memory optimization

[Alich13]

• use std::vector instead of std:set
• use a transparent lookup
• Lightweight lookup helper - avoids constructing objects for map lookups

The fixes above ensure cache locality and reduce mem fragmentation risks.

TL;DR: Cache locality means accessing memory that's physically close together.

• std::vector: All elements next to each other → CPU loads many at once
• std::set: Elements scattered in tree nodes → CPU must fetch each separately

Memory fragmentation might happen when we have free memory, but it's scattered in small chunks that can't be used efficiently, which is the case when using std::set.

Oversimplified illustration of mem fragmentation

# std::set allocations
Free memory, but fragmented (can't allocate 5 contiguous blocks): 
[Used][Free][Used][Free][Free][Used][Free][Used][Free]
# std::vector allocations
Free memory, contiguous (can easily allocate):
[Used][Used][Used][Free][Free][Free][Free][Free][Free]

Also, std::vector allocates 4 bytes per element , 4 to 5 times less than std::set which allocates ~24-32 bytes per node (pointers for left child, right child, parent, plus color bit for red-black tree)

[Alich13]

avoid constructing these tmp objects each time we look up in the cache and use a transparent lookup