Given $n$ drugs such that each drug $d_i$ should maintain in interval $[c_i,h_i]$.We want to minimize number of containers to maintain medicines in compatible interval.
My answer is as follows:
I use following greedy algorithm:
in each iteration, for remaining drugs, find an interval that have maximum number of compatible drugs, and remove that drugs, and add to container.
any one can help to find an counter example or proving above idea?