
10 // saying 1st property should be 10(in total)
10 // saying 2d property should be 10 (in total)
5 // saying theres 5 records below
// (1st property) (2nd property) (cost)
2 5 8
7 3 10
4 2 9
4 3 5
8 5 15
In this case, the output would look like that:
22 // lowest possible cost
1 3 4 // indexes of records, we've been using (indexing starts with 1)
2 5 8
4 2 9
4 3 5
+---------
10 10 22
If there wasn't possible way to achieve those properties to be 10 and 10, program would output -1; I do know how to solve knapsack problem, however I've got no clue how to solve this prob.
You can use the same approach of knapsack problem, but instead of 2D matrix, you will have a 3D table, a dimension for each parameter (2 constraint + index).
The recursive formula will be similar, but of course will be done for both parameters.
f(item,cost1,cost2) = max {
f(item-1,cost1,cost2),
f(item,cost1-firstCost[i],cost2-secondCost[i]) + profit[i]
}
(Base clauses will be similar as well, but with an extra dimension.)
来源：https://stackoverflow.com/questions/13404173/whats-the-fastest-way-to-solve-knapsack-prob-with-two-properties