Licence: public domain
This is an implementation of a persistent array data structure which can be used as a
general-purpose random-access array in functional programming languages. It is modeled after
Clojure's Vector, but supports amortized O(1) modification on both ends, and can therefore
be used both as a stack and as a queue.
The basic idea is simple - we take 2 Clojure's Vectors and join them together; since Clojure's
Vector supports efficient modification on one end (the tail), we can use 2 of them (joined
together at the head) to support efficient modification on both sides.
[tail ... tree] [tree ... tail]
↑ <- rotceV Vector -> ↑
┃ ┃
┗━ efficiently `push` / `pop` ━┛
However, the devil is in the details. First of all, in order to enable structural sharing, we the
direction of data on the Left and Right halves must be the same (so that we can move a subtree
from one side to the other without copying), so we need to implement slightly different code for the
Left and Right sub-vectors.
Additionally, we maintain the invariant that the depth of the tree on the Left and Right sides
differ for at most 1 - therefore, we have to make sure to rebalance both halves as necessary. This is
fairly straightforward when adding elements (push) but can get quite complicated when removing
elements (pop):
[tail ... tree] [tree ... tail]
/ \ | \
N N N N
/ | / | / \
N N N N N N
/| |\
N N N N
If we pop_left on the tree above, we'll have to reduce the depth of the Left side (otherwise
the root of the tree would have a single child). Then, the depth of the Left side will be 1,
while the depth of the Right side will be 3, breaking the invariant. To maintain the invariant,
we'll have to "steal" some data from the Right side. But if we take the whole left subtree of
the Right tree (depth=3), we will break the invariant in the other direction (Left.depth=3
but Right.depth=1). Therefore, we have to split the left subtree of the Right tree.
Quick benchmark (miliseconds - less is better):
mean std min max
Clojure
append: 480.00 270.96 269 1057
get: 2478.83 228.00 2113 2812
stack: 2726.67 337.09 2230 3294
update: 8958.67 1228.49 7749 10796
Scala2
append: 719.67 195.52 506 991
get: 1939.33 564.50 1275 2796
queue: 3754.67 478.91 3189 4575
stack: 5615.33 1227.48 4267 7940
update: 7484.83 895.97 6926 9466
Vector
append: 401.17 41.57 361 489
get: 1815.17 309.99 1498 2413
queue: 1637.17 410.76 1208 2317
stack: 2924.83 422.32 2620 3857
update: 8403.33 1265.10 6931 9791