CS 2300 Permutation Example

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-- This code is a basic assignment given to me in my CS 2300 Discrete Math course.
-- Matthew K. Crandall, 11.28.2016
-- I needed to write the function for Permutations in two ways:
--    A long way, (the full formula)
--    and a shortcut method to optimize things.
-- This code is available at: YubBVqbu
-- This code should be executable in just about any LUA interpreter...
-- An online interpreter is located at: https://repl.it/languages/lua
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-- Factorial function, with a provided Start / Stop point
--   To perform a true "factorial" function, provide either 1 or nil as the 2nd parameter.
-- Parameters:
--     <start> : The number to start performing factorial at.
--     <stop>  : The number to end performing factorial at. (nil or 1 to perform full factorial)
function factorial(start, stop)
    local cachedStop = stop

    -- Create a variable to cache the stopping location. This is here in case nil is provided for stop.
    if not cachedStop or cachedStop <= 0 then
        cachedStop = 1
    end

    if start <= cachedStop then
        return 1
    else
        return start * factorial(start - 1, cachedStop)
    end

end

-- Calculates the shorthand permutation.
function permutationShort(n, s)
    return factorial(n, n - s)
end

function permutationLong(n, s)
    return factorial(n) / factorial(n-s)
end

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--      Testing my stuff....
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-- Test function for unit testing my factorial function.
function testFactorial()
    print("Unit Testing Factorial: ")
    for i = 0, 10, 1 do
        print("input of: "..i.." Resulted in: "..factorial(i))
    end
    print("\r\nTest Complete.")
end

-- This function tests special cases with my special factorial function, with partial factorials.
function testSpecialCases()
    print("Testing Special Partial Factorials")
    print("Input of: 20, 19 resulted in: "..factorial(20, 19))
    print("Input of: 5, 3 resulted in: "..factorial(5, 3))
    print("Input of: 2, 0 resulted in: "..factorial(2, 0))
end

-- Function to test permutations, with the long-cut and the shortcut.
function testPermutations()
    print("Testing Permutations.")

    for i = 2, 8, 1 do
        for j = 1, i, 1 do
            --print("Inputs: n="..i..", s="..j.." - Short="..permutationShortVal.." | Long="..permutationLongVal)
            print("P("..i..", "..j..") : pshort="..permutationShort(i, j).." - plong="..permutationLong(i, j))
        end
    end
end

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-- Main Code
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--testFactorial()
--testSpecialCases()
testPermutations()