Add solution to Project Euler Problem 014 (#186)

* added project euler 14

* added to ProjectEuler.jl

* add tests for project euler 14

* switch to Int64

* switch to Int64 in tests

src/project_euler/ProjectEuler.jl

@@ -18,6 +18,7 @@ export problem_010
 export problem_011
 export problem_012
 export problem_013
+export problem_014
 
 include("../math/divisors.jl")
 include("../math/sieve_of_eratosthenes.jl")
@@ -34,5 +35,6 @@ include("problem_010.jl")
 include("problem_011.jl")
 include("problem_012.jl")
 include("problem_013.jl")
+include("problem_014.jl")
 
 end

src/project_euler/problem_014.jl

@@ -0,0 +1,42 @@
+"""
+    Longest Collatz Sequence
+
+The following iterative sequence is defined for the set of positive integers:
+n -> n/2  (n is even)
+n -> 3n+1 (n is odd)
+Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.
+Which starting number, under one million, produces the longest chain?
+
+# Input parameters:
+- `n` : upper bound on the starting number
+
+# Examples/Tests:
+```julia
+problem_014(10)         # returns 9
+problem_014(250)        # returns 231
+problem_014(1000000)    # returns 837799
+problem_014(-1)         # throws DomainError
+```
+
+# Reference
+- https://projecteuler.net/problem=14
+
+Contributed by: [Praneeth Jain](https://www.github.com/PraneethJain)
+"""
+function problem_014(n::Int64)
+    n < 1 && throw(DomainError("n must be a natural number"))
+    return argmax(collatz_length, 1:n)
+end
+
+cache = Dict{Int64,Int64}(1 => 1)
+function collatz_length(x::Int64)
+    # If result already in cache, then return it
+    haskey(cache, x) && return cache[x]
+
+    # Recursively call the function and update the cache
+    return cache[x] = if x % 2 == 0
+        1 + collatz_length(x ÷ 2)
+    else
+        2 + collatz_length((3x + 1) ÷ 2)
+    end
+end

test/project_euler.jl

@@ -76,4 +76,11 @@ using TheAlgorithms.ProjectEuler
     @testset "Project Euler: Problem 013" begin
         @test problem_013() == "5537376230"
     end
+
+    @testset "Project Euler: Problem 014" begin
+        @test problem_014(Int64(10)) == 9
+        @test problem_014(Int64(250)) == 231
+        @test problem_014(Int64(1000000)) == 837799
+        @test_throws DomainError problem_014(Int64(-1))
+    end
 end