From e3ef255bf58d895144f3c72b70d8517b22259a3a Mon Sep 17 00:00:00 2001
From: Lars Mueller <appgurulars@gmx.de>
Date: Wed, 19 Jan 2022 16:45:47 +0100
Subject: [PATCH] Add hashheap

---
 hashheap.lua | 117 +++++++++++++++++++++++++++++++++++++++++++++++++++
 init.lua     |   1 +
 test.lua     |  47 +++++++++++++++------
 3 files changed, 153 insertions(+), 12 deletions(-)
 create mode 100644 hashheap.lua

diff --git a/hashheap.lua b/hashheap.lua
new file mode 100644
index 0000000..5917b54
--- /dev/null
+++ b/hashheap.lua
@@ -0,0 +1,117 @@
+-- Localize globals
+local assert, math_floor, setmetatable, table_insert = assert, math.floor, setmetatable, table.insert
+
+-- Set environment
+-- Min. heap + Lua hash table to allow updating the stored values
+local _ENV = {}
+setfenv(1, _ENV)
+
+local metatable = { __index = _ENV }
+
+function less_than(a, b)
+	return a < b
+end
+
+--> empty, duplicate-free min heap with priority queue functionality
+function table_heap.new(less_than)
+	return setmetatable({ less_than = less_than, indices = {} }, metatable)
+end
+
+local function swap(self, child_index, parent_index)
+	local child_value, parent_value = self[child_index], self[parent_index]
+	self.indices[parent_value], self.indices[child_value] = child_index, parent_index
+	self[parent_index], self[child_index] = child_value, parent_value
+end
+
+local function heapify_up(self, index)
+	if index == 1 then
+		return
+	end
+	local parent_index = math_floor(index / 2)
+	if self.less_than(self[index], self[parent_index]) then
+		swap(self, index, parent_index)
+		heapify_up(self, parent_index)
+	end
+end
+
+local function heapify_down(self, index)
+	local left_child = index * 2
+	if left_child > #self then
+		return
+	end
+	local smallest_child = left_child + 1
+	if smallest_child > #self or self.less_than(self[left_child], self[smallest_child]) then
+		smallest_child = left_child
+	end
+	if self.less_than(self[smallest_child], self[index]) then
+		swap(self, smallest_child, index)
+		heapify_down(self, smallest_child)
+	end
+end
+
+function push(self, value)
+	table_insert(self, value)
+	local last = #self
+	self.indices[value] = last
+	heapify_up(self, last)
+end
+
+function top(self)
+	return self[1]
+end
+
+-- TODO what if empty?
+function pop(self)
+	local value = self[1]
+	self.indices[value] = nil
+	local last = #self
+	if last == 1 then
+		self[1] = nil
+		return value
+	end
+	self[1], self[last] = self[last], nil
+	heapify_down(self, 1)
+	return value
+end
+
+function find_index(self, element)
+	return self.indices[element]
+end
+
+-- Notify heap that the element has been decreased
+function decrease(self, element)
+	heapify_up(self, assert(self:find_index(element)))
+end
+
+-- Notify heap that the element has been increased
+function increase(self, element)
+	heapify_down(self, assert(self:find_index(element)))
+end
+
+-- Replaces the specified element - by identity - with the new element
+function replace(self, element, new_element)
+	local index = assert(self:find_index(element))
+	assert(self:find_index(new_element) == nil, "no duplicates allowed")
+	self[index] = new_element
+	self.indices[element] = nil
+	self.indices[new_element] = index;
+	(self.less_than(new_element, element) and heapify_up or heapify_down)(self, index)
+end
+
+function remove(self, element)
+	local index = assert(self:find_index(element), "element not found")
+	self.indices[element] = nil
+	if index == #self then
+		self[index] = nil
+	else
+		local last_index = #self
+		local last_element = self[last_index]
+		self[last_index] = nil
+		self[index] = last_element
+		self.indices[last_element] = index;
+		(self.less_than(last_element, element) and heapify_up or heapify_down)(self, index)
+	end
+end
+
+-- Export environment
+return _ENV
diff --git a/init.lua b/init.lua
index d4e0ad1..f2cd830 100644
--- a/init.lua
+++ b/init.lua
@@ -48,6 +48,7 @@ for _, file in pairs{
 	"trie",
 	"kdtree",
 	"hashlist",
+	"hashheap",
 	"heap",
 	"ranked_set",
 	"binary",
diff --git a/test.lua b/test.lua
index 3cf45db..5031a48 100644
--- a/test.lua
+++ b/test.lua
@@ -146,21 +146,44 @@ do
 	end
 end
 
--- heap
+-- heaps
 do
 	local n = 100
-	local list = {}
-	for index = 1, n do
-		list[index] = index
+	for _, heap in pairs{heap, hashheap} do
+		local list = {}
+		for index = 1, n do
+			list[index] = index
+		end
+		table.shuffle(list)
+		local heap = heap.new()
+		for index = 1, #list do
+			heap:push(list[index])
+		end
+		for index = 1, #list do
+			local popped = heap:pop()
+			assert(popped == index)
+		end
 	end
-	table.shuffle(list)
-	local heap = heap.new()
-	for index = 1, #list do
-		heap:push(list[index])
-	end
-	for index = 1, #list do
-		local popped = heap:pop()
-		assert(popped == index)
+	do -- just hashheap
+		local heap = hashheap.new()
+		for i = 1, n do
+			heap:push(i)
+		end
+		heap:replace(42, 0)
+		assert(heap:pop() == 0)
+		heap:replace(69, 101)
+		assert(not heap:find_index(69))
+		assert(heap:find_index(101))
+		heap:remove(101)
+		assert(not heap:find_index(101))
+		heap:push(101)
+		local last = 0
+		for _ = 1, 98 do
+			local new = heap:pop()
+			assert(new > last)
+			last = new
+		end
+		assert(heap:pop() == 101)
 	end
 end