Add Towers of Hanoi exercise

18_towers_of_hanoi.lua

@@ -0,0 +1,81 @@
+-- The Towers of Hanoi is a mathematical puzzle consisting of three
+-- rods and a number of disks of various diameters which can slide
+-- onto any rod.  Initially, all the disks are stacked in decreasing
+-- size order so that they form a conical shape.  The objective to
+-- move the entire stack to one of the other two rods, with each move
+-- consisting of taking the uppermost disk from one of the rods and
+-- placing it on top of the stack on another one.  A disk cannot be
+-- placed on top of a disk of smaller diameter.
+--
+-- Write a function which generates an optimal solution to the puzzle.
+-- The rods are numbered 1-3, with the stack starting on rod 1.  Your
+-- function should return a list of {from = <rod>, to = <rod>} tables,
+-- and will receive the number of disks in the original stack as its
+-- argument.
+--
+-- Solution --------------------------------------------------------------------
+function towers_of_hanoi_solution(disk_count)
+	-- Your implementation here
+end
+
+-- Tests -----------------------------------------------------------------------
+
+local luaunit = require("luaunit.luaunit")
+
+local function disk_stack(count)
+	local stack = {}
+	for i = count, 1, -1 do table.insert(stack, i) end
+	return stack
+end
+
+local function assert_valid(state)
+	for _, rod in ipairs(state) do
+		local previous = rod[1]
+		for _, disk in ipairs(rod) do
+			luaunit.assertTrue(disk <= previous)
+			previous = disk
+		end
+	end
+	return true
+end
+
+local function assert_solved(state, disk_count)
+	luaunit.assertEquals(state[1], {})
+	if #state[2] ~= 0 then
+		luaunit.assertEquals(state[2], disk_stack(disk_count))
+		luaunit.assertEquals(state[3], {})
+	else
+		luaunit.assertEquals(state[2], {})
+		luaunit.assertEquals(state[3], disk_stack(disk_count))
+	end
+end
+
+local function assert_is_solution(solution, disk_count)
+	local state = {disk_stack(disk_count), {}, {}}
+	for i, move in ipairs(solution) do
+		local disk = table.remove(state[move.from])
+		table.insert(state[move.to], disk)
+		assert_valid(state)
+	end
+	assert_solved(state, disk_count)
+end
+
+local function test_with_count(disk_count)
+	local solution = towers_of_hanoi_solution(disk_count)
+	assert_is_solution(solution, disk_count)
+	luaunit.assertEquals(#solution, 2 ^ disk_count - 1)
+end
+
+function test_with_1_disk()
+	test_with_count(1)
+end
+
+function test_with_7_disks()
+	test_with_count(7)
+end
+
+function test_with_12_disks()
+	test_with_count(12)
+end
+
+os.exit(luaunit.LuaUnit.run())