palindrome-products

config.json

@@ -478,6 +478,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 6
+      },
+      {
+        "slug": "palindrome-products",
+        "name": "Palindrome Products",
+        "uuid": "ee7bdced-c0f3-4435-a9c4-1dec3b14540f",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 6
       }
     ]
   },

exercises/practice/palindrome-products/.busted

@@ -0,0 +1,5 @@
+return {
+  default = {
+    ROOT = { '.' }
+  }
+}

exercises/practice/palindrome-products/.docs/instructions.md

@@ -0,0 +1,36 @@
+# Instructions
+
+Detect palindrome products in a given range.
+
+A palindromic number is a number that remains the same when its digits are reversed.
+For example, `121` is a palindromic number but `112` is not.
+
+Given a range of numbers, find the largest and smallest palindromes which
+are products of two numbers within that range.
+
+Your solution should return the largest and smallest palindromes, along with the factors of each within the range.
+If the largest or smallest palindrome has more than one pair of factors within the range, then return all the pairs.
+
+## Example 1
+
+Given the range `[1, 9]` (both inclusive)...
+
+And given the list of all possible products within this range:
+`[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 15, 21, 24, 27, 20, 28, 32, 36, 25, 30, 35, 40, 45, 42, 48, 54, 49, 56, 63, 64, 72, 81]`
+
+The palindrome products are all single digit numbers (in this case):
+`[1, 2, 3, 4, 5, 6, 7, 8, 9]`
+
+The smallest palindrome product is `1`.
+Its factors are `(1, 1)`.
+The largest palindrome product is `9`.
+Its factors are `(1, 9)` and `(3, 3)`.
+
+## Example 2
+
+Given the range `[10, 99]` (both inclusive)...
+
+The smallest palindrome product is `121`.
+Its factors are `(11, 11)`.
+The largest palindrome product is `9009`.
+Its factors are `(91, 99)`.

exercises/practice/palindrome-products/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "glennj"
+  ],
+  "files": {
+    "solution": [
+      "palindrome_products.moon"
+    ],
+    "test": [
+      "palindrome_products_spec.moon"
+    ],
+    "example": [
+      ".meta/example.moon"
+    ]
+  },
+  "blurb": "Detect palindrome products in a given range.",
+  "source": "Problem 4 at Project Euler",
+  "source_url": "https://projecteuler.net/problem=4"
+}

exercises/practice/palindrome-products/.meta/example.moon

@@ -0,0 +1,43 @@
+reverse_number = (num) ->
+  rev = 0
+  while num > 0
+    rev = rev * 10 + num % 10
+    num = num // 10
+  rev
+
+
+is_palindrome = (number) ->
+  number == reverse_number number
+
+
+bounded_factors = (number, min, max) ->
+  factors = {}
+  limit = math.min(max, math.floor math.sqrt number)
+  for f = min, limit
+    g = number // f
+    if f * g == number and g <= max
+      table.insert factors, {f, g}
+  factors
+
+
+solve = (start, stop, step, min, max) ->
+  assert min <= max, "min must be <= max"
+
+  for product = start, stop, step
+    if is_palindrome product
+      fs = bounded_factors product, min, max
+      if #fs > 0
+        return {value: product, factors: fs}
+
+  {value: nil, factors: {}}
+
+
+{
+  smallest: (min, max) ->
+    result = solve min * min, max * max,  1, min, max
+    result.value, result.factors
+
+  largest:  (min, max) ->
+    result = solve max * max, min * min, -1, min, max
+    result.value, result.factors
+}

exercises/practice/palindrome-products/.meta/spec_generator.moon

@@ -0,0 +1,26 @@
+int_list = (list) -> "{#{table.concat list, ', '}}"
+
+int_lists = (lists) ->
+  "{#{table.concat [int_list list for list in *lists], ', '}}"
+
+
+{
+  module_name: 'PalindromeProducts',
+
+  generate_test: (case, level) ->
+    local lines
+    if case.expected.error
+      lines = {
+        "f = -> PalindromeProducts.#{case.property} #{case.input.min}, #{case.input.max}",
+        "assert.has.errors f, #{quote case.expected.error}",
+      }
+    else
+      lines = {
+        "palindrome, factors = PalindromeProducts.#{case.property} #{case.input.min}, #{case.input.max}",
+        "expected_palindrome = #{case.expected.value}",
+        "expected_factors    = #{int_lists case.expected.factors}",
+        "assert.are.equal expected_palindrome, palindrome",
+        "assert.are.same  expected_factors, factors",
+      }
+    table.concat [indent line, level for line in *lines], '\n'
+}

exercises/practice/palindrome-products/.meta/tests.toml

@@ -0,0 +1,49 @@
+# This is an auto-generated file.
+#
+# Regenerating this file via `configlet sync` will:
+# - Recreate every `description` key/value pair
+# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
+# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
+# - Preserve any other key/value pair
+#
+# As user-added comments (using the # character) will be removed when this file
+# is regenerated, comments can be added via a `comment` key.
+
+[5cff78fe-cf02-459d-85c2-ce584679f887]
+description = "find the smallest palindrome from single digit factors"
+
+[0853f82c-5fc4-44ae-be38-fadb2cced92d]
+description = "find the largest palindrome from single digit factors"
+
+[66c3b496-bdec-4103-9129-3fcb5a9063e1]
+description = "find the smallest palindrome from double digit factors"
+
+[a10682ae-530a-4e56-b89d-69664feafe53]
+description = "find the largest palindrome from double digit factors"
+
+[cecb5a35-46d1-4666-9719-fa2c3af7499d]
+description = "find the smallest palindrome from triple digit factors"
+
+[edab43e1-c35f-4ea3-8c55-2f31dddd92e5]
+description = "find the largest palindrome from triple digit factors"
+
+[4f802b5a-9d74-4026-a70f-b53ff9234e4e]
+description = "find the smallest palindrome from four digit factors"
+
+[787525e0-a5f9-40f3-8cb2-23b52cf5d0be]
+description = "find the largest palindrome from four digit factors"
+
+[58fb1d63-fddb-4409-ab84-a7a8e58d9ea0]
+description = "empty result for smallest if no palindrome in the range"
+
+[9de9e9da-f1d9-49a5-8bfc-3d322efbdd02]
+description = "empty result for largest if no palindrome in the range"
+
+[12e73aac-d7ee-4877-b8aa-2aa3dcdb9f8a]
+description = "error result for smallest if min is more than max"
+
+[eeeb5bff-3f47-4b1e-892f-05829277bd74]
+description = "error result for largest if min is more than max"
+
+[16481711-26c4-42e0-9180-e2e4e8b29c23]
+description = "smallest product does not use the smallest factor"

exercises/practice/palindrome-products/palindrome_products.moon

@@ -0,0 +1,7 @@
+{
+  smallest: (min, max) ->
+    error 'Implement me'
+
+  largest: (min, max) ->
+    error 'Implement me'
+}

exercises/practice/palindrome-products/palindrome_products_spec.moon

@@ -0,0 +1,87 @@
+PalindromeProducts = require 'palindrome_products'
+
+describe 'palindrome-products', ->
+  it 'find the smallest palindrome from single digit factors', ->
+    palindrome, factors = PalindromeProducts.smallest 1, 9
+    expected_palindrome = 1
+    expected_factors    = {{1, 1}}
+    assert.are.equal expected_palindrome, palindrome
+    assert.are.same  expected_factors, factors
+
+  pending 'find the largest palindrome from single digit factors', ->
+    palindrome, factors = PalindromeProducts.largest 1, 9
+    expected_palindrome = 9
+    expected_factors    = {{1, 9}, {3, 3}}
+    assert.are.equal expected_palindrome, palindrome
+    assert.are.same  expected_factors, factors
+
+  pending 'find the smallest palindrome from double digit factors', ->
+    palindrome, factors = PalindromeProducts.smallest 10, 99
+    expected_palindrome = 121
+    expected_factors    = {{11, 11}}
+    assert.are.equal expected_palindrome, palindrome
+    assert.are.same  expected_factors, factors
+
+  pending 'find the largest palindrome from double digit factors', ->
+    palindrome, factors = PalindromeProducts.largest 10, 99
+    expected_palindrome = 9009
+    expected_factors    = {{91, 99}}
+    assert.are.equal expected_palindrome, palindrome
+    assert.are.same  expected_factors, factors
+
+  pending 'find the smallest palindrome from triple digit factors', ->
+    palindrome, factors = PalindromeProducts.smallest 100, 999
+    expected_palindrome = 10201
+    expected_factors    = {{101, 101}}
+    assert.are.equal expected_palindrome, palindrome
+    assert.are.same  expected_factors, factors
+
+  pending 'find the largest palindrome from triple digit factors', ->
+    palindrome, factors = PalindromeProducts.largest 100, 999
+    expected_palindrome = 906609
+    expected_factors    = {{913, 993}}
+    assert.are.equal expected_palindrome, palindrome
+    assert.are.same  expected_factors, factors
+
+  pending 'find the smallest palindrome from four digit factors', ->
+    palindrome, factors = PalindromeProducts.smallest 1000, 9999
+    expected_palindrome = 1002001
+    expected_factors    = {{1001, 1001}}
+    assert.are.equal expected_palindrome, palindrome
+    assert.are.same  expected_factors, factors
+
+  pending 'find the largest palindrome from four digit factors', ->
+    palindrome, factors = PalindromeProducts.largest 1000, 9999
+    expected_palindrome = 99000099
+    expected_factors    = {{9901, 9999}}
+    assert.are.equal expected_palindrome, palindrome
+    assert.are.same  expected_factors, factors
+
+  pending 'empty result for smallest if no palindrome in the range', ->
+    palindrome, factors = PalindromeProducts.smallest 1002, 1003
+    expected_palindrome = nil
+    expected_factors    = {}
+    assert.are.equal expected_palindrome, palindrome
+    assert.are.same  expected_factors, factors
+
+  pending 'empty result for largest if no palindrome in the range', ->
+    palindrome, factors = PalindromeProducts.largest 15, 15
+    expected_palindrome = nil
+    expected_factors    = {}
+    assert.are.equal expected_palindrome, palindrome
+    assert.are.same  expected_factors, factors
+
+  pending 'error result for smallest if min is more than max', ->
+    f = -> PalindromeProducts.smallest 10000, 1
+    assert.has.errors f, 'min must be <= max'
+
+  pending 'error result for largest if min is more than max', ->
+    f = -> PalindromeProducts.largest 2, 1
+    assert.has.errors f, 'min must be <= max'
+
+  pending 'smallest product does not use the smallest factor', ->
+    palindrome, factors = PalindromeProducts.smallest 3215, 4000
+    expected_palindrome = 10988901
+    expected_factors    = {{3297, 3333}}
+    assert.are.equal expected_palindrome, palindrome
+    assert.are.same  expected_factors, factors