Solve p14 in lua

README.rst

@@ -95,7 +95,7 @@ Olivia's Project Euler Solutions
    |            | Browser [#]_               |        | |CodeQL| |br|     |
    |            |                            |        | |ESLint|          |
    +------------+----------------------------+--------+-------------------+
-   | Lua        | Lua 5+ [#]_                | 15     | |Luai| |br|       |
+   | Lua        | Lua 5+ [#]_                | 17     | |Luai| |br|       |
    |            |                            |        | |Lu-Cov| |br|     |
    |            |                            |        | |LuaCheck|        |
    +------------+----------------------------+--------+-------------------+

docs/index.rst

@@ -103,9 +103,9 @@ Problems Solved
   +-----------+-----------+------------+------------+------------+------------+------------+------------+------------+
   |:prob:`013`|:c-d:`0013`|:cp-d:`0013`|:cs-d:`0013`|:ja-d:`0013`|:js-d:`0013`|:lu-d:`0013`|:py-d:`0013`|:rs-d:`0013`|
   +-----------+-----------+------------+------------+------------+------------+------------+------------+------------+
-  |:prob:`014`|:c-d:`0014`|:cp-d:`0014`|:cs-d:`0014`|:ja-d:`0014`|:js-d:`0014`|            |:py-d:`0014`|:rs-d:`0014`|
+  |:prob:`014`|:c-d:`0014`|:cp-d:`0014`|:cs-d:`0014`|:ja-d:`0014`|:js-d:`0014`|:lu-d:`0014`|:py-d:`0014`|:rs-d:`0014`|
   +-----------+-----------+------------+------------+------------+------------+------------+------------+------------+
-  |:prob:`015`|:c-d:`0015`|:cp-d:`0015`|:cs-d:`0015`|:ja-d:`0015`|:js-d:`0015`|            |:py-d:`0015`|:rs-d:`0015`|
+  |:prob:`015`|:c-d:`0015`|:cp-d:`0015`|:cs-d:`0015`|:ja-d:`0015`|:js-d:`0015`|:lu-d:`0015`|:py-d:`0015`|:rs-d:`0015`|
   +-----------+-----------+------------+------------+------------+------------+------------+------------+------------+
   |:prob:`016`|:c-d:`0016`|:cp-d:`0016`|:cs-d:`0016`|:ja-d:`0016`|:js-d:`0016`|            |:py-d:`0016`|:rs-d:`0016`|
   +-----------+-----------+------------+------------+------------+------------+------------+------------+------------+

docs/src/lua/p0014.rst

@@ -0,0 +1,18 @@
+Lua Implementation of Problem 14
+================================
+
+View source code :source:`lua/src/p0014.lua`
+
+Solution
+--------
+
+.. lua:function:: solution()
+
+    :return: The solution to problem 14
+    :rtype: number
+
+.. literalinclude:: ../../../lua/src/p0014.lua
+   :language: Lua
+   :linenos:
+
+.. tags:: collatz, recursion, longest-path

docs/src/lua/p0015.rst

@@ -20,4 +20,4 @@ Solution
    :language: Lua
    :linenos:
 
-.. tags:: large-numbers
+.. tags:: combinatorics

lua/README.rst

@@ -69,6 +69,8 @@ Problems Solved
 -  ☒ `9 <./src/p0009.lua>`__
 -  ☒ `11 <./src/p0011.lua>`__
 -  ☒ `13 <./src/p0013.lua>`__
+-  ☒ `14 <./src/p0014.lua>`__
+-  ☒ `15 <./src/p0015.lua>`__
 -  ☒ `17 <./src/p0017.lua>`__
 -  ☒ `28 <./src/p0028.lua>`__
 -  ☒ `34 <./src/p0034.lua>`__

lua/src/p0014.lua

@@ -0,0 +1,55 @@
+-- Project Euler Problem 14
+--
+-- Problem:
+--
+-- The following iterative sequence is defined for the set of positive integers:
+--
+-- n → n/2 (n is even)
+-- n → 3n + 1 (n is odd)
+--
+-- Using the rule above and starting with 13, we generate the following sequence:
+-- 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
+--
+-- It can be seen that this sequence (starting at 13 and finishing at 1) contains
+-- 10 terms. 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?
+--
+-- NOTE: Once the chain starts the terms are allowed to go above one million.
+
+local function collatz_len(n, cache)
+    if cache[n] then
+        return cache[n]
+    end
+
+    local result
+    if n == 1 then
+        result = 0
+    elseif n % 2 == 0 then
+        result = 1 + collatz_len(math.floor(n / 2), cache)
+    else
+        result = 2 + collatz_len(math.floor((3 * n + 1) / 2), cache)
+    end
+
+    cache[n] = result
+    return result
+end
+
+return {
+    solution = function()
+        local max_seen = 0
+        local answer = 0
+        local cache = {}
+
+        for i = 1,999999 do
+            local result = collatz_len(i, cache)
+            if result > max_seen then
+                max_seen = result
+                answer = i
+            end
+        end
+
+        return answer
+    end
+}

lua/test.lua

@@ -83,6 +83,7 @@ local problems = {
     ["p0009.lua"] = {31875000, false},
     ["p0011.lua"] = {70600674, false},
     ["p0013.lua"] = {5537376230, false},
+    ["p0014.lua"] = {837799, false},
     ["p0015.lua"] = {137846528820, false},
     ["p0017.lua"] = {21124, false},
     ["p0028.lua"] = {669171001, false},