Exotic Data Structures

Or maybe not so exotic...

1. Dynamic arrays

2. Linked lists

3. Unordered maps

4. Ordered maps

5. Ordered maps (over finite keys)

The last one is starting to sound exotic though.

1. Compact dynamic array (compact-arrays)

Based on the deque variant of [1].

Bounds:

• O(1) worst case access (get/set)
• O(1) amortized, O(sqrtN) worst case update (push/pop) at both ends
• N + O(sqrtN) space

This is simply a O(sqrtN) array of O(sqrtN) sub-arrays.

Two lists of arrays are maintained, small and big (twice bigger)

Also, pointers to head/tail indexes, and the big/small separation are maintained.

Conceptually, the virtual array is the concatenation of all small sub-arrays followed by the big sub-arrays, and indexed between head/tail.

All operations are straightforward. In order to maintain the global invariants, small sub-arrays are sometimes merged into big arrays, or big arrays are split into small arrays (this happens at the boundary between the two lists). when one of both lists is empty, we swap the lists (big arrays become small and vice-versa)

Variant: Compact integer arrays

Has the same time complexity bounds, but takes NlgM +o(N) bits in the worst case, where M is the biggest integer stored in the array. This is implemented by growing sub-arrays dynamically when an update overflows. it makes updates O(sqrtN) worst case (amortized if O(N) numbers take O(lgM) bits).

2. Succinct lists (succinct-lists)

[1] A. Brodnik, S. Carlsson, E. D. Demaine, J. I. Munro, and R. Sedgewick. Resizable arrays in optimal time and space. Technical Report CS-99-09, U. Waterloo, 1999.