From fa482c9809c57cadae9057929db49f007f3b5e65 Mon Sep 17 00:00:00 2001
From: ikselven <ikselven@users.noreply.github.com>
Date: Tue, 11 Jul 2017 21:52:05 +0200
Subject: [PATCH] julia implementation for problems 2, 3 and 5

---
 2/euler002.jl | 23 +++++++++++++++++++++++
 3/euler003.jl | 41 +++++++++++++++++++++++++++++++++++++++++
 5/euler005.jl | 38 ++++++++++++++++++++++++++++++++++++++
 3 files changed, 102 insertions(+)
 create mode 100755 2/euler002.jl
 create mode 100755 3/euler003.jl
 create mode 100644 5/euler005.jl

diff --git a/2/euler002.jl b/2/euler002.jl
new file mode 100755
index 0000000..2afefbf
--- /dev/null
+++ b/2/euler002.jl
@@ -0,0 +1,23 @@
+#!/usr/bin/julia
+
+function euler002(limit)
+    prevFib = 1
+    fib = 1
+    fibSum = 0
+
+    while fib < limit
+        if fib % 2 == 0
+            fibSum += fib
+        end
+
+        nextFib = prevFib + fib
+        prevFib = fib
+        fib = nextFib
+    end
+
+    return fibSum
+end
+
+euler002(1)
+
+@time euler002(4*10^6)
diff --git a/3/euler003.jl b/3/euler003.jl
new file mode 100755
index 0000000..76be093
--- /dev/null
+++ b/3/euler003.jl
@@ -0,0 +1,41 @@
+#!/usr/bin/julia
+
+function isPrime(number)
+    if number in [2,3, 5]
+        return true
+    elseif number % 2 == 0
+        return false
+    end
+
+    for i ∈ range(3, 2, floor(Int64, √number))
+        if number % i == 0
+            return false
+        end
+    end
+    return true
+end
+
+function findDivisors(number)
+    divisors = Set{Int64}(1)
+    LIMIT = trunc(√number)
+    for num ∈ 2:LIMIT
+        if number % num == 0
+            push!(divisors, num)
+            continue
+        end
+    end
+
+    union!(divisors, map(x -> div(number, x), divisors))
+    return divisors
+end
+
+function euler003(number)
+    divisors = findDivisors(number)
+    primeFactors = filter(isPrime, divisors)
+    println("$(number) -> $(maximum(primeFactors))")
+end
+
+# trigger compilation
+euler003(3)
+# now solve the actual task
+@time euler003(600851475143)
diff --git a/5/euler005.jl b/5/euler005.jl
new file mode 100644
index 0000000..94f2e21
--- /dev/null
+++ b/5/euler005.jl
@@ -0,0 +1,38 @@
+#!/usr/bin/julia
+
+function isPrime(number::UInt64)
+    if number in [2,3,5]
+        return true
+    elseif number % 2 == 0
+        return false
+    end
+
+    for i ∈ range(3, 2, floor(UInt64, √number))
+        if number % i == 0
+            return false
+        end
+    end
+    return true
+end
+
+function generatePrimeList(number::UInt64)
+    primeList = Array{UInt64,1}([2])
+    limit = div(number-1, 2)
+
+    for i ∈ range(3, 2, limit)
+        if isPrime(i)
+            push!(primeList, i)
+        end
+    end
+
+    primeList
+end
+
+function euler005(number::UInt64)
+    primeList = generatePrimeList(number)
+    exponents = floor.(UInt64, log.(primeList, number))
+    prod(primeList .^ exponents)
+end
+
+euler005(1)
+@time euler005(20)