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theFox6's solution

to All Your Base in the Lua Track

Published at Apr 07 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)
  -- no bases smaller than 2
  if from_base < 2 then
    error("invalid input base",2)
  end
  local number = 0
  do
    local total = #from_digits
    -- iterate through digits
    for index,digit in pairs(from_digits) do
      -- error on bad digits
      if digit < 0 then
        error("negative digits are not allowed",2)
      elseif digit >= from_base then
        error("digit out of range",2)
      end
      -- add the digit multiplied by it's base to the power of it's reversed index
      number = number + digit * from_base^(total - index)
    end
  end
  return {to = function(to_base)
    -- no bases smaller than 2
    if to_base < 2 then
      error("invalid output base",2)
    end
    local ret = {}
    local remain = number
    -- calculate at least one digit
    repeat
      -- calculate next digit from the right
      local digit = remain % to_base
      -- add it to the beginning of the table
      table.insert(ret,1,digit)
      -- remove it from the remain and divide it to calculate the next digit
      remain = (remain - digit) / to_base
      -- until no digits are left
    until remain < 1
    return ret
  end}
end

return all_your_base

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