## ยง Thoughts on implicit heaps

Some musings I had on the ability to represent heaps as arrays, and in general,
the benifits of knowing the total number of elements.
- Knowing the total number of elements allows us to pre-ordain a memory layout. We can decide that for a node at index
`i`

, left child is at `2*i`

, and right child is at `2*i+1`

. This gives parent at `i//2`

.

- This immediately gives us
`O(1)`

access to parent ( `i//2`

) and sibling `(i^1)`

with no extra memory usage. S

- This cannot be done for data structures where we need to splice into the middle: For example, an implicit treap where we wish to splice sub-arrays together.

- On coding a heap, we can decide whether to use the left or right sibling by using
`next = 2*i + predicate`

. If `predicate = false = 0`

, we will pick the left child, otherwise the right child. This allows us to compress some annoying if/then/elses into one-liners.