Data structure to handle the requirement of following use case

Question

All the records in a database is saved in (key, value) pair formats.Records can always be retrieved by specifying key value. Data structure needs to be developed to handle follo

Answer 1

Store the keys in a trie. For the numbers in your example (assuming 4 digit numbers) it looks like this:

*root*
 |
 0 -- 2 - 5 - 6
 | |
 | +- 3 - 6 - 2
 | |
 | +- 8 - 7 - 4
 |
 1 - 4 - 5 - 2

This data structure can be traversed in a way that returns (1) or (3). It won't be quite as fast for (3) as would maintaining an index for each digit, so I guess it's a question of whether space or lookup time is your primary concern. For (2), it is already O(log n), but if you need O(1), you could store the keys in both the trie and a hash table.