Solve p15 in lua

README.rst

@@ -95,7 +95,7 @@ Olivia's Project Euler Solutions
    |            | Browser [#]_               |        | |CodeQL| |br|     |
    |            |                            |        | |ESLint|          |
    +------------+----------------------------+--------+-------------------+
-   | Lua        | Lua 5+ [#]_                | 14     | |Luai| |br|       |
+   | Lua        | Lua 5+ [#]_                | 15     | |Luai| |br|       |
    |            |                            |        | |Lu-Cov| |br|     |
    |            |                            |        | |LuaCheck|        |
    +------------+----------------------------+--------+-------------------+

docs/src/lua/lib/math.rst

@@ -8,6 +8,11 @@ View source code :source:`lua/src/lib/math.lua`
     :return: The factorial of n
     :rtype: number
 
+.. lua:function:: n_choose_r(n, r)
+
+    :return: The number of ways to choose r elements from a sample of size n
+    :rtype: number
+
 .. literalinclude:: ../../../../lua/src/lib/math.lua
    :language: Lua
    :linenos:

docs/src/lua/p0015.rst

@@ -0,0 +1,23 @@
+Lua Implementation of Problem 15
+================================
+
+View source code :source:`lua/src/p0015.lua`
+
+Includes
+--------
+
+- `math <./lib/math.html>`
+
+Solution
+--------
+
+.. lua:function:: solution()
+
+    :return: The solution to problem 15
+    :rtype: number
+
+.. literalinclude:: ../../../lua/src/p0015.lua
+   :language: Lua
+   :linenos:
+
+.. tags:: large-numbers

lua/src/lib/math.lua

@@ -9,6 +9,90 @@ 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 factors = {}
+    local answer
+    local tmp
+
+    -- collect factors of final number
+    for i = 2,n,1
+    do
+        factors[i] = 1
+    end
+
+    -- negative factor values indicate need to divide
+    for i = 2,r,1
+    do
+        factors[i] = factors[i] - 1
+    end
+    for i = 2,(n - r),1
+    do
+        factors[i] = factors[i] - 1
+    end
+
+    -- this loop reduces to prime factors only
+    for i = n,2,-1
+    do
+        for j = 2,(i - 1),1
+        do
+            if i % j == 0
+            then
+                factors[j] = factors[j] + factors[i]
+                factors[i / j] = factors[i / j] + factors[i]
+                factors[i] = 0
+                break
+            end
+        end
+    end
+
+    local i = 2
+    local j = 2
+    answer = 1;
+    while i <= n
+    do
+        while factors[i] > 0
+        do
+            tmp = answer
+            answer = answer * i
+            while answer < tmp and j <= n
+            do
+                while factors[j] < 0
+                do
+                    tmp = math.floor(tmp / j)
+                    factors[j] = factors[j] + 1
+                end
+                j = j + 1;
+                answer = tmp * i
+            end
+
+            if answer < tmp
+            then
+                return nil, "math error: overflow"
+            end
+            factors[i] = factors[i] - 1
+        end
+        i = i + 1
+    end
+
+    while j <= n
+    do
+        while factors[j] < 0
+        do
+            answer = answer / j
+            factors[j] = factors[j] + 1
+        end
+        j = j + 1
+    end
+
+    return answer
+end
+
 return {
     factorial = factorial,
 }

lua/src/p0013.lua

@@ -1,4 +1,4 @@
--- Project Euler Problem 11
+-- Project Euler Problem 13
 --
 -- Problem:
 --

lua/src/p0015.lua

@@ -0,0 +1,22 @@
+-- Project Euler Problem 15
+--
+-- 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.
+--
+-- Problem:
+--
+-- Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6
+-- routes to the bottom right corner.
+
+-- How many such routes are there through a 20×20 grid?
+
+local n_choose_r = loadlib("math").n_choose_r
+
+return {
+    solution = function()
+        return n_choose_r(40, 20)
+    end
+}

lua/src/p0028.lua

@@ -45,7 +45,7 @@
 --
 -- What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?
 
-local range_entry = loadfile("src/lib/range.lua")().range_entry3
+local range_entry = loadlib("range").range_entry3
 
 return {
     solution = function()

lua/src/p0034.lua

@@ -13,7 +13,7 @@
 --
 -- Note: as 1! = 1 and 2! = 2 are not sums they are not included.
 
-local factorial = loadfile('src/lib/math.lua')().factorial
+local factorial = loadlib('math').factorial
 
 return {
     solution = function()

lua/test.lua

@@ -87,6 +87,7 @@ local problems = {
     ["p0009.lua"] = {31875000, false},
     ["p0011.lua"] = {70600674, false},
     ["p0013.lua"] = {5537376230, false},
+    ["p0015.lua"] = {137846528820, false},
     ["p0017.lua"] = {21124, false},
     ["p0028.lua"] = {669171001, false},
     ["p0034.lua"] = {40730, false},