Published at Jul 13 2018
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Instructions

Test suite

Solution

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 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.

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)`

.

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)`

.

Execute the tests with:

```
$ elixir palindrome_products_test.exs
```

In the test suites, all but the first test have been skipped.

Once you get a test passing, you can unskip the next one by
commenting out the relevant `@tag :pending`

with a `#`

symbol.

For example:

```
# @tag :pending
test "shouting" do
assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"
end
```

Or, you can enable all the tests by commenting out the
`ExUnit.configure`

line in the test suite.

```
# ExUnit.configure exclude: :pending, trace: true
```

For more detailed information about the Elixir track, please see the help page.

Problem 4 at Project Euler http://projecteuler.net/problem=4

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

```
if !System.get_env("EXERCISM_TEST_EXAMPLES") do
Code.load_file("palindrome_products.exs", __DIR__)
end
ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)
defmodule PalindromeProductsTest do
use ExUnit.Case
# @tag :pending
test "largest palindrome from single digit factors" do
palindromes = Palindromes.generate(9)
assert palindromes |> Map.keys() |> Enum.sort() |> List.last() == 9
assert Enum.sort(palindromes[9]) == [[1, 9], [3, 3]]
end
@tag :pending
test "largest palindrome from double digit factors" do
palindromes = Palindromes.generate(99, 10)
assert palindromes |> Map.keys() |> Enum.sort() |> List.last() == 9009
assert palindromes[9009] == [[91, 99]]
end
@tag :pending
test "smallest palindrome from double digit factors" do
palindromes = Palindromes.generate(99, 10)
assert palindromes |> Map.keys() |> Enum.sort() |> hd == 121
assert palindromes[121] == [[11, 11]]
end
@tag :pending
test "largest palindrome from triple digit factors" do
palindromes = Palindromes.generate(999, 100)
assert palindromes |> Map.keys() |> Enum.sort() |> List.last() == 906_609
assert palindromes[906_609] == [[913, 993]]
end
@tag :pending
test "smallest palindromes from triple digit factors" do
palindromes = Palindromes.generate(999, 100)
assert palindromes |> Map.keys() |> Enum.sort() |> hd == 10201
assert palindromes[10201] == [[101, 101]]
end
end
```

```
defmodule Palindromes do
@doc """
Generates all palindrome products from an optionally given min factor (or 1) to a given max factor.
"""
@spec generate(non_neg_integer, non_neg_integer) :: map
def generate(max_factor, min_factor \\ 1) do
do_generate(min_factor, min_factor, max_factor + 1, %{})
end
defp do_generate(too_high, _, too_high, acc), do: acc
defp do_generate(cur1, too_high, too_high, acc), do:
do_generate(cur1 + 1, cur1 + 1, too_high, acc)
defp do_generate(cur1, cur2, too_high, acc) do
do_generate(cur1, cur2 + 1, too_high,
revise_accumulator(cur1, cur2, acc))
end
defp revise_accumulator(cur1, cur2, acc) do
product = cur1 * cur2
if palindrome?(Integer.to_string(product)) do
Map.put(acc, product, [[cur1, cur2] | Map.get(acc, product, [])])
else
acc
end
end
defp palindrome?(str), do: String.reverse(str) == str
end
```

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