# fannkuch-redux Lua program

## source code

```-- The Computer Language Benchmarks Game
-- https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
-- contributed by Mike Pall

local function fannkuch(n)
local p, q, s, sign, maxflips, sum = {}, {}, {}, 1, 0, 0
for i=1,n do p[i] = i; q[i] = i; s[i] = i end
repeat
-- Copy and flip.
local q1 = p[1]				-- Cache 1st element.
if q1 ~= 1 then
for i=2,n do q[i] = p[i] end		-- Work on a copy.
local flips = 1
repeat
local qq = q[q1]
if qq == 1 then				-- ... until 1st element is 1.
sum = sum + sign*flips
if flips > maxflips then maxflips = flips end -- New maximum?
break
end
q[q1] = q1
if q1 >= 4 then
local i, j = 2, q1 - 1
repeat q[i], q[j] = q[j], q[i]; i = i + 1; j = j - 1; until i >= j
end
q1 = qq; flips = flips + 1
until false
end
-- Permute.
if sign == 1 then
p[2], p[1] = p[1], p[2]; sign = -1	-- Rotate 1<-2.
else
p[2], p[3] = p[3], p[2]; sign = 1		-- Rotate 1<-2 and 1<-2<-3.
for i=3,n do
local sx = s[i]
if sx ~= 1 then s[i] = sx-1; break end
if i == n then return sum, maxflips end	-- Out of permutations.
s[i] = i
-- Rotate 1<-...<-i+1.
local t = p[1]; for j=1,i do p[j] = p[j+1] end; p[i+1] = t
end
end
until false
end

local n = tonumber(arg and arg[1]) or 1
local sum, flips = fannkuch(n)
io.write(sum, "\nPfannkuchen(", n, ") = ", flips, "\n")
```

## notes, command-line, and program output

```NOTES: