Add median (#19)

Author: vil02

.spec/math/median_spec.lua

@@ -0,0 +1,32 @@
+describe("median", function()
+	local median = require("math.median")
+
+	local function check(expected, nums)
+		assert.equal(expected, median(nums))
+		local shuffle = require("random.shuffle")
+		for _ = 1, 2 * #nums do
+			shuffle(nums)
+			assert.equal(expected, median(nums))
+		end
+	end
+
+	it("should handle general cases", function()
+		check(1, { 1 })
+		check(1.5, { 1, 2 })
+		check(3, { 3, 1, 2, 5, 5 })
+		check(2.5, { 2, 3, 1, 4 })
+		check(0, { 11, 0, 0, 0, 0, 0, 0, 0, 10 })
+		check(4, { 1, 2, 3, 4, 5, 6, 7 })
+		check(4.5, { 1, 2, 3, 4, 5, 6, 7, 8 })
+	end)
+
+	it("should return nil for empty input", function()
+		assert.equal(nil, median({}))
+	end)
+
+	it("should not change the input", function()
+		local some_nums = { 4, 3, 5, 1 }
+		median(some_nums)
+		assert.same(some_nums, { 4, 3, 5, 1 })
+	end)
+end)

src/math/median.lua

@@ -0,0 +1,21 @@
+local quickselect = require("sorting.quickselect_median_of_medians")
+
+-- Computes the median of the input list `nums`.
+return function(nums)
+	if #nums == 0 then
+		return nil
+	end
+	if #nums == 1 then
+		return nums[1]
+	end
+	local copy = {}
+	for i = 1, #nums do
+		copy[i] = nums[i]
+	end
+	local mid_pos = quickselect(copy, math.ceil(#copy / 2))
+	if #nums % 2 == 1 then
+		return copy[mid_pos]
+	end
+	local next_mid_pos = quickselect(copy, 1, nil, mid_pos + 1)
+	return (copy[mid_pos] + copy[next_mid_pos]) / 2
+end