Project Euler - Problem 5

function reduceDivisors(rangeMin::UInt64, rangeMax::UInt64)
	divisorsForRemoval = Array{UInt64,1}();
	for i in rangeMax:-1:rangeMin
		for j in rangeMax:-1:rangeMin
			if i!=j && i!=1  && j!=1 && mod(j,i) ==0 && (i in divisorsForRemoval) == false
				push!(divisorsForRemoval,i);
			end

		end
	end
	listOfDivisors = collect(rangeMin:rangeMax);
	reducedListOfDivisors = setdiff(listOfDivisors, divisorsForRemoval);
	return reducedListOfDivisors
end



function getSmallestNumberBF(rangeMin::UInt64, rangeMax::UInt64)
	divisors = reduceDivisors(rangeMin, rangeMax);
	number::Bool = false;
	i::UInt64 = rangeMax; # testing multiples of rangeMax which is the highest number in divisors by definition
	while number == false
		currentNumber::UInt64 = i;
		testResult = Array{UInt64,1}();
		for divisor in divisors
			push!(testResult, mod(currentNumber, divisor))
		end
		if sum(testResult) == 0
			smallestNumber::UInt64 = currentNumber;
			number = true;
			return smallestNumber
		end
		i += rangeMax;
	end

end

function isPrime(n::UInt64)
	isPrimeNumber::Bool = true;
	for i in 2:1:(n-1)
		if n%i == 0
			isPrimeNumber = false;
			return isPrimeNumber
		end
	end
	return isPrimeNumber
end

function getAllPrimes(rangeMax::UInt64)
	listOfPrimesInRange = Array{UInt64,1}()
	for i in 2:1:rangeMax
		if isPrime(i)
			push!(listOfPrimesInRange,i);
		end
	end
	return listOfPrimesInRange

end

function primeDecomposition(n::UInt64, listOfPrimesInRange::Array{UInt64,1}, dictOfPrimesInRange::Dict{UInt64,UInt64})
	for prime in listOfPrimesInRange
		power = 0
		while mod(n,prime) == 0
			power += 1
			n = div(n,prime)
		end
		if dictOfPrimesInRange[prime] < power
			dictOfPrimesInRange[prime] = power
		end
	end
	return dictOfPrimesInRange
end

function getSmallestNumberPF(rangeMin::UInt64, rangeMax::UInt64)
	listOfPrimesInRange = getAllPrimes(rangeMax);
	dictOfPrimesInRange = Dict{UInt64,UInt64}(i => 0 for i in listOfPrimesInRange);
	for i in rangeMin:1:rangeMax
		dictOfPrimesInRange = primeDecomposition(i, listOfPrimesInRange, dictOfPrimesInRange);
	end
	smallestNumber = prod([key^dictOfPrimesInRange[key] for key in keys(dictOfPrimesInRange)]);
	return smallestNumber
	# lcm is the product of primes with the highest power

end


function JuliaLCM(rangeMin::UInt64,rangeMax::UInt64)
	numbers = collect(rangeMin:rangeMax);
	leastCommonMultiple = lcm(numbers);
	return leastCommonMultiple
end

function parseARGS()
	if isempty(ARGS)
		rangeMin::UInt64 = 1;
		rangeMax::UInt64 = 20;
		method::String = "PF";
	else
		rangeMin = tryparse(UInt64, ARGS[1])
		rangeMax = tryparse(UInt64, ARGS[2])
		method = ARGS[3]
	end
	return rangeMin, rangeMax, method
end

function main()
	rangeMin, rangeMax, method = parseARGS();
	if method == "BF"
		smallestNumber = getSmallestNumberBF(rangeMin,rangeMax);
	elseif method == "PF"
		smallestNumber = getSmallestNumberPF(rangeMin,rangeMax);
	else
		smallestNumber = JuliaLCM(rangeMin,rangeMax);
	end
	println(smallestNumber);
end

main()