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Better data structure for the following restrictions?

Here are some limitations for the data structure that I need. It seems that none of the common data structures (I mentioned those that I thought below) are consistent with these. Can someone suggest one that I might not have thought of?

  • I need to be able to search using unsigned integer keys.
  • Elements to be stored are user-defined structures.
  • These indexes will be meager, usually extremely. There are no regular arrays.
  • The frequency of each index will have an uneven distribution, with small indices much more often than large indices.
  • N will usually be small, probably no more than 5 or 10, but I do not want to rely on it too much, because sometimes it can be much more.
  • The constant term is of great importance. I need to search very quickly when N is small. I have already tried shared hash tables and, empirically, they are too slow, even when N = 1, which means there are no collisions , probably due to the amount of indirection. However, I would be open to suggestions about specialized hash tables that take advantage of the other limitations mentioned.
  • Insert time is not important if search time is fast. Even the insertion time of O (N) is good enough.
  • Space efficiency is not very important, although it is important not just to use regular arrays.
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