sum.lua

-- Summing the sequence 1..n in as many ways as I can think of!

-- With the closed form
function sum(n)
   return ((n+1) * n) / 2
end

print(sum(6)) -- Had better be 21

-- With tail recursion
function sum2(n)
   local sum_help -- Must declare this first so it's in the function's scope

   sum_help = function(k, total)
      if k == 0 then
	 return total
      else
	 return sum_help(k-1, total+k)
      end
   end

   return sum_help(n, 0)
end

print(sum2(6)) -- had better be 21

-- By making an array (method 1)
function sum3(n)
   local a = {}
   local k = 1

   while k <= n do
      a[k] = k
      k = k + 1
   end

   local sum = 0
   k = 1

   while k <= #a do
      sum = sum + a[k]
      k = k + 1
   end

   return sum
end

print(sum3(6)) -- had better be 21

-- By making an array (method 2)
function sum4(n)
   local a = {}

   for k=1,n do
      a[k] = k
   end

   local sum = 0

   for k,v in pairs(a) do
      sum = sum + v
   end

   return sum
end

print(sum4(6)) -- had better be 21

-- With a numeric for loop
function sum5(n)
   local total = 0

   for k=1,n do
      total = total + k
   end

   return total
end

print(sum5(6)) -- had better be 21

-- Another tail recursion, no helper
function sum6(n,total)
   total = total or 0 -- Standard idiom for a default argument
   if n == 0 then
      return total
   else
      return sum6(n-1, total+n)
   end
end

print(sum6(6)) -- had better be 21

-- Defining an iterator
function sum7(n)
   local function upto(max)
      local current = 0
      return function()
		current = current + 1

		if current > max then
		   return nil
		else
		   return current
		end
	     end
   end

   total = 0

   for k in upto(n) do
      total = total + k
   end

   return total
end

print(sum7(6)) -- had better be 21

-- Iterator with a state
function sum8(n)
   local function range_iterator(state)
      state.current = state.current + 1
      if state.current <= state.max then
	 return state.current
      else
	 return nil
      end
   end

   local function range(max)
      return range_iterator, {max=max, current=0}
   end

   total = 0

   for k in range(n) do
      total = total + k
   end

   return total
end

print(sum8(6)) -- had better be 21

-- Another iterator, just using the current value
function sum9(n)
   local function range_iterator(state, current)
      if current > 0 then
	 return current-1
      else
	 return nil
      end
   end

   local function range(max)
      return range_iterator, nil, max+1
   end

   total = 0

   for k in range(n) do
      total = total + k
   end

   return total
end

print(sum9(6)) -- had better be 21

-- Using a coroutine
function sum10(n)
   local co = coroutine.create(function()
				  for k = 1,n do coroutine.yield(k) end
			       end)

   local total = 0
   local current

   -- Resume returns whether the coroutine is still running, and *then* the yield.
   -- So, we use select to pull just the second value.
   local function it()
      return select(2, coroutine.resume(co))
   end

   for current in it do
      total = total + current
   end

   return total
end

print(sum10(6)) -- had better be 21

-- Using metatables
function sum11(n)   
   local mt = { __index = function(t,n)
			     if n == 1 then return 1
			     else return n + t[n-1] end
			  end }
   local t = {}
   setmetatable(t,mt)

   return t[n]
end

print(sum11(6)) -- had better be 21