JaeHyoLee's solution to Sieve on the Lua track

Instructions

Test suite

Solution

Use the Sieve of Eratosthenes to find all the primes from 2 up to a given number.

The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e. not prime) the multiples of each prime, starting with the multiples of 2.

Create your range, starting at two and continuing up to and including the given limit. (i.e. [2, limit])

The algorithm consists of repeating the following over and over:

take the next available unmarked number in your list (it is prime)
mark all the multiples of that number (they are not prime)

Repeat until you have processed each number in your range.

When the algorithm terminates, all the numbers in the list that have not been marked are prime.

The wikipedia article has a useful graphic that explains the algorithm: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Notice that this is a very specific algorithm, and the tests don't check that you've implemented the algorithm, only that you've come up with the correct list of primes.

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.

Source

Sieve of Eratosthenes at Wikipedia http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Submitting Incomplete Solutions

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

sieve_spec.lua

local sieve = require('sieve')

describe('sieve', function()
  local select = select or function(n, ...)
    return table.pack(...)[n]
  end

  local function primes_from(co)
    local primes = {}
    while true do
      local _, prime = coroutine.resume(co)
      if prime == nil then return primes end
      table.insert(primes, prime)
    end
  end

  it('should return a coroutine that generates primes', function()
    local co = sieve(9)
    assert.equal(2, select(2, coroutine.resume(co)))
    assert.equal(3, select(2, coroutine.resume(co)))
    assert.equal(5, select(2, coroutine.resume(co)))
    assert.equal(7, select(2, coroutine.resume(co)))
    assert.is_nil(select(2, coroutine.resume(co)))
  end)

  it('should find primes up to 10', function()
    assert.same({ 2, 3, 5, 7 }, primes_from(sieve(10)))
  end)

  it('should find primes up to 1000', function()
    assert.same(
      { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 },
      primes_from(sieve(1000))
    )
  end)

  it('should include the limit if it is prime', function()
    assert.same({ 2, 3, 5, 7, 11, 13 }, primes_from(sieve(13)))
  end)

  it('should find the first prime', function()
    assert.same({ 2 }, primes_from(sieve(2)))
  end)

  it('should not find any primes under 2', function()
    assert.same({}, primes_from(sieve(1)))
  end)
end)

local function find_smallest_nil(t, s, e)
  for i=s,e do
    if t[i] == nil then return i end
  end
  return nil
end

return function (n)
  
  local prime_numbers = {}
  local i = 2
  
  return coroutine.create(
    function()      
      repeat        
        local new_prime = find_smallest_nil(prime_numbers, i, n)
        if new_prime == nil then break end
        
        local j = 2
        
        repeat
          prime_numbers[new_prime * j] = true
          j=j+1 
        until new_prime*j > n
        
        i = (new_prime or n) + 1
        coroutine.yield(new_prime)        
      until i > n
      
    end
  )
end

Community comments

Find this solution interesting? Ask the author a question to learn more.

ryanplusplus

commented almost 4 years ago

For really large n the number of prime numbers will be significantly smaller than the number of composite numbers. Right now you are storing all non-primes in your prime_numbers table, but if you could store only primes then you'd use less memory for really large sieves.

Looks good otherwise. Coroutines are really cool :)

JaeHyoLee

Solution Author

commented almost 4 years ago

yeah you are right.. but I am not sure how to less the memory usage. like your solution if we set 1~n to true and set it as false to non-prime numbers.. does that reduce the memory usage? having 'false' as a value of the key would take the memory space, wouldn't it?

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JaeHyoLee's solution

to Sieve in the Lua Track