Trie vs Radix tree vs Patricia trie

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As I understand (also from here) memory-complexity of these DSs can be ordered like Trie > Radix > Patricia. But what about time-complexity? I assume they are almost same.

If to mention my problem, I want to do a lot of prefix search queries from pre-constructed dictionary. Memory is not a big concern for me. I want to use the fastest DS.

HAT-trie is best suit for me but it is too complex to implement. Should I use Ternary Search Trees instead of any DSs mentioned above?

Thanks a lot!

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