Efficient data structure for storing a long sequence of (mostly consecutive) integers

Question

I\'d like a data structure to efficiently store a long sequence of numbers. The numbers should always be whole integers, let\'s say Longs.

The feature of the inputs

Answer 1

Another alternative might be a rope data structure ( https://en.m.wikipedia.org/wiki/Rope_(data_structure) ), which seems to support the operations you are asking for, implemented in O(log n) time. As opposed to the example in Wikipedia, yours would store [start,end] rather than string subsequences.

What's interesting about the rope is its efficient lookup of index-within-interval. It accomplishes this by ordering all value positions from left to right - a lower to higher positioning (of which your intervals would be a straightforward representation) can be either upwards or downwards as long as the movement is to the right - as well as relying on storing subtree size, which orients current position based on the weight on the left. Engulfing partial intervals by larger encompassing intervals could be accomplished in O(log n) time by updating and unlinking relevant tree segments.