Convert a number, represented as a sequence of digits in one base, to any other base.
Implement general base conversion. Given a number in base a, represented as a sequence of digits, convert it to base b.
In positional notation, a number in base b can be understood as a linear combination of powers of b.
The number 42, in base 10, means:
(4 * 10^1) + (2 * 10^0)
The number 101010, in base 2, means:
(1 * 2^5) + (0 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0)
The number 1120, in base 3, means:
(1 * 3^3) + (1 * 3^2) + (2 * 3^1) + (0 * 3^0)
I think you got the idea!
Yes. Those three numbers above are exactly the same. Congratulations!
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defmodule AllYourBaseTest do
use ExUnit.Case
test "convert single bit one to decimal" do
assert AllYourBase.convert([1], 2, 10) == [1]
end
@tag :pending
test "convert binary to single decimal" do
assert AllYourBase.convert([1, 0, 1], 2, 10) == [5]
end
@tag :pending
test "convert single decimal to binary" do
assert AllYourBase.convert([5], 10, 2) == [1, 0, 1]
end
@tag :pending
test "convert binary to multiple decimal" do
assert AllYourBase.convert([1, 0, 1, 0, 1, 0], 2, 10) == [4, 2]
end
@tag :pending
test "convert decimal to binary" do
assert AllYourBase.convert([4, 2], 10, 2) == [1, 0, 1, 0, 1, 0]
end
@tag :pending
test "convert trinary to hexadecimal" do
assert AllYourBase.convert([1, 1, 2, 0], 3, 16) == [2, 10]
end
@tag :pending
test "convert hexadecimal to trinary" do
assert AllYourBase.convert([2, 10], 16, 3) == [1, 1, 2, 0]
end
@tag :pending
test "convert 15-bit integer" do
assert AllYourBase.convert([3, 46, 60], 97, 73) == [6, 10, 45]
end
@tag :pending
test "convert empty list" do
assert AllYourBase.convert([], 2, 10) == nil
end
@tag :pending
test "convert single zero" do
assert AllYourBase.convert([0], 10, 2) == [0]
end
@tag :pending
test "convert multiple zeros" do
assert AllYourBase.convert([0, 0, 0], 10, 2) == [0]
end
@tag :pending
test "convert leading zeros" do
assert AllYourBase.convert([0, 6, 0], 7, 10) == [4, 2]
end
@tag :pending
test "convert first base is one" do
assert AllYourBase.convert([0], 1, 10) == nil
end
@tag :pending
test "convert first base is zero" do
assert AllYourBase.convert([], 0, 10) == nil
end
@tag :pending
test "convert first base is negative" do
assert AllYourBase.convert([1], -2, 10) == nil
end
@tag :pending
test "convert negative digit" do
assert AllYourBase.convert([1, -1, 1, 0, 1, 0], 2, 10) == nil
end
@tag :pending
test "convert invalid positive digit" do
assert AllYourBase.convert([1, 2, 1, 0, 1, 0], 2, 10) == nil
end
@tag :pending
test "convert second base is one" do
assert AllYourBase.convert([1, 0, 1, 0, 1, 0], 2, 1) == nil
end
@tag :pending
test "convert second base is zero" do
assert AllYourBase.convert([7], 10, 0) == nil
end
@tag :pending
test "convert second base is negative" do
assert AllYourBase.convert([1], 2, -7) == nil
end
@tag :pending
test "convert both bases are negative" do
assert AllYourBase.convert([1], -2, -7) == nil
end
end
ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)
defmodule AllYourBase do
@spec convert(list, integer, integer) :: list | nil
def convert([], _, _), do: nil
def convert(_, base_a, base_b) when base_a < 2 or base_b < 2, do: nil
def convert(digits, base_a, base_b) do
cond do
Enum.all?(digits, & &1 === 0) -> [0]
Enum.any?(digits, & &1 < 0 or &1 >= base_a) -> nil
true -> digits |> to_base10(base_a) |> from_base10(base_b)
end
end
defp to_base10([], _), do: 0
defp to_base10([digit | rest] = digits, base),
do: (digit * pow(base, length(digits) - 1)) + to_base10(rest, base)
defp pow(base, exponent),
do: base |> :math.pow(exponent) |> round()
defp from_base10(0, _), do: []
defp from_base10(digit, base),
do: from_base10(div(digit, base), base) ++ [rem(digit, base)]
end
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Community comments
Just, to let you now:
https://github.com/cj1128/exercism-elixir/blob/master/all-your-base/all-your-base.exs#L15
This part, I find supper. He don't work with the pow function.
def to_base10(digits, base) do digits |> Enum.reduce(fn x, acc -> acc * base + x end) end
Interesting, it's hard to wrap my head around that solution. I suspect the program is faster without
pow
?