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-- The Computer Language Benchmarks Game
-- http://benchmarksgame.alioth.debian.org/
-- contributed by Mike Pall

local function BottomUpTree(item, depth)
  if depth > 0 then
    local i = item + item
    depth = depth - 1
    local left, right = BottomUpTree(i-1, depth), BottomUpTree(i, depth)
    return { item, left, right }
  else
    return { item }
  end
end

local function ItemCheck(tree)
  if tree[2] then
    return tree[1] + ItemCheck(tree[2]) - ItemCheck(tree[3])
  else
    return tree[1]
  end
end

local N = tonumber(arg and arg[1]) or 4

if N == 0 then
  N = 0
elseif N == 1 then
  N = 9.5
elseif N == 2 then
  N = 11.99
elseif N == 3 then
  N = 12.85
elseif N == 4 then
  N = 14.72
elseif N == 5 then
  N = 15.82
end

local mindepth = 4
local maxdepth = mindepth + 2
if maxdepth < N then maxdepth = N end

do
  local stretchdepth = maxdepth + 1
  local stretchtree = BottomUpTree(0, stretchdepth)
  io.write(string.format("stretch tree of depth %d\t check: %d\n",
    stretchdepth, ItemCheck(stretchtree)))
end

local longlivedtree = BottomUpTree(0, maxdepth)

for depth=mindepth,maxdepth,2 do
  local iterations = 2 ^ (maxdepth - depth + mindepth)
  local check = 0
  for i=1,iterations do
    check = check + ItemCheck(BottomUpTree(1, depth)) +
            ItemCheck(BottomUpTree(-1, depth))
  end
  io.write(string.format("%d\t trees of depth %d\t check: %d\n",
    iterations*2, depth, check))
end

io.write(string.format("long lived tree of depth %d\t check: %d\n",
  maxdepth, ItemCheck(longlivedtree)))