From 6a7c6c10c7f7d229afc7192c1666c21e0dba259c Mon Sep 17 00:00:00 2001
From: Olivia Appleton <olivia.kay.appleton@gmail.com>
Date: Thu, 12 Sep 2024 18:25:14 -0500
Subject: [PATCH] Refactor

---
 lua/src/lib/math.lua | 24 +++++++++++++++---------
 lua/src/p0015.lua    |  4 ++--
 2 files changed, 17 insertions(+), 11 deletions(-)

diff --git a/lua/src/lib/math.lua b/lua/src/lib/math.lua
index 6192f1b0..286b325a 100644
--- a/lua/src/lib/math.lua
+++ b/lua/src/lib/math.lua
@@ -9,16 +9,8 @@ local function factorial(n)
     return answer
 end
 
-local function n_choose_r(n, r)
-    if n < 20  -- fast path if number is small
-    then
-        return factorial(n) / factorial(r) / factorial(n - r)
-    end
-
-    -- slow path for big numbers// slow path for larger numbers
+local function factor_gen(n, r)
     local factors = {}
-    local answer
-    local tmp
 
     -- collect factors of final number
     for i = 2,n,1
@@ -51,6 +43,19 @@ local function n_choose_r(n, r)
         end
     end
 
+    return factors
+end
+
+local function n_choose_r(n, r)
+    if n < 20  -- fast path if number is small
+    then
+        return factorial(n) / factorial(r) / factorial(n - r)
+    end
+
+    -- slow path for big numbers// slow path for larger numbers
+    local factors = factor_gen(n, r)
+    local answer
+    local tmp
     local i = 2
     local j = 2
     answer = 1;
@@ -95,4 +100,5 @@ end
 
 return {
     factorial = factorial,
+    n_choose_r = n_choose_r,
 }
diff --git a/lua/src/p0015.lua b/lua/src/p0015.lua
index 8932692e..b19690ec 100644
--- a/lua/src/p0015.lua
+++ b/lua/src/p0015.lua
@@ -3,8 +3,8 @@
 -- Turns out this is easy, if you think sideways a bit
 --
 -- You can only go down or right. If we say right=1, then you can only have 20 1s, since otherwise you go off the grid.
--- You also can't have fewer than 20 1s, since then you go off the grid the other way. This means you can look at it as a
--- bit string, and the number of 40-bit strings with 20 1s is 40c20.
+-- You also can't have fewer than 20 1s, since then you go off the grid the other way. This means you can look at it as
+-- a bit string, and the number of 40-bit strings with 20 1s is 40c20.
 --
 -- Problem:
 --