red-black tree implementation by pattern-match
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# ported from http://www.cs.kent.ac.uk/people/staff/smk/redblack/Untyped.hs | |
require "pattern-match" | |
module RedBlack | |
class Tree | |
include PatternMatch::Extractable | |
include Enumerable | |
def insert(key, value) | |
ins(key, value).make_black | |
end | |
def delete(key) | |
match del(key) do | |
with(EMPTY) { EMPTY } | |
with(node) { node.make_black } | |
end | |
end | |
end | |
EMPTY = Tree.new | |
def EMPTY.inspect | |
"RedBlack::EMPTY" | |
end | |
def EMPTY.[](key) | |
nil | |
end | |
def EMPTY.ins(key, value) | |
RedNode[EMPTY, key, value, EMPTY] | |
end | |
def EMPTY.del(key) | |
EMPTY | |
end | |
def EMPTY.each | |
end | |
class Node < Tree | |
attr_reader :left, :key, :value, :right | |
def initialize(left, key, value, right) | |
@left, @key, @value, @right = left, key, value, right | |
end | |
def self.extract(val) | |
accept_self_instance_only(val) | |
[val.left, val.key, val.value, val.right] | |
end | |
class << self | |
alias [] new | |
end | |
def [](key) | |
if key < self.key | |
left[key] | |
elsif key > self.key | |
right[key] | |
else | |
value | |
end | |
end | |
def del(key) | |
if key < self.key | |
del_left(left, self.key, self.value, right, key) | |
elsif key > self.key | |
del_right(left, self.key, self.value, right, key) | |
else | |
app(left, right) | |
end | |
end | |
def each(&block) | |
left.each(&block) | |
yield key, value | |
right.each(&block) | |
end | |
private | |
def balance(left, key, value, right) | |
match [left, key, value, right] do | |
with _[RedNode.(a, x, xv, b), y, yv, RedNode.(c, z, zv, d)] do | |
RedNode[BlackNode[a, x, xv, b], y, yv, BlackNode[c, z, zv, d]] | |
end | |
with _[RedNode.(RedNode.(a, x, xv, b), y, yv, c), z, zv, d] do | |
RedNode[BlackNode[a, x, xv, b], y, yv, BlackNode[c, z, zv, d]] | |
end | |
with _[RedNode.(a, x, xv, RedNode.(b, y, yv, c)), z, zv, d] do | |
RedNode[BlackNode[a, x, xv, b], y, yv, BlackNode[c, z, zv, d]] | |
end | |
with _[a, x, xv, RedNode.(b, y, yv, RedNode.(c, z, zv, d))] do | |
RedNode[BlackNode[a, x, xv, b], y, yv, BlackNode[c, z, zv, d]] | |
end | |
with _[a, x, xv, RedNode.(RedNode.(b, y, yv, c), z, zv, d)] do | |
RedNode[BlackNode[a, x, xv, b], y, yv, BlackNode[c, z, zv, d]] | |
end | |
with _[a, x, xv, b] do | |
BlackNode[a, x, xv, b] | |
end | |
end | |
end | |
def del_left(left, key, value, right, del_key) | |
match left do | |
with(BlackNode.(_)) { bal_left(left.del(del_key), key, value, right) } | |
with(_) { RedNode[left.del(del_key), key, value, right] } | |
end | |
end | |
def del_right(left, key, value, right, del_key) | |
match right do | |
with(BlackNode.(_)) { bal_right(left, key, value, right.del(del_key)) } | |
with(_) { RedNode[left, key, value, right.del(del_key)] } | |
end | |
end | |
def bal_left(left, key, value, right) | |
match [left, key, value, right] do | |
with _[RedNode.(a, x, xv, b), y, yz, c] do | |
RedNode[BlackNode[a, x, xv, b], y, yz, c] | |
end | |
with _[bl, x, xv, BlackNode.(a, y, yv, b)] do | |
balance(bl, x, xv, RedNode[a, y, yv, b]) | |
end | |
with _[bl, x, xv, RedNode.(BlackNode.(a, y, yv, b), z, zv, c)] do | |
RedNode[BlackNode[bl, x, xv, a], y, yz, balance(b, z, zv, sub1(c))] | |
end | |
end | |
end | |
def bal_right(left, key, value, right) | |
match [left, key, value, right] do | |
with _[a, x, xv, RedNode.(b, y, yv, c)] do | |
RedNode[a, x, xv, BlackNode[b, y, yv, c]] | |
end | |
with _[BlackNode.(a, x, xv, b), y, yv, bl] do | |
balance(RedNode[a, x, xv, b], y, yz, bl) | |
end | |
with _[RedNode.(a, x, xv, BlackNode.(b, y, yz, c)), z, zv, bl] do | |
RedNode[balance(sub1(a), x, xv, b), y, yz, BlackNode[c, z, zv, bl]] | |
end | |
end | |
end | |
def sub1(node) | |
match node do | |
with BlackNode.(a, x, xv, b) do | |
RedNode[a, x, xv, b] | |
end | |
with _ do | |
raise "invariance violation" | |
end | |
end | |
end | |
def app(left, right) | |
match [left, right] do | |
with(_[EMPTY, x]) { x } | |
with(_[x, EMPTY]) { x } | |
with _[RedNode.(a, x, xv, b), RedNode.(c, y, yz, d)] do | |
app_RR(a, x, xv, b, c, y, yz, d) | |
end | |
with _[BlackNode.(a, x, xv, b), BlackNode.(c, y, yz, d)] do | |
app_BB(a, x, xv, b, c, y, yz, d) | |
end | |
with _[a, RedNode.(b, x, xv, c)] do | |
app_BR(a, b, x, xv, c) | |
end | |
with _[RedNode.(a, x, xv, b), c] do | |
app_RB(a, x, xv, b, c) | |
end | |
end | |
end | |
def app_RR(a, x, xv, b, c, y, yz, d) | |
match app(b, c) do | |
with RedNode.(b2, z, zv, c2) do | |
RedNode[RedNode[a, x, xv, b2], z, zv, RedNode[c2, y, yz, d]] | |
end | |
with bc do | |
RedNode[a, x, xv, RedNode[bc, y, yz, d]] | |
end | |
end | |
end | |
def app_BB(a, x, xv, b, c, y, yz, d) | |
match app(b, c) do | |
with RedNode.(b2, z, zv, c2) do | |
RedNode[BlackNode[a, x, xv, b2], z, zv, BlackNode[c2, y, yz, d]] | |
end | |
with bc do | |
bal_left(a, x, xv, BlackNode[bc, y, yz, d]) | |
end | |
end | |
end | |
def app_BR(a, b, x, xv, c) | |
RedNode[app(a, b), x, xv, c] | |
end | |
def app_RB(a, x, xv, b, c) | |
RedNode[a, x, xv, app(b, c)] | |
end | |
end | |
class RedNode < Node | |
def make_black | |
BlackNode[left, key, value, right] | |
end | |
def ins(key, value) | |
if key < self.key | |
RedNode[left.ins(key, value), self.key, self.value, right] | |
elsif key > self.key | |
RedNode[left, self.key, self.value, right.ins(key, value)] | |
else | |
RedNode[left, key, value, right] | |
end | |
end | |
end | |
class BlackNode < Node | |
def make_black | |
self | |
end | |
def ins(key, value) | |
if key < self.key | |
balance(left.ins(key, value), self.key, self.value, right) | |
elsif key > self.key | |
balance(left, self.key, self.value, right.ins(key, value)) | |
else | |
BlackNode[left, key, value, right] | |
end | |
end | |
end | |
end | |
if __FILE__ == $0 | |
require "pp" | |
tree = ("a".."z").to_a.shuffle.each_with_index.inject(RedBlack::EMPTY) { | |
|t, (k, v)| | |
t.insert(k, v) | |
} | |
p tree["a"] | |
tree2 = ("a".."g").inject(tree) { |t, k| t.delete(k) } | |
p tree2["a"] | |
p tree["a"] | |
end |
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