Special factorials: Difference between revisions

=={{header|Lua}}==

{{trans|C}}

<lang lua>-- n! = 1 * 2 * 3 * ... * n-1 * n

function factorial(n)

local result = 1

local i = 1

while i <= n do

result = result * i

i = i + 1

end

return result

end

-- if(n!) = n

function inverse_factorial(f)

local p = 1

local i = 1

if f == 1 then

return 0

end

while p < f do

p = p * i

i = i + 1

end

if p == f then

return i - 1

end

return -1

end

-- sf(n) = 1! * 2! * 3! * ... * (n-1)! * n!

function super_factorial(n)

local result = 1

local i = 1

while i <= n do

result = result * factorial(i)

i = i + 1

end

return result

end

-- H(n) = 1^1 * 2^2 * 3^3 * ... * (n-1)^(n-1) * n^n

function hyper_factorial(n)

local result = 1

for i=1, n do

result = result * i ^ i

end

return result

end

-- af(n) = -1^(n-1)*1! + -1^(n-1)*2! + ... + -1^(1)*(n-1)! + -1^(0)*n!

function alternating_factorial(n)

local result = 0

for i=1, n do

if (n - i) % 2 == 0 then

result = result + factorial(i)

else

result = result - factorial(i)

end

end

return result

end

-- n$ = n ^ (n-1) ^ ... ^ 2 ^ 1

function exponential_factorial(n)

local result = 0

for i=1, n do

result = i ^ result

end

return result

end

function test_factorial(count, f, name)

print("First " .. count .. " " .. name)

for i=1,count do

io.write(math.floor(f(i - 1)) .. " ")

end

print()

print()

end

function test_inverse(f)

local n = inverse_factorial(f)

if n < 0 then

print("rf(" .. f .. " = No Solution")

else

print("rf(" .. f .. " = " .. n)

end

end

test_factorial(9, super_factorial, "super factorials")

test_factorial(8, hyper_factorial, "hyper factorials")

test_factorial(10, alternating_factorial, "alternating factorials")

test_factorial(5, exponential_factorial, "exponential factorials")

test_inverse(1)

test_inverse(2)

test_inverse(6)

test_inverse(24)

test_inverse(120)

test_inverse(720)

test_inverse(5040)

test_inverse(40320)

test_inverse(362880)

test_inverse(3628800)

test_inverse(119)</lang>

{{out}}

<pre>First 9 super factorials

1 1 2 12 288 34560 24883200 125411328000 5056584744960000

First 8 hyper factorials

1 1 4 108 27648 86400000 4031078400000 3319766398771200000

First 10 alternating factorials

0 1 1 5 19 101 619 4421 35899 326981

First 5 exponential factorials

0 1 2 9 262144

rf(1 = 0

rf(2 = 2

rf(6 = 3

rf(24 = 4

rf(120 = 5

rf(720 = 6

rf(5040 = 7

rf(40320 = 8

rf(362880 = 9

rf(3628800 = 10

rf(119 = No Solution</pre>