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to All Your Base in the Lua Track

Published at Aug 06 2020 · 0 comments
Instructions
Test suite
Solution

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.

Note

  • Try to implement the conversion yourself. Do not use something else to perform the conversion for you.

About Positional Notation

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!

Running the tests

To run the tests, run the command busted from within the exercise directory.

Further information

For more detailed information about the Lua track, including how to get help if you're having trouble, please visit the exercism.io Lua language page.

Submitting Incomplete Solutions

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

all-your-base_spec.lua

local all_your_base = require 'all-your-base'

describe('all-your-base', function()
  it('should convert a single binary digit to a single decimal digit', function()
    assert.are.same({ 1 }, all_your_base.convert({ 1 }, 2).to(10))
  end)

  it('should convert multiple binary digits to a single decimal digit', function()
    assert.are.same({ 5 }, all_your_base.convert({ 1, 0, 1 }, 2).to(10))
  end)

  it('should convert a single decimal digit to binary', function()
    assert.are.same({ 1, 0, 1 }, all_your_base.convert({ 5 }, 10).to(2))
  end)

  it('should convert binary to decimal', function()
    assert.are.same({ 1, 0, 1, 0, 1, 0 }, all_your_base.convert({ 4, 2 }, 10).to(2))
  end)

  it('should convert decimal to binary', function()
    assert.are.same({ 4, 2 }, all_your_base.convert({ 1, 0, 1, 0, 1, 0 }, 2).to(10))
  end)

  it('should convert trinary to hexadecimal', function()
    assert.are.same({ 2, 10 }, all_your_base.convert({ 1, 1, 2, 0 }, 3).to(16))
  end)

  it('should convert hexadecimal to trinary', function()
    assert.are.same({ 1, 1, 2, 0 }, all_your_base.convert({ 2, 10 }, 16).to(3))
  end)

  it('should convert between large bases', function()
    assert.are.same({ 6, 10, 45 }, all_your_base.convert({ 3, 46, 60 }, 97).to(73))
  end)

  it('should convert no digits to 0', function()
    assert.are.same({ 0 }, all_your_base.convert({ }, 2).to(10))
  end)

  it('should convert no digits to 0', function()
    assert.are.same({ 0 }, all_your_base.convert({ }, 10).to(2))
  end)

  it('should convert multiple 0 digits to 0', function()
    assert.are.same({ 0 }, all_your_base.convert({ 0, 0, 0 }, 10).to(2))
  end)

  it('should ignore leading zeros', function()
    assert.are.same({ 4, 2 }, all_your_base.convert({ 0, 6, 0 }, 7).to(10))
  end)

  it('should not allow negative digits', function()
    assert.has_error(function()
      all_your_base.convert({ 1, -1, 1, 0, 1, 0 }, 2).to(10)
    end, 'negative digits are not allowed')
  end)

  it('should not allow digits that are out of range', function()
    assert.has_error(function()
      all_your_base.convert({ 1, 2, 1, 0, 1, 0 }, 2).to(10)
    end, 'digit out of range')
  end)

  it('should not allow an input base less than 2', function()
    assert.has_error(function()
      all_your_base.convert({ 1, 0, 1, 0, 1, 0 }, -1).to(10)
    end, 'invalid input base')

    assert.has_error(function()
      all_your_base.convert({ 1, 0, 1, 0, 1, 0 }, 0).to(10)
    end, 'invalid input base')

    assert.has_error(function()
      all_your_base.convert({ 1, 0, 1, 0, 1, 0 }, 1).to(10)
    end, 'invalid input base')
  end)

  it('should not allow an output base less than 2', function()
    assert.has_error(function()
      all_your_base.convert({ 1, 0, 1, 0, 1, 0 }, 2).to(-1)
    end, 'invalid output base')

    assert.has_error(function()
      all_your_base.convert({ 1, 0, 1, 0, 1, 0 }, 2).to(0)
    end, 'invalid output base')

    assert.has_error(function()
      all_your_base.convert({ 1, 0, 1, 0, 1, 0 }, 2).to(1)
    end, 'invalid output base')
  end)
end)
local all_your_base = {}

all_your_base.convert = function(from_digits, from_base)
  return {
    to = function(new_base)
      assert(new_base >= 2, "invalid output base")
      assert(from_base >= 2, "invalid input base")

      while from_digits[1] == 0 do table.remove(from_digits, 1) end
      if #from_digits == 0 then return {0} end

      local sum = 0
      for i, v in pairs(from_digits) do
        assert(v >= 0, "negative digits are not allowed")
        assert(v < from_base, "digit out of range")
        position = #from_digits - i
        sum = sum + v * from_base ^ position
      end

      local result = {}
      while sum > 0 do
        table.insert(result, 1, sum % new_base)
        sum = sum // new_base
      end

      return result
    end
  }
end

return all_your_base

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