equivalent to a sorted dictionary that allows duplicate keys

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I need a data structure that can sort objects by the float keys they're associated with, lowest first. The trouble is that the keys represent cost so there are often duplicates, I don't care about this because if two have the same cost I'll just grab the first as it makes no difference, the problem is that the compiler complains.

Is there a data structure that behaves in the same way but allows duplicate keys?

EDIT - I still need the duplicates though because if one turns out to be a dead-end, I grab the next (they're nodes in an a* search)

so just to be clear, it needs to allow duplicate keys that are sorted in order.

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