Add counting sort (#38)

Author: icemberg

Diff for: .spec/sorting/sort_spec.lua

@@ -75,3 +75,6 @@ end)
 describe("Bogosort", function()
 	check_sort(require("sorting.bogosort"), 5)
 end)
+describe("Countingsort", function()
+	check_sort(require("sorting.countingsort"), nil, true)
+end)

Diff for: src/sorting/countingsort.lua

@@ -0,0 +1,50 @@
+return function(
+	-- list to be sorted in-place
+	list,
+	-- key_function to map elements to integer keys, defaults to identity
+	key_function
+)
+	if list[1] == nil then
+		return
+	end
+
+	key_function = key_function or function(x)
+		return x
+	end
+
+	-- Find the range of keys (min_key and max_key)
+	local min_key, max_key = math.huge, -math.huge
+	for _, elem in ipairs(list) do
+		local key = key_function(elem)
+		min_key = math.min(min_key, key)
+		max_key = math.max(max_key, key)
+	end
+
+	local count = {}
+	for i = 1, max_key - min_key + 1 do
+		count[i] = 0
+	end
+
+	-- Count the occurrences of each key
+	for _, elem in ipairs(list) do
+		local key = key_function(elem)
+		count[key - min_key + 1] = count[key - min_key + 1] + 1
+	end
+
+	-- Compute cumulative counts for final positions
+	for i = 2, #count do
+		count[i] = count[i] + count[i - 1]
+	end
+
+	local output = {}
+	for i = #list, 1, -1 do
+		local element = list[i]
+		local key = key_function(element)
+		output[count[key - min_key + 1]] = element
+		count[key - min_key + 1] = count[key - min_key + 1] - 1
+	end
+
+	for i, elem in ipairs(output) do
+		list[i] = elem
+	end
+end