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