Selecting A combination of minimum cost

Question

I have data of different items in a different restaurants

    Rest    Item     Price
    ----------------------
    ABC     dosa      14
    ABC     idly             


        

Answer 1

A sketch of one possible greedy algorithm is:

1. Iterate through all unary offers (e.g. dosa, idly or upma) to find the minimum of each.
2. Iterate through all binaray (e.g. idly+upma) / tertiary (...) offers, compare if it's cheaper than the unary offers and replace if so.

You will have to code the offer deparsing still, but it shouldn't be that hard. This algorithm will find good, but not necessary the best solution, and might work on very small smaples.

Actually, your problem compares to the Rucksack or TSP problems, which are NP-complete and thus only solvable in exponentially time. If you want a solution for that, consider reading a lot of papers and coding even more. That's the holy grail of computer science. ;-)

UPDATE: On request of the TO here's some exponentially pseudocode sketch:

foreach restaurant
    create a list of all possible combinations of the offers // here's the exp!
    filter those combinations that hold more/less than 1 dosy/idly/umpa
    select minimum of the remaining ones

Comment: This is really ugly, yuk! :-(